Journal articles on the topic 'Elastic-viscoelastic correspondence principle'
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1
Mukherjee, S., and Glaucio H. Paulino. "The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited." Journal of Applied Mechanics 70, no. 3 (May 1, 2003): 359–63. http://dx.doi.org/10.1115/1.1533805.
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Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.
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Kovarik, V. "Distributional Concept of the Elastic-Viscoelastic Correspondence Principle." Journal of Applied Mechanics 62, no. 4 (December 1, 1995): 847–52. http://dx.doi.org/10.1115/1.2896010.
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Distribution concept of physical variables in viscoelasticity theory enables to represent the stress-strain relations in the form of convolution equations, that is algebraic equations in the convolution algebra of right-sided distributions. These equations can be handled in much the same way that one handles matrix equations. Distributional correspondence principle is formulated as a transition process from the algebra of numbers (elastic solution) to the convolution algebra of distributions (viscoelastic solution). Corresponding elements and operations, respectively, in both algebras are established. Applications to a wide class of problems of the plate and shell theory are shown.
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Igumnov, Leonid, I. P. Маrkov, and A. V. Amenitsky. "A Three-Dimensional Boundary Element Approach for Transient Anisotropic Viscoelastic Problems." Key Engineering Materials 685 (February 2016): 267–71. http://dx.doi.org/10.4028/www.scientific.net/kem.685.267.
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This paper presents a three-dimensional direct boundary element approach for solving transient problems of linear anisotropic elasticity and viscoelasticity. In order to take advantage of the correspondence principle between viscoelasticity and elasticity the formulation is given in the Laplace domain. Anisotropic viscoelastic fundamental solutions are obtained using the correspondence principle and anisotropic elastic Green’s functions. The standard linear solid model is used to represent the mechanical behavior of viscoelastic material. Solution in time domain is calculated via numerical inversion by modified Durbin’s method. Numerical example is provided to validate the proposed boundary element formulation.
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Hui, D. "Viscoelastic response of floating ice plates under distributed or concentrated loads." Journal of Strain Analysis for Engineering Design 21, no. 3 (July 1, 1986): 135–43. http://dx.doi.org/10.1243/03093247v213135.
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This paper deals with the elastic and viscoelastic deflections and stresses of non-homogeneous rectangular or infinite floating ice plates subjected to central distributed lateral loads, where the loading region is of rectangular shape, or concentrated loads. The analysis takes into account the variation of Young's modulus of ice in the thickness direction. The Rayleigh—Ritz procedure is used to obtain the elastic solution for the deflections and bending moments, while the viscoelastic solution is obtained from the elastic response using the correspondence principle. Closed form Bessel-type elastic and viscoelastic solutions are obtained for infinite floating ice plates. Comparisons are made between the time-dependent response of infinite and finite square floating ice plates.
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Schanz, M., and A. H. D. Cheng. "Dynamic Analysis of a One-Dimensional Poroviscoelastic Column." Journal of Applied Mechanics 68, no. 2 (July 1, 2000): 192–98. http://dx.doi.org/10.1115/1.1349416.
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The response due to a dynamic loading of a poroviscoelastic one-dimensional column is treated analytically. Biot’s theory of poroelasticity is generalized to poroviscoelasticity using the elastic-viscoelastic correspondence principle in the Laplace domain. Damping effects of the solid skeletal structure and the solid material itself are taken into account. The fluid is modeled as in the original Biot’s theory without any viscoelastic effects. The solution of the governing set of two coupled differential equations known from the purely poroelastic case is converted to the poroviscoelastic solution using the developed elastic-viscoelastic correspondence in Laplace domain. The time-dependent response of the column is achieved by the “Convolution Quadrature Method” proposed by Lubich. Some interesting effects of viscoelasticity on the response of the column caused by a stress, pressure, and displacement loading are studied.
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Zhang, W. X., R. G. Liu, and Y. Bai. "Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials." Engineering Computations 34, no. 4 (June 12, 2017): 1314–31. http://dx.doi.org/10.1108/ec-02-2016-0063.
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Purpose For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs. Design/methodology/approach Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods. Findings In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints. Originality/value The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.
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Kachuck, S. B., and L. M. Cathles. "Benchmarked computation of time-domain viscoelastic Love numbers for adiabatic mantles." Geophysical Journal International 218, no. 3 (June 11, 2019): 2136–49. http://dx.doi.org/10.1093/gji/ggz276.
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SUMMARYThe viscoelastic load Love numbers encapsulate the Earth’s rheology in a remarkably efficient fashion. When multiplied by a sudden increment of spherical harmonic load change, they give the horizontal and vertical surface displacements and gravity change at all later times. Incremental glacial load changes thus need only be harmonically decomposed, multiplied by the Love numbers and summed to predict the Earth’s response to glacial load redistributions. The computation of viscoelastic Love numbers from the elastic, viscous and adiabatic profiles of the Earth is thus the foundation upon which many glacial isostatic adjustment models are based. Usually, viscoelastic Love numbers are computed using the Laplace transform method, employing the correspondence principle to convert the viscoelastic equations of motion into the elastic equations with complex material parameters. This method works well for a fully non-adiabatic Earth, but can accommodate realistic partially adiabatic and fully adiabatic conditions only by changing the Earth’s density profile. An alternative method of Love number computation developed by Cathles (1975) avoids this dilemma by separating the elastic and viscous equations of motion. The separation neglects a small solid-elastic/fluid-elastic transition for compressible deformation, but allows freely defining adiabatic, partially adiabatic or fully non-adiabatic profiles in the mantle without changing the Earth’s density profile. Here, we update and fully describe this method and show that it produces Love numbers closely similar to those computed for fully non-adiabatic earth models computed by the correspondence principle, finite element and other methods. The time-domain method produces Love numbers as good as those produced by other methods and can also realistically accommodate any degree of mantle adiabaticity. All method implementations are available open source.
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Yancey, R. N., and Marek-Jerzy Pindera. "Micromechanical Analysis of the Creep Response of Unidirectional Composites." Journal of Engineering Materials and Technology 112, no. 2 (April 1, 1990): 157–63. http://dx.doi.org/10.1115/1.2903302.
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The paper outlines the use of the micromechanics model proposed by Aboudi in predicting the creep response of unidirectional composites consisting of linearly viscoelastic matrices and elastic fibers. The closed-form expressions for the effective elastic moduli given in terms of the phase moduli and volume fractions provided by the micromechanics model facilitate a straightforward application of the viscoelastic Correspondence Principle. The inversion of the effective moduli in the Laplace transform domain to the time domain is subsequently accomplished using the Bellman method. The predictions of the model are compared with the creep response of T300/934 graphite/epoxy unidirectional coupons at two different temperatures. Very good correlation between theory and experiment is illustrated for the linearly viscoelastic response characterized by relatively small creep strains.
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Hilton, Harry. "The elusive and fickle viscoelastic Poisson’s ratio and its relation to the elastic-viscoelastic correspondence principle." Journal of Mechanics of Materials and Structures 4, no. 7-8 (December 26, 2009): 1341–64. http://dx.doi.org/10.2140/jomms.2009.4.1341.
