Journal articles: 'Linear elastic deformation'

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Fu, Bo-Ye, and Li-Yun Fu. "Poro-acoustoelasticity with compliant pores for fluid-saturated rocks." GEOPHYSICS 83, no. 3 (May 1, 2018): WC1—WC14. http://dx.doi.org/10.1190/geo2017-0423.1.

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Stress-induced influences on elastic wave velocities include elastic and inelastic behaviors. In general, deformation of rocks is primarily linear elastic for small-magnitude stresses; such behavior can be predicted by the conventional poro-acoustoelasticity theory. On the contrary, large-magnitude stresses induce linear elastic deformation in stiff pores and rock grains and nonlinear elastic deformation in compliant pores. Conventional poro-acoustoelasticity combines the kinetic and strain energy functions via the Lagrange equation. This theory reveals the strain energy transformation of the stiff pores and rock grains for velocity variation. The dual-porosity model uses a semiempirical equation to express the influence of the nonlinear elastic deformation of compliant pores on velocity variations; however, this model does not include the strain energy transformation of compliant pores. We incorporate the dual-porosity model into the conventional poro-acoustoelasticity theory to account for linear and nonlinear elastic deformations through the strain energy transformation of rock grains, stiff pores, and compliant pores. We determine that the work of the loading stress is transformed into two parts: the strain energy for the linear elastic deformation of rock grains and stiff pores and the nonlinear elastic deformation of compliant pores. On applying this theory to ultrasonic measurements under different differential pressures for a saturated sandstone sample, we see that the resulting solution of stress-associated velocity variations is more precise than that obtained using the conventional poro-acoustoelasticity theory, especially in the low-effective-pressure regime.

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Müller, Tobias M., and Pratap N. Sahay. "Elastic potential energy in linear poroelasticity." GEOPHYSICS 84, no. 4 (July 1, 2019): W1—W20. http://dx.doi.org/10.1190/geo2018-0216.1.

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Biot’s theory of linear poroelasticity dates back to the mid-20th century and is still currently the backbone for understanding deformation processes in fluid-saturated porous rocks with applications in geomechanics, hydrogeology, reservoir engineering, and exploration geophysics. Therein, the elastic potential energy is the critical concept to derive the macroscopic stress tensors and constitutive equations. The potential energy is taken as the single function that forms an exact differential in macroscopic strains of the solid and fluid phases. This choice intrinsically implies a reciprocal interaction between the compressive stresses of the two phases. However, it leaves out the possibility that the phases can interact in a nonreciprocal manner, which is sometimes inferred from experimental observations. The limited scope of the Biot theory is overcome by upscaling the pore-scale governing equations using volume averaging aided by the physical argument that the conservation of mass, momentum, energy, and principle of equivalence must hold at all scales. This upscaling reveals that the proper measures of deformations are not only the deformation gradient terms but also a porosity change term that accounts for the emergent pore-interface kinematics at the macroscale. It also reveals that the elastic potential energy of a porocontinuum is the sum of the potential energies of the solid and fluid phases, which are functions of their so-defined respective measure of deformation only. Such potential energy is no longer limited to only the reciprocal interaction of the compressive stresses of the phases, but it enables us to capture nonreciprocal interactions still within the realm of linearity. A nonreciprocal interaction arises whenever the potential energy density is not uniformly distributed at the pore scale but partially localized in the vicinity of pore interfaces or within the bulk part of the phases. A direct consequence is that the coupling coefficients in the linear constitutive equations are expected to be different.

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Golovina, Natalya Ya. "Modeling the Stress-Strain Curve of Elastic-Plastic Materials." Solid State Phenomena 316 (April 2021): 936–41. http://dx.doi.org/10.4028/www.scientific.net/ssp.316.936.

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The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

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Lu, Yi, Cong Cong, Chen Liwei, and Peng Wang. "Solving elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 12 (February 19, 2013): 2810–24. http://dx.doi.org/10.1177/0954406213478374.

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It has been a significant and challenging issue to determine the elastic deformation of parallel manipulators for their precision analysis and control. A new method is proposed and studied for solving the elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry. First, an original simulation mechanism of a parallel manipulator is constructed; each of the vectors in the force transformation matrix of the parallel manipulators is constructed by this simulation mechanism. The active/constrained wrench and their pose are determined based on the Newton–Euler formulation. Second, the elastic deformed dimensions of the active legs are determined based on the elastic deformation equation and the active/constrained wrench. Third, a new simulation mechanism of this parallel manipulator is constructed by replacing the original dimensions of active legs with the deformed dimensions of active legs and the elastic deformations of parallel manipulators are solved using the pose difference between the original and new simulation mechanisms. Finally, two parallel manipulators are illustrated and their elastic deformations are solved and verified by both analytic approach and finite element method.