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Wu, Jun. "Uniaxial Compression Creep Prediction of Asphalt Mixture Using the Eshelby Equivalent Inclusion Method." Advanced Materials Research 1061-1062 (December 2014): 410–13. http://dx.doi.org/10.4028/www.scientific.net/amr.1061-1062.410.
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Asphalt mixture was simply treated as a two-phase composite, in which coarse aggregates are embedded into asphalt mastic matrix. According to the elastic-viscoelastic correspondence principle, an elastic micromechanical method is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded into viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different stress conditions in order to determine the matrix constitutive parameters, the presented framework is validated by comparison with the experiment, and then some predictions to uniaxial compression creep behavior of asphalt mixture in different stress conditions are given.
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Kamiński, Marcin, Agnieszka Lenartowicz, Michał Guminiak, and Maciej Przychodzki. "Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers." Materials 15, no. 19 (September 30, 2022): 6811. http://dx.doi.org/10.3390/ma15196811.
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The main motivation of this work was to present a semi-analytical extension of the correspondence principle in stochastic dynamics. It is demonstrated for the stochastic structural free vibrations of Kirchhoff–Love elastic, isotropic and rectangular plates supported by viscoelastic generalized Maxwell dampers. The ambient temperature of the plate affects the dampers only and is included in a mathematical model using the frequency–temperature correspondence principle. The free vibration problem of the plate–viscoelastic damper system is solved using the continuation method and also the Finite Element Method (FEM). The stochastic approach begins with an initial deterministic sensitivity analysis to detect the most influential parameters and numerical FEM recovery of the polynomial representation for lower eigenfrequencies versus these parameters. A final symbolic integration leads to the first four basic probabilistic characteristics, all delivered as functions of the input uncertainties.
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Hwu, Chyanbin, and Wilfried Becker. "Stroh formalism for various types of materials and deformations." Journal of Mechanics 38 (2022): 433–44. http://dx.doi.org/10.1093/jom/ufac031.
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Abstract The Stroh formalism is a complex variable formulation developed originally for solving the problems of two-dimensional linear anisotropic elasticity. By separation of the third variable for the linear variation of displacements along the thickness direction, it was proved to be applicable for the problems with coupled stretching-bending deformation. By the Radon transform which maps a three-dimensional solid to a two-dimensional plane, it can be applied to the three-dimensional deformation. By the elastic-viscoelastic correspondence principle, it is also valid for the viscoelastic materials in the Laplace domain. By expansion of the matrix dimension, it can be generalized to the coupled-field materials such as piezoelectric, piezomagnetic and magneto-electro-elastic materials. By introducing a small perturbation on the material constants, it can also be applied to the degenerate materials such as isotropic materials. Thus, in this paper, the Stroh formalism for several different types of materials (anisotropic elastic, piezoelectric, piezomagnetic, magneto-electro-elastic, viscoelastic) and deformations (two-dimensional, coupled stretching-bending, three-dimensional) are organized together and presented in the same mathematical form.
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Igumnov, Leonid, S. Yu Litvinchuk, A. A. Belov, and A. A. Ipatov. "Boundary Element Formulation for Numerical Surface Wave Modelling in Poroviscoelastisity." Key Engineering Materials 685 (February 2016): 172–76. http://dx.doi.org/10.4028/www.scientific.net/kem.685.172.
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Problems of the poroviscodynamics are considered. Theory of poroviscoelasticity is based on Biot’s equations of fluid saturated porous media under assumption that the skeleton is viscoelastic. Viscoelastic effects of solid skeleton are modeled by mean of elastic-viscoelastic correspondence principle, using such viscoelastic models as a standard linear solid model and model with weakly singular kernel. The fluid is taken as original in Biot’s formulation without viscoelastic effects. Boundary integral equations method is applied to solve three-dimensional boundary-value problems. Boundary-element method with mixed discretization and matched approximation of boundary functions is used. Solution is obtained in Laplace domain, and then Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. An influence of viscoelastic parameters on dynamic responses is studied. Numerical example of the surface waves modelling is considered.
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Shibuya, Y., and Hideki Sekine. "Multi-Scale Analysis of Viscoelastic Behavior of Laminated Composite Structures." Key Engineering Materials 430 (March 2010): 115–32. http://dx.doi.org/10.4028/www.scientific.net/kem.430.115.
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For high temperature applications of laminated composite structures, viscoelastic behavior of laminated composite structures is investigated by multi-scale analysis based on a homogenization theory. Effective viscoelastic properties of the laminas are evaluated by a boundary integral method at a micro-scale level, and viscoelastic analysis for laminated composite structures is performed by a finite element method at a macro-scale level using the effective viscoelastic properties of lamina obtained by the micro-scale analysis. In the multi-scale analysis, the Laplace transformation is adopted and the correspondence principle between elastic and viscoelastic solutions in the Laplace domain is applied. The inverse Laplace transform is formulated by the Duhamel integral, and is calculated numerically. As a numerical example, a laminated composite plate with a hole is treated and the viscoelastic behavior of the laminated composite structure is elucidated.
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Sias Daniel, Jo, Y. Richard Kim, and Hyun-Jong Lee. "Effects of Aging on Viscoelastic Properties of Asphalt-Aggregate Mixtures." Transportation Research Record: Journal of the Transportation Research Board 1630, no. 1 (January 1998): 21–27. http://dx.doi.org/10.3141/1630-03.
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The effects of aging on asphalt-aggregate mixtures is a topic that has been gaining attention in recent years. Of special interest is how the fatigue performance of asphalt concrete mixtures changes with time because of changing material properties. The fatigue performance of a mixture is related to its viscoelastic material properties. An investigation of the effects of aging on viscoelastic properties of an asphalt-aggregate mixture, such as creep compliance, relaxation modulus, dynamic modulus, and phase angle, is discussed in this paper. The framework for including the effect of aging in an existing uniaxial constitutive model is established, and the applicability of Schapery’s elastic-viscoelastic correspondence principle to aged mixtures is validated.
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Krishna, Arvind, B. D. Harper, and J. K. Lee. "Finite Element Viscoelastic Analysis of Temperature and Moisture Effects in Electronic Packaging." Journal of Electronic Packaging 117, no. 3 (September 1, 1995): 192–200. http://dx.doi.org/10.1115/1.2792091.
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Several workers have demonstrated the presence of singular stress fields near the edge of a bimaterial interface subject to thermal gradients. Many of the analyses in the literature are limited to linear elastic materials and are useful as first estimates of stresses in such assemblies. However, a time-dependent stress analysis is necessary when viscoelastic materials such as polymer films are bonded to elastic substrates. This paper shows the relevance of viscoelastic modeling in demonstrating the effects of combined temperature and moisture loading on bimaterial interfaces and viscoelastic films sandwiched between elastic substrates. A 2-D finite element method for linear hygrothermoviscoelasticity based on an incremental creep strain rate form is developed. The correspondence principle of linear viscoelasticity is invoked and comparisons between FEA and analytical solutions are demonstrated. Moisture is modeled using Fick’s law and the thermorheologically simple material (TSM) postulate is extended to incorporate a moisture shift function in analogy with temperature. The analysis of a polyimide film sandwiched between elastic substrates subject to a thermal cycle with diffusion from the free edge shows stress reversals for the peel stresses that may explain failure modes not anticipated by an elastic analysis.
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Khatri, K. N. "Vibration Control of Conical Shells Using Viscoelastic Materials." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 206, no. 3 (May 1992): 167–78. http://dx.doi.org/10.1243/pime_proc_1992_206_113_02.
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The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.
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Bhattacharjee, Sudip, Aravind Krishna Swamy, and Jo Sias Daniel. "Application of Elastic–Viscoelastic Correspondence Principle to Determine Fatigue Endurance Limit of Hot-Mix Asphalt." Transportation Research Record: Journal of the Transportation Research Board 2126, no. 1 (January 2009): 12–18. http://dx.doi.org/10.3141/2126-02.
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Khazanovich, Lev. "The elastic–viscoelastic correspondence principle for non-homogeneous materials with time translation non-invariant properties." International Journal of Solids and Structures 45, no. 17 (August 2008): 4739–47. http://dx.doi.org/10.1016/j.ijsolstr.2008.04.011.
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Zhao, Rong Guo, and Wen Bo Luo. "Time-Dependent Mechanical Behaviors of Polyamide 6/Nano-SiO2 Composite." Key Engineering Materials 368-372 (February 2008): 1080–83. http://dx.doi.org/10.4028/www.scientific.net/kem.368-372.1080.
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The uniaxial tension under various strain rates, creep under various sustained loads, and equalamplitude- strain loading and unloading tests are carried out at room temperature with polyamide 6/nano- SiO2 composite specimens. According to the elasticity recovery correspondence principle, the recovered elastic stresses (strains) in the case of prescribed strain (stress) history are calculated, and the instantaneous elastic constitutive equations are deduced. The nonlinear viscoelastic constitutive relations in single integral form on the basis of the instantaneous elastic constitutive equations are constructed and applied to model the current stress (strain) responses of polyamide 6/nano-SiO2 composite. The theoretic results agree well with the experimental data, which demonstrates that the single integral constitutive relations used in this work can accurately simulate the physical nonlinear viscoelastic properties of polyamide 6/nano-SiO2 composite. Finally, the creep curve at higher stress level is horizontally shifted along logarithmic timescale using a stress shift factor in terms of the time-stress superposition principle and superposed on that at relative lower stress level to form a master creep compliance curve that spans a longer timescale interval than the short-term test curve does, which suggests that TSSP provides an accelerated characterization method for the long-term creep performance of polyamide 6/nano-SiO2 composite.
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Lee, Hyun, Y. Richard Kim, and Seung Lee. "Prediction of Asphalt Mix Fatigue Life with Viscoelastic Material Properties." Transportation Research Record: Journal of the Transportation Research Board 1832, no. 1 (January 2003): 139–47. http://dx.doi.org/10.3141/1832-17.
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A simplified fatigue model is presented that can predict the fatigue life of asphalt mixes using viscoelastic properties only. This fatigue model was originally developed with the elastic-viscoelastic correspondence principle and continuum damage mechanics and was reduced to a simple version that can predict fatigue life with viscoelastic properties only. On the basis of the experimental study conducted on 12 different types of asphalt mixes, it was observed that the fatigue behavior of asphalt mixes is affected by both the viscoelastic properties and the fatigue characteristics, but mostly by the viscoelastic properties. In addition, it was found that the coefficient of conventional strain-based fatigue models could be expressed in terms of viscoelastic material properties. In the verification study, the fatigue model was able to predict the fatigue life of various types of mixes at the same level of prediction accuracy without change in model coefficients. The fatigue model was also able to accurately predict the changes in the fatigue life of an asphalt mix due to the changes in the volumetric mix properties.
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Guo, Jie-Tao, Zhe-Ming Zhang, Yao-Lan Tang, and Jian Ji. "A Simplified Viscoelastic Solution of the Frost Heaving Force of Cavity Water behind Tunnel Linings." Advances in Civil Engineering 2020 (July 27, 2020): 1–8. http://dx.doi.org/10.1155/2020/8857580.
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With the high demand for construction of tunnels in China’s severe cold regions, the problem of frost heaving has become an important factor that endangers tunnel safety. This paper attempts to investigate the effect of frost heave of cavity water that widely exists in the tunneling engineering on the tunnel stability. According to the actual deformation of the surrounding rock of the tunnel, the viscoelastic behavior is considered to the surrounding rock. On the premise of the elastic solution of stagnant water frost heave, the viscoelastic solution of frost heaving pressure is deduced by Laplace transform using the generalized Kelvin model based on the elastic-viscoelastic correspondence principle. The frost heaving force is analyzed through a case study with variations in the size of the cavity defect as well as the constitutive model parameters. It is concluded that the frost heaving force increases with the cavity defect size; over time, the frost heaving force gradually increases, but it will eventually stabilize. It is found that when the frost heaving force reaches a certain level, the surrounding rock with low strength or the lining with insufficient strength will crack, and the frost heaving force will not continue to increase.
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Yartsev, Boris, Viktor Ryabov, and Lyudmila Parshina. "Dissipative properties of composite structures. 1. Statement of problem." Transactions of the Krylov State Research Centre 4, no. 398 (November 15, 2021): 24–34. http://dx.doi.org/10.24937/2542-2324-2021-4-398-24-34.
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Object and purpose of research. The object under study is a sandwich plate with two rigid anisotropic layers and a filler of soft isotropic viscoelastic polymer. Each rigid layer is an anisotropic structure formed by a finite number of orthotropic viscoelastic composite plies of arbitrary orientation. The purpose is to develop a mathematical model of sandwich plate. Materials and methods. The mathematical model of sandwich plate decaying oscillations is based on Hamilton variational principle, Bolotin’s theory of multilayer structures, improved theory of the first order plates (Reissner-Mindlin theory), complex modulus model and principle of elastic-viscoelastic correspondence in the linear theory of viscoelasticity. In description of physical relations for rigid layers the effects of oscillation frequencies and ambient temperature are considered as negligible, while for the soft viscoelastic polymer layer the temperaturefrequency relation of elastic-dissipative characteristics are taken into account based on experimentally obtained generalized curves. Main results. Minimization of the Hamilton functional makes it possible to reduce the problem of decaying oscillations of anisotropic sandwich plate to the algebraic problem of complex eigenvalues. As a specific case of the general problem, the equations of decaying longitudinal and transversal oscillations are obtained for the globally orthotropic sandwich rod by neglecting deformations of middle surfaces of rigid layers in one of the sandwich plate rigid layer axes directions. Conclusions. The paper will be followed by description of a numerical method used to solve the problem of decaying oscillations of anisotropic sandwich plate, estimations of its convergence and reliability are given, as well as the results of numerical experiments are presented.
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Ipatov, A. A. "BEM ANALYSIS OF WAVE PROPAGATION IN POROVISCOELASTIC LAYERED HALFSPACE AND HALFSPACE WITH CAVITY." Problems of strenght and plasticity 82, no. 3 (2020): 364–76. http://dx.doi.org/10.32326/1814-9146-2020-82-3-364-376.
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The paper is dedicated to the wave propagation a porous-viscoelastic material. As a mathematical model of a fully saturated poroelastic medium, we consider the Biot model with four basic functions – pore pressure and skeleton movements. The Biot model is supplemented by the principle of elastic and viscoelastic reaction correspondence. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is spplied to describe the viscoelastic properties of a skeleton. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. To solve boundary integral equations, the boundary element method is performed. Quadrangular eight-node biquadratic elements are used for boundary element discretization. Numerical integration is carried out according to Gaussian quadrature formulas using algorithms for lowering the order and eliminating features. To obtain a solution in explicit time, numerical inversion of the Laplace transform is applied based on the Durbin algorithm with a variable frequency step. This study is a development of the existing boundary-element technique for solving problems on layered porous-elastic half-spaces. This will allow you to take into account the heterogeneity of the soil in depth. The problem of the action of a vertical force in the form of the Heaviside function on the surface of a layered porous-elastic half-space and a half-space with a cavity is considered. Variants of a homogeneous and heterogeneous half-space are considered. Under the model of heterogeneity we understand the piecewise homogeneous solid. The responses of the boundary displacements on the surface of the half-space are presented. The effect of the viscoelastic material model parameter on the dynamic response of displacements is demonstrated. It is established that the viscosity parameters have a significant effect on the nature of the distribution of parameters of wave processes.
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You, Zhanping, and William G. Buttlar. "Application of Discrete Element Modeling Techniques to Predict the Complex Modulus of Asphalt–Aggregate Hollow Cylinders Subjected to Internal Pressure." Transportation Research Record: Journal of the Transportation Research Board 1929, no. 1 (January 2005): 218–26. http://dx.doi.org/10.1177/0361198105192900126.
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An extension of the discrete element modeling (DEM) approach, or clustered DEM, was used to simulate the hollow cylinder tensile (HCT) test, in which various material phases (e.g., aggregates, mastic) are modeled with bonded clusters of discrete elements. The basic principle of the HCT test is the application of internal pressure to the inner cavity of a hollow cylinder specimen, which produces circumferential strain. In the present study an experimental program was conducted to measure the complex modulus of asphalt concrete mixtures at various loading rates and temperatures. The HCT test was then modeled with a two-dimensional, linear elastic DEM simulation. The current approach uses the correspondence principle to bridge between the elastic simulation and viscoelastic response. The two-dimensional morphology of the asphalt concrete mixture was captured with a high-resolution scanner, enhanced with image-processing techniques, and reconstructed into an assembly of discrete elements. The mixture complex moduli predicted in the HCT simulations were found to be in good agreement with experimental measurements across a range of test temperatures and loading frequencies for the coarse-grained mixtures investigated. Ongoing work in the area of viscoelastic constitutive modeling, fracture modeling, and three-dimensional tomography and modeling will extend the capabilities of this promising technique for fundamental studies of asphalt concrete and other particulate composites.
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Luciano, R., and E. J. Barbero. "Analytical Expressions for the Relaxation Moduli of Linear Viscoelastic Composites With Periodic Microstructure." Journal of Applied Mechanics 62, no. 3 (September 1, 1995): 786–93. http://dx.doi.org/10.1115/1.2897015.
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In this paper the viscoelastostatic problem of composite materials with periodic microstructure is studied. The matrix is assumed linear viscoelastic and the fibers elastic. The correspondence principle in viscoelasticity is applied and the problem in the Laplace domain is solved by using the Fourier series technique and assuming the Laplace transform of the homogenization eigenstrain piecewise constant in the space. Formulas for the Laplace transform of the relaxation functions of the composite are obtained in terms of the properties of the matrix and the fibers and in function of nine triple series which take into account the geometry of the inclusions. The inversion to the time domain of the relaxation and the creep functions of composites reinforced by long fibers is carried out analytically when the four-parameter model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results are presented.
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Heinrich, S. M., S. Shakya, J. Liang, and P. S. Lee. "An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects." Journal of Electronic Packaging 122, no. 4 (January 28, 2000): 328–34. http://dx.doi.org/10.1115/1.1289631.
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An analytical model is developed for predicting the time-dependent shearing displacement in area-array solder interconnects due to global CTE mismatch under thermal cycling. As a first step toward incorporating the creep deformation of the solder, the material is modeled as viscoelastic and temperature-independent. This permits one to invoke the correspondence principle of viscoelasticity to map the authors’ previously derived, closed-form solution for an elastic nonprismatic (concave, convex, or cylindrical) Timoshenko beam under shear loading into the associated viscoelastic solution. This leads to general analytical results for the frequency-dependent shear displacement amplitude in the critical joint. The results are expressed conveniently in terms of a “full-creep correction factor” and a “frequency correction factor,” which explicitly show the effects of the following parameters on the joint deformation: joint shape; array population; array, component, and substrate dimensions; viscoelastic material properties of the interconnect material; elastic properties of the component and substrate materials; and loading frequency. To demonstrate the technique for a particular viscoelastic constitutive law, the solder is assumed to behave elastically under hydrostatic loads and as a viscoelastic Kelvin solid under deviatoric conditions. For this special case the creep portion of the deformation is shown to be dependent upon only two dimensionless parameters: a dimensionless loading frequency and a material- and shape-dependent joint parameter. The results of the study may be useful in identifying design and process modifications that may improve the thermal fatigue life of area arrays. [S1043-7398(00)00404-7]
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Sol, Hugo, Hubert Rahier, and Jun Gu. "Prediction and Measurement of the Damping Ratios of Laminated Polymer Composite Plates." Materials 13, no. 15 (July 29, 2020): 3370. http://dx.doi.org/10.3390/ma13153370.
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Laminated composites materials are mostly used in dynamically loaded structures. The design of these structures with finite element packages is focused on vibrations, elastic deformations and failure control. Damping is often neglected because of its assumed secondary importance and also because of dearth of information on relevant material properties. This trend is prone to change as it is now realised that damping plays an increasingly important role in vibration comfort, noise radiation and crash simulations. This paper shows in a first step how to identify the orthotropic elastic and damping properties of single layer fibre-reinforced composite material sheets using a new extended version of the Resonalyser procedure. The procedure is based on the elastic-viscoelastic correspondence principle and uses a mixed numerical experimental method. In a subsequent step, the complex laminate stiffness values are computed using the identified single layer material properties. To validate this approach, the modal damping ratios of arbitrary laminated plates of different materials at several resonance frequencies are predicted and experimentally verified.
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Spinu, Sergiu. "Viscoelastic Contact Simulation under Harmonic Cyclic Load." Advances in Tribology 2018 (2018): 1–16. http://dx.doi.org/10.1155/2018/9432894.
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Characterization of viscoelastic materials from a mechanical point of view is often performed via dynamic mechanical analysis (DMA), consisting in the arousal of a steady-state undulated response in a uniaxial bar specimen, allowing for the experimental measurement of the so-called complex modulus, assessing both the elastic energy storage and the internal energy dissipation in the viscoelastic material. The existing theoretical investigations of the complex modulus’ influence on the contact behavior feature severe limitations due to the employed contact solution inferring a nondecreasing contact radius during the loading program. In case of a harmonic cyclic load, this assumption is verified only if the oscillation indentation depth is negligible compared to that due to the step load. This limitation is released in the present numerical model, which is capable of contact simulation under arbitrary loading profiles, irregular contact geometry, and complicated rheological models of linear viscoelastic materials, featuring more than one relaxation time. The classical method of deriving viscoelastic solutions for the problems of stress analysis, based on the elastic-viscoelastic correspondence principle, is applied here to derive the displacement response of the viscoelastic material under an arbitrary distribution of surface tractions. The latter solution is further used to construct a sequence of contact problems with boundary conditions that match the ones of the original viscoelastic contact problem at specific time intervals, assuring accurate reproduction of the contact process history. The developed computer code is validated against classical contact solutions for universal rheological models and then employed in the simulation of a harmonic cyclic indentation of a polymethyl methacrylate half-space by a rigid sphere. The contact process stabilization after the first cycles is demonstrated and the energy loss per cycle is calculated under an extended spectrum of harmonic load frequencies, highlighting the frequency for which the internal energy dissipation reaches its maximum.
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Paulino, G. H., and Z. H. Jin. "Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture." Journal of Applied Mechanics 68, no. 2 (July 13, 2000): 284–93. http://dx.doi.org/10.1115/1.1354205.
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In this paper, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions. The shear relaxation function of the material is assumed as μ=μ0 expβy/hft, where h is a length scale and f(t) is a nondimensional function of time t having either the form ft=μ∞/μ0+1−μ∞/μ0exp−t/t0 for a linear standard solid, or ft=t0/tq for a power-law material model. We also consider the shear relaxation function μ=μ0 expβy/h[t0 expδy/h/t]q in which the relaxation time depends on the Cartesian coordinate y exponentially. Thus this latter model represents a power-law material with position-dependent relaxation time. In the above expressions, the parameters β, μ0,μ∞,t0; δ, q are material constants. An elastic crack problem is first solved and the correspondence principle (revisited) is used to obtain stress intensity factors for the viscoelastic functionally graded material. Formulas for stress intensity factors and crack displacement profiles are derived. Results for these quantities are discussed considering various material models and loading conditions.
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Maslov, B. P. "Hereditary creep of isotropic composites of random structure under a complex stress state." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2021): 77–80. http://dx.doi.org/10.17721/1812-5409.2021/3.13.
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Nonlinear hereditary creep problem of the mechanics of composites is solved within the framework of a second-order theory. The hereditary functionals are used to construct general constitutive relations. A stochastic boundary value problem for determining the stress concentration and its relaxation in metal matrix composite (PMC) is solved in Laplace-Carson image space. Shapery's correspondence principle for quasi-linear viscoelastic media is generalised on the hereditary creep problem and the method of successive approximation is used. The reduced creep functions and the stress concentration parameters are determined. Examples are given showing the importance of the mutual influence of nonlinear elastic and viscous properties of the components on stress redistribution near inclusions with possibility to predicting the long-term strength.
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Feng, G., and A. H. W. Ngan. "Effects of Creep and Thermal Drift on Modulus Measurement Using Depth-sensing Indentation." Journal of Materials Research 17, no. 3 (March 2002): 660–68. http://dx.doi.org/10.1557/jmr.2002.0094.
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In modulus measurement by depth-sensing indentation, previous considerations assume elastic recovery to be the sole process during unloading, but in reality creep and thermal drift may also occur, causing serious errors in the measured modulus. In this work, the problem of indentation on a linear viscoelastic half-space is solved using the correspondence principle between elasticity and linear viscoelasticity. The correction term due to creep in the apparent contact compliance is found to be equal to the ratio of the indenter displacement rate at the end of the load hold to the unloading rate. A condition for nullifying the effect of thermal drift on modulus measurement is also proposed. With this condition satisfied, the effect of thermal drift on the calculated modulus is negligible irrespective of the magnitude of the drift rate.
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Wang, Zhichen, Naisheng Guo, Xu Yang, and Shuang Wang. "Micromechanical Prediction Model of Viscoelastic Properties for Asphalt Mastic Based on Morphologically Representative Pattern Approach." Advances in Materials Science and Engineering 2020 (June 28, 2020): 1–12. http://dx.doi.org/10.1155/2020/7915140.
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This paper is devoted to the introduction of physicochemical, filler size, and distribution effect in micromechanical predictions of the overall viscoelastic properties of asphalt mastic. In order to account for the three effects, the morphologically representative pattern (MRP) approach was employed. The MRP model was improved due to the arduous practical use of equivalent modulus formula solution. Then, a homogeneous morphologically representative model (H-MRP) with the explicit solution was established based on the homogenization theory. Asphalt mastic is regarded as a composite material consisting of filler particles coated structural asphalt and free asphalt considering the physicochemical effect. An additional interphase surrounding particles was introduced in the H-MRP model. Thus, a modified H-MRP model was established. Using the proposed model, a viscoelastic equation was derived to predict the complex modulus and subsequently the dynamic modulus of asphalt mastic based on the elastic-viscoelastic correspondence principle. The dynamic shear rheological tests were conducted to verify the prediction model. The results show that the predicted modulus presents an acceptable precision for asphalt mastic mixed with 10% and 20% fillers volume fraction, as compared to the measured ones. The predicted modulus agrees reasonably well with the measured ones at high frequencies for asphalt mastic mixed with 30% and 40% fillers volume fraction. However, it exhibits underestimated modulus at low frequencies. The reasons for the discrepancy between predicted and measured dynamic shear modulus and the factors affecting the dynamic shear modulus were also explored in the paper.
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Zhao, Liming, Hanjun Yin, Tongjun Chen, Genyang Tang, Chao Sun, Mingjin Zhang, Ningjun Zhu, and Fanjia Li. "Theoretical prediction of elastic modulus at different states and squirt-flow-related attenuation: extension of Cracks-Pores Effective Medium model." Geophysical Journal International 229, no. 1 (November 10, 2021): 186–202. http://dx.doi.org/10.1093/gji/ggab461.
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SUMMARY Squirt flow plays an essential role in elastic modulus dispersion and attenuation for fluid-saturated cracked porous rocks. The Mavko–Jizba model and relevant modified models can describe the squirt flow well based on the related elastic moduli, such as dry/drained bulk modulus. However, when these elastic moduli are challenging to attain, it is impossible to model the squirt-flow-related elastic moduli and attenuations with the models. On the other hand, the effective medium theory (EMT) model can estimate these elastic moduli, but cannot predict the undrained/relaxed and partially relaxed saturated elastic moduli and the squirt-flow-related attenuations. This paper extended an EMT model—Cracks–Pores Effective Medium (CPEM) model—to cover the undrained/relaxed and partially relaxed states following the elastic–viscoelastic correspondence principle. The proposed model [i.e. frequency-dependent CPEM (CPEMF) model] can thus estimate the elastic moduli over the different states (dry/drained, undrained/relaxed, partially relaxed and unrelaxed) and associated attenuations. It agrees well with the prediction of the modified Mavko–Jizba–Gurevich model (MJGZ-HF) at unrelaxed state and is precisely consistent with the prediction of Gassmann at undrained/relaxed state. Also, it analytically shows good consistency with the modified Mavko–Jizba–Gurevich model (MJGZ-MF) at partially relaxed state. The numerical simulations of CPEM/CPEMF models and MJGZ-HF/MJGZ-MF models show good agreement at the different states. Furthermore, we interpreted the experimental data on a basaltic sample and a sandstone sample with the CPEM/CPEMF models. The CPEMF model's predictions of elastic modulus at different states and associated modulus dispersion/attenuation are in good agreement with the corresponding measured ones, suggesting that the proposed CPEMF model can efficiently predict the elastic moduli at different states (dry/drained, undrained/relaxed, partially relaxed and unrelaxed) and quantify the squirt-flow-related elastic modulus dispersion and attenuation among different states well.
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Igumnov, Leonid A., and Aleksandr A. Ipatov. "The Dynamic Analysis of a Slab on a Poroviscoelastic Halfspace under Vertical Load via BEM." Key Engineering Materials 743 (July 2017): 166–71. http://dx.doi.org/10.4028/www.scientific.net/kem.743.166.
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Mechanics of advanced materials, such as poro-, visco-or poroviscoelastic materials, is relevant to such disciplines as geophysics, geo-and biomechanics, seismology, constricting. Because of the complexity of the inertial viscosity and mechanical phases coupling in porous media most transient response problems can only be solved via numerical methods. The present work is dedicated to numerical modelling of a problem of a Heaviside-type impact load acting on a brittle slab situated above a fluid saturated foundation. Slab is treated as elastic or poroelastic rock. Fluid saturated foundation is a soil and modeled as a poroviscoelastic media. Poroviscoelastic formulation is based on Biot’s theory of poroelasticity in combination with elastic-viscoelastic correspondence principle. Classical models of viscoelasticity are employed, such as Kelvin-Voight model, standard linear solid model and model with weakly singular kernel. The problem is treated in Laplace domain. Direct boundary integral method approach is used to obtain solution. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. A problem of Heaviside-type vertical load acting on a slab bonded on a poroviscoelastic halfspace is considered. The comparison of dynamic responses when poroviscoelastic halfspace is described by different viscoelactic models is presented.
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Li, Tianpeng, Junli Han, Shixin Wang, Yong He, Xiong Chen, and Bang Lu. "Constitutive Model of N15 Propellant considering the Confining Pressure Effect." International Journal of Aerospace Engineering 2021 (December 8, 2021): 1–12. http://dx.doi.org/10.1155/2021/2661184.
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To describe the effect of confining pressure on the mechanical responses of N15 propellant, a constitutive model considering the confining pressure effect was first established for N15 propellant based on the elastic-viscoelastic correspondence principle. Then, the mechanical properties of N15 solid propellant under different confining pressures were obtained using confining pressure test system, and the obtained results indicate that the initial modulus of propellant did not change with confining pressure, but the maximum tensile strength, rupture strength, the maximum elongation, and elongation at break increased with increasing confining pressure. In conjunction with propellants’ mesoscopic structure and cross-section analysis, the mechanical mechanism of confining pressure effect on propellant was initially disclosed. Due to confining pressure, the particle dewetting inside the propellant was reduced, the hole propagation was delayed, and crack extension inhibited germination, proving that confining pressure has a strengthening impact on the propellant. Finally, assuming that the model parameters were dependent on pressure, the model parameters acquisition and validation were conducted. The results demonstrated that constitutive model can describe confining pressure influence on the mechanical properties of N15 propellant accurately.
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Lysenko, A., L. Parshina, and B. Yartsev. "Effective mechanical characteristics of symmetric layered composite in different loading conditions." Transactions of the Krylov State Research Centre 1, no. 399 (March 15, 2022): 75–88. http://dx.doi.org/10.24937/2542-2324-2022-1-399-75-88.
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Object and purpose of research. This paper discusses balanced and quasi-isotropic (in the reinforcement plane) symmetric layered composite structures made up by the layers of cloth-reinforced GRP. The purpose of this work was to demonstrate the necessity to justify the applicability of experimental results for effective mechanical parameters determined in the conditions of uniaxial tension/compression to the calculation of thin-walled layered composite structures that work in bending/twisting conditions. Materials and methods. The straining of layered composite structures is simulated as per the updated theory of first-order plates, the model of complex moduli and the principle of elastic-viscoelastic correspondence in linear viscoelasticity theory. Limit state predictions are based on Tsai-Wu tensor-polynomial strength criterion. Main results. This paper suggests the expressions that predict effective elastic constants, dissipation properties and strength limits for symmetric layered structures under investigation. The study shows that balanced symmetric structure made up by four layers of composite may be regarded, with the accuracy sufficient for engineering calculations, as an ortho-tropic material for all loading conditions. At the same time, symmetric quasi-isotropic (in the reinforcement plane) structure made up by thirty two composite layers must be regarded as orthotropic in case of tension/compression and monoclinic in case of bending/twisting. Conclusion. The study has shown the necessity to justify the application of experimental effective mechanical properties for uniaxial tension/compression to calculation of thin-walled layered composite structures exposed to bending/twisting.
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Yee, K. C., and T. J. Moon. "Plane Thermal Stress Analysis of an Orthotropic Cylinder Subjected to an Arbitrary, Transient, Asymmetric Temperature Distribution." Journal of Applied Mechanics 69, no. 5 (August 16, 2002): 632–40. http://dx.doi.org/10.1115/1.1491268.
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A closed-form, analytical solution is presented for the transient, plane thermal stress analysis of a linearly elastic, homogeneously orthotropic hollow cylinder subjected to an arbitrary temperature distribution. The thermoelastic solution, obtained by a stress function approach, can be used as the basis for the corresponding thermoviscoelastic solution for thermorheologically simple viscoelastic materials by invoking the viscoelastic Correspondence Principle. This solution can also be directly extended to the class of weakly inhomogeneously orthotropic cylinders using perturbation methods. The transient asymmetric temperature field is characterized by Fourier-Bessel eigenfunction expansions. The analytically derived stress function satisfies a linear, fourth-order inhomogeneous partial differential equation and the Cesaro integral conditions, which assure the existence of a single-valued displacement field. The corresponding thermal stresses are then computed by the stress-stress function relations. A key feature of the analytical solution is that the hoop, radial, and shear stresses, due to the transient arbitrary temperature distribution, are expressed explicitly in terms of the scalar temperature field. A polymer composite example is presented to validate the current method and to qualitatively illustrate the distribution of thermal stresses due to an asymmetric temperature distribution. Numerical results are presented for the thermally driven hoop, radial and (interlaminar) shear stresses in a hollow, hoop-wound glass/epoxy cylinder. This analysis demonstrates that potentially debilitating interlaminar shear stresses can develop in laminated composites when subjected to an even modest transient asymmetric temperature distribution. Their magnitudes depend on the severity of the spatial and temporal thermal gradients in the circumferential direction. While still relatively low compared to the hoop stress, the shear stress may cause thermal failure due to the typically low interlaminar shear strengths of laminated composite materials.
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Huang, Wenjun, Deli Gao, and Yinghua Liu. "Short-Term and Long-Term Mechanical Models of Wellbores Considering Cement Consolidation and Formation Creep." SPE Journal 24, no. 05 (April 17, 2019): 2064–82. http://dx.doi.org/10.2118/195573-pa.
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Summary With oil and gas wells extending deeper and deeper, downhole conditions become increasingly complicated, and thus increasingly sophisticated wellbore models are needed. Current wellbore models usually neglect the coupling effect in the cement–consolidation process and do not sufficiently consider the whole operation process of the wellbore. To overcome these shortcomings, short–term and long–term mechanical wellbore models while considering the relevant stages in wellbore life are built. In the short–term model, wellbore–operation stages include casing running, cement displacement, and cement consolidation. The governing equation of cement consolidation while considering the coupling effect between cement hardening and volume change is presented. In the long–term model, the governing equation of formation creep while considering prestresses and initial strains is given. The elastic/viscoelastic–correspondence principle and stress–superposition method are used to simplify the derivation. Next, the effects of relevant factors on short–term and long–term wellbore stresses are analyzed. The results show that wellbore stresses caused by cement consolidation will be underestimated when the coupling effects are neglected. The most vulnerable positions for wellbore failure are on different cylinder elements under different wellbore stages. Wellbore properties, short–term stresses, and formation creep greatly affect wellbore mechanical behaviors. Therefore, the new model provides an important basis for wellbore–failure prediction and optimal design.
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Ryabov, Victor M., and Boris A. Yartsev. "Nonclassical vibrations of a monoclinic composite strip." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 4 (2021): 695–708. http://dx.doi.org/10.21638/spbu01.2021.415.
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A mathematical model of damped flexural-torsional vibrations of monoclinic composite strip of constant length rectangular cross section is proposed. The model is based on the refined bending theory Timoshenko beams, the theory of generalized Voigt — Lekhnitskii torsion and the elastic-viscoelastic correspondence principle in the linear theory of viscoelasticity. A two-stage method for solving a coupled system of differential equations is developed. First, using the Laplace transform in spatial variable, real natural frequencies and natural forms are found. To determine the complex natural frequencies of the strip in found real values are used as their initial values of natural frequencies, and then the complex frequencies are calculated by the method iterations of the third order. An assessment of the reliability of the mathematical model and method of numerical solution, performed by comparing calculated and experimental values of natural frequencies and loss factors is given. The results of a numerical study of the effect angles of orientation of reinforcing fibers and lengths by the values of natural frequencies and loss factors for free-free and cantilever monoclinic stripes are discussed. It is shown that for the free-free strip the region of mutual transformation eigenmodes of coupled vibration modes arise for quasi-bending and quasi-twisting vibrations of either even or odd tones. In the console strip of the region of mutual transformation of eigenforms of coupled modes vibrations occur for both even and odd tones.
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Zhan, Qiwei, Mingwei Zhuang, Yuan Fang, and Qing Huo Liu. "Discontinuous Galerkin modeling of 3D arbitrary anisotropic Q." GEOPHYSICS 84, no. 6 (November 1, 2019): C295—C309. http://dx.doi.org/10.1190/geo2019-0119.1.
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For wave propagation problems, conventional time-domain anelastic attenuation modeling involves either Caputo fractional time derivatives for an exactly constant-[Formula: see text] model, thus leading to globally temporal memory effects; or auxiliary partial differential equations (PDEs) for a nearly constant-[Formula: see text] model, thus resulting in globally spatial operators. Therefore, memory and time consumptions increase tremendously, compared with the purely elastic counterpart. Moreover, the numerical models are usually limited to isotropic or transversely isotropic attenuation, due to the ambiguity of anisotropic attenuation parameterization. Therefore, it is indispensable to investigate an efficient method, to easily incorporate the general anisotropic attenuation effects in the time domain. To tackle these problems, we have first developed a [Formula: see text]-transformation rule, via the correspondence principle, revealing the validity range for a large enough [Formula: see text] value. Then, we construct a new constitutive equation, by extending the generalized Maxwell body, from the isotropic viscoelastic media to fully anisotropic scenario, i.e., as complex as triclinic attenuation. As a result, global memory effects are effectively localized, with several anelastic functions subject to ordinary differential equations, while preserving the original governing equations. An efficient hp-adaptive discontinuous Galerkin (DG) time-domain algorithm is implemented, where the Riemann problem is exactly solved. Consequently, the extra computation cost to incorporate [Formula: see text] effects is nearly negligible. Furthermore, we derive an analytical solution for the general anisotropic attenuation to verify this DG implementation.
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Haider, Mansoor A., and Farshid Guilak. "An Axisymmetric Boundary Integral Model for Incompressible Linear Viscoelasticity: Application to the Micropipette Aspiration Contact Problem." Journal of Biomechanical Engineering 122, no. 3 (February 6, 2000): 236–44. http://dx.doi.org/10.1115/1.429654.
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The micropipette aspiration test has been used extensively in recent years as a means of quantifying cellular mechanics and molecular interactions at the microscopic scale. However, previous studies have generally modeled the cell as an infinite half-space in order to develop an analytical solution for a viscoelastic solid cell. In this study, an axisymmetric boundary integral formulation of the governing equations of incompressible linear viscoelasticity is presented and used to simulate the micropipette aspiration contact problem. The cell is idealized as a homogenous and isotropic continuum with constitutive equation given by three-parameter E,τ1,τ2 standard linear viscoelasticity. The formulation is used to develop a computational model via a “correspondence principle” in which the solution is written as the sum of a homogeneous (elastic) part and a nonhomogeneous part, which depends only on past values of the solution. Via a time-marching scheme, the solution of the viscoelastic problem is obtained by employing an elastic boundary element method with modified boundary conditions. The accuracy and convergence of the time-marching scheme are verified using an analytical solution. An incremental reformulation of the scheme is presented to facilitate the simulation of micropipette aspiration, a nonlinear contact problem. In contrast to the halfspace model (Sato et al., 1990), this computational model accounts for nonlinearities in the cell response that result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell–micropipette contact region, and curvature of the edges of the micropipette (inner radius a, edge curvature radius ε). Using 60 quadratic boundary elements, a micropipette aspiration creep test with ramp time t*=0.1 s and ramp pressure p*/E=0.8 is simulated for the cases a/R=0.3, 0.4, 0.5 using mean parameter values for primary chondrocytes. Comparisons to the half-space model indicate that the computational model predicts an aspiration length that is less stiff during the initial ramp response t=0-1 s but more stiff at equilibrium t=200 s. Overall, the ramp and equilibrium predictions of aspiration length by the computational model are fairly insensitive to aspect ratio a/R but can differ from the half-space model by up to 20 percent. This computational approach may be readily extended to account for more complex geometries or inhomogeneities in cellular properties. [S0148-0731(00)00503-3]
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Gu, Zhi Xu, Jian Zheng, Wei Peng, and Xi Nan Tang. "Two Analytical Models to Determine the Stress Singularities in Elastic-Viscoelastic Joints." Advanced Materials Research 834-836 (October 2013): 1391–94. http://dx.doi.org/10.4028/www.scientific.net/amr.834-836.1391.
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The stress singularities are obtained by two methods in elastic-viscoelastic joints, one is extending the corresponding solutions for elastic-elastic joints by using elastic-viscoelastic correspondence principles and the other is replacing the elastic material parameters with viscoelastic ones in Dundurs parameters directly. The difference between the two methods and the validity are discussed.
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Cleveland, Gregory S., Robert L. Lytton, and Joe W. Button. "Using Pseudostrain Damage Theory to Characterize Reinforcing Benefits of Geosynthetic Materials in Asphalt Concrete Overlays." Transportation Research Record: Journal of the Transportation Research Board 1849, no. 1 (January 2003): 202–11. http://dx.doi.org/10.3141/1849-22.
Full textAbstract:
Reflective cracking is one of the more serious distresses associated with existing hot-mix asphalt (HMA) or portland concrete cement pavements overlaid with a thin bituminous layer. Preventive maintenance techniques have included incorporating geosynthetic materials (defined here as grids, fabrics, or composites) into the pavement structure. These materials have exhibited varying degrees of success, and their use within a particular agency has been based primarily on local experience or a willingness to try a product that appears to have merit. A methodology is described that was used to compare the relative effectiveness of six commercially available geosynthetic materials in reducing the severity or delaying the appearance of reflective cracking in HMA overlay. Each geosynthetic material was incorporated into compacted HMA specimens and tested to failure. Engineering fracture mechanics and pseudostrain energy concepts based on the elastic-viscoelastic correspondence principle were used and demonstrated to be appropriate and efficient in characterizing the fatigue damage process. By considering the effects of the geosynthetic products on the loading and unloading paths of the HMA specimens, a new concept was developed and termed the reinforcing factor, R. The use of this value allows the industry to characterize the relative reinforcing benefits of geosynthetic materials in reducing reflective cracking in HMA overlays. A crack speed index was then derived to summarize the complex interactions of the material properties. In general, grids and composites performed better than fabrics, which in turn performed better than a thin tacked surface as compared with unreinforced specimens. Design equations were developed between the fracture properties of the geosyntheticmixture system and the relaxation modulus properties of the HMA, which can be used in forward-calculating design methods to predict the rate of crack growth and support the design of an HMA overlay to resist reflective cracking. To calibrate the design equations, comparative field test pavements were constructed in three regions of Texas (Amarillo, Waco, and McAllen) using each geosynthetic material. These pavements will be monitored over the next 4 years.
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Snoeijer, J. H., A. Pandey, M. A. Herrada, and J. Eggers. "The relationship between viscoelasticity and elasticity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (November 2020): 20200419. http://dx.doi.org/10.1098/rspa.2020.0419.
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Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ , over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.
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Su, Xing, and Amin Mehrabian. "The Viscoelastic Solution to Geertsma’s Subsidence Problem." Journal of Applied Mechanics 89, no. 5 (March 4, 2022). http://dx.doi.org/10.1115/1.4053790.
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Abstract This paper presents the viscoelastic analytical solution for stress and displacement due to prescribed time-varying changes in the pore fluid pressure of a disk-shaped inclusion embedded within a semi-infinite, viscoelastic medium. The correspondence principle of viscoelasticity, along with Hankel–Fourier and Laplace transforms, is used to derive the solution. The instantaneous viscoelastic solution, corresponding to the response immediately after the inclusion pore pressure change, recovers the elastic solution to the same problem (Geertsma 1973). Results are presented for fractional Maxwell and Burgers models of viscoelasticity after being applied to a set of experimental data from creep tests on shale. Solution results are demonstrated and discussed for the cases of constant inclusion depletion, as well as delayed injection of fluid into a previously depleted inclusion.
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Garzon, J., C. S. Ramos, M. H. C. Bento, S. P. B. Proença, and C. A. Duarte. "Analysis of fractures in linear viscoelastic media using a generalized finite element method and the elastic-viscoelastic correspondence principle." Theoretical and Applied Fracture Mechanics, January 2023, 103759. http://dx.doi.org/10.1016/j.tafmec.2023.103759.
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Gupta, Abhay, Satyajit Panda, and Rajidi S. Reddy. "An actively constrained viscoelastic layer with the inclusion of dispersed graphite particles for control of plate vibration." Journal of Vibration and Control, September 22, 2020, 107754632095653. http://dx.doi.org/10.1177/1077546320956533.
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In this work, the damping characteristics of an actively constrained viscoelastic material layer are examined because of the inclusion of dispersed graphite particles within the viscoelastic material layer. The study is carried out by analysing the active–passive damping in a layered plate made of a substrate layer, a constrained viscoelastic particulate composite layer and a thin constraining piezoelectric actuator layer. The effective properties of the viscoelastic particulate composite are estimated using a differential scheme and the elastic–viscoelastic correspondence principle. The piezoelectric layer is activated according to the velocity feedback control law, and a closed-loop finite element model of the overall plate is derived for the analysis. The results reveal that the inclusion of graphite particles not only causes an improved transfer of active action from the piezoelectric layer to the substrate plate but also enhances the energy dissipation capability of the constrained viscoelastic layer. It is found that the maximum transfer of active action and the maximum passive damping capability of the viscoelastic particulate composite layer arise almost at the same volume fraction of inclusion. So, an optimal volume fraction of inclusion is obtained for significantly improved active–passive damping in the overall plate. The overall study presents a potential means of improved active–passive damping treatment of structural vibration.
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Wayne Chen, W., Q. Jane Wang, Z. Huan, and X. Luo. "Semi-Analytical Viscoelastic Contact Modeling of Polymer-Based Materials." Journal of Tribology 133, no. 4 (October 1, 2011). http://dx.doi.org/10.1115/1.4004928.
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Contact of viscoelastic materials with complicated properties and surface topography require numerical solution approaches. This paper presents a 3-D semianalytical contact model for viscoelastic materials. With the hereditary integral operator and elastic-viscoelastic correspondence principle, surface displacement is expressed in terms of viscoelastic creep compliance and contact pressure distribution history in the course of a contact process. Through discretizing the contact equations in both spatial and temporal dimensions, a numerical algorithm based on the robust Conjugate Gradient method and Fast Fourier transform has been developed to solve the normal approach, contact pressure, and real contact area simultaneously. The transient contact analysis in the time domain is computationally expensive. The fast Fourier transform algorithm can help reduce the computation cost significantly. The comparisons of the new numerical results with an analytical viscoelastic contact solution for Maxwell materials and with an indentation test measurement reported in the literature has validated and demonstrated the accuracy of the proposed model. Moreover, the present model has been used to simulate the contact between a polymethyl methacrylate (PMMA) substrate and a rigid sphere driven by step, ramped, and harmonic normal loads. The validated model and numerical method can successfully compute the viscoelastic contact responses of polymer-based materials with time-dependent properties and surface roughness subjected to complicated loading profiles.
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Sun, Lu, and Feiquan Luo. "Transient Wave Propagation in Multilayered Viscoelastic Media: Theory, Numerical Computation, and Validation." Journal of Applied Mechanics 75, no. 3 (April 8, 2008). http://dx.doi.org/10.1115/1.2839906.
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This paper extends the classical problem of transient wave propagation in multilayered solids to transient wave propagation in multilayered viscoelastic solids. Laplace and Hankel transforms and the transfer-matrix approach are used in the formulation together with the elastic-viscoelastic correspondence principle in linear viscoelasticity. The derived formula provides a theoretical basis to allow effective and efficient numerical algorithms to be developed. MATLAB is used to develop a computer program DYNALAYERT that implements the theory developed. The numerical results are compared with the existing data available in literature and those obtained from finite element analysis using ANSYS. Excellent agreement has been observed from comprehensive comparisons, which verifies the validity of the theory, algorithm, and computer program developed in this study. The conclusion and findings of this study may result in a number of engineering applications, such as nondestructive evaluation of highway and airport pavements, petroleum exploration, countermine technology, geophysical inversion, structural health monitoring, and vehicle weigh-in-motion systems.