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Keller, Joseph B. "Finite Elastic Deformation Governed by Linear Equations." Journal of Applied Mechanics 53, no. 4 (December 1, 1986): 819–20. http://dx.doi.org/10.1115/1.3171864.

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It is observed that the equations of motion governing finite elastic deformation are linear if and only if the Piola-Kirchhoff stress tensor is linear in the deformation gradient. Then the three components of displacement satisfy uncoupled linear equations. These equations are used to solve some problems of finite deformation.

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AZEGAMI, Hideyuki, Akihiro SATAKE, and Kazumi KODAMA. "Creation of Mechanism Using Linear Elastic Deformation." Proceedings of the JSME annual meeting 2000.1 (2000): 133–34. http://dx.doi.org/10.1299/jsmemecjo.2000.1.0_133.

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Silling, S. A. "Linear Elastic Materials Sustaining a Prescribed Deformation." Journal of Applied Mechanics 56, no. 2 (June 1, 1989): 479–81. http://dx.doi.org/10.1115/1.3176110.

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Lu, Yi, Zhuohong Dai, and Yang Lu. "Precise Stiffness and Elastic Deformations of Serial–Parallel Manipulators by Considering Inertial Wrench of Moving Links." Robotica 38, no. 12 (January 31, 2020): 2204–20. http://dx.doi.org/10.1017/s0263574720000041.

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SUMMARYA general serial–parallel manipulator connected in series by two different parallel manipulators with linear active legs is constructed. Its precise stiffness and elastic deformations are studied systematically. Its unified precise stiffness and precise elastic deformation models are established by considering both the moving links inertial wrench and the dynamic active/constrained wrench. A 3SPR+3RPS-type serial–parallel manipulator is illustrated for solving its precise stiffness and precise elastic deformation. The derived formulae of the precise stiffness and the precise elastic deformations of the general serial–parallel manipulator are verified by the theoretical solutions of the 3SPR+3RPS serial–parallel manipulator.

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Song, Jialin, Yang Lu, Yongli Wang, and Yi Lu. "Stiffness and Elastic Deformation of 4-DoF Parallel Manipulator with Three Asymmetrical Legs for Supporting Helicopter Rotor." Journal of Robotics 2020 (February 1, 2020): 1–11. http://dx.doi.org/10.1155/2020/8571318.

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The stiffness and elastic deformation of a 4-DoF parallel manipulator with three asymmetrical legs are studied systematically for supporting helicopter rotor. First, a 4-DoF 2SPS + RRPR type parallel manipulator with two linear SPS type legs and one RRPR type composite leg is constructed and its constraint characteristics are analyzed. Second, the formulas for solving the elastic deformation and the stiffness matrix of the above mentioned three asymmetrical legs are derived. Third, the formulas for solving the total stiffness matrix and the elastic deformation of this manipulator are derived and analyzed. Finally, its finite element model is constructed and its elastic deformations are solved using both the derived theoretical formulas and the finite element model. The theoretical solutions of the elastic deformations are verified by that of the finite element model.

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Domichev, K. "MODELING THE BEHAVIOR OF THE PHYSICAL AND GEOMETRIC NON-LINEAR FUNCTIONAL HETEROGENEOUS MATERIALS." Innovative Solution in Modern Science 1, no. 45 (February 17, 2021): 82. http://dx.doi.org/10.26886/2414-634x.1(45)2021.5.

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The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions

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Huang, Chun Ying, Man Hua Wan, and Xiao Jun Wang. "FeSiB Annealing Technology Based on Amorphous Ribbons of the Linear Expansion Coefficient." Key Engineering Materials 428-429 (January 2010): 537–39. http://dx.doi.org/10.4028/www.scientific.net/kem.428-429.537.

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The 4.5mm wide 25μm thick Fe78Si9B13 amorphous alloys were prepared by single-roller method, and it was annealed. The elastic modulus, tensile deformation and line expansion coefficient were investigated by Q800 (dynamic mechanical thermal analyses, DMA). The results showed that the elastic modulus, tensile deformation and line expansion coefficient were enhanced when annealed. Comparing with the annealed ribbons, the change rules of elastic modulus, tensile deformation and line expansion coefficient of the quenched are evident, that the elastic modulus decreases and tensile deformation increase with temperature increases, but line expansion coefficient firstly increase then decrease with temperature increases.

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Bubenchkov, A. M., M. A. Bubenchkov, T. I. Nikipelova, V. B. Tsyrenova, N. R. Shcherbakov, and A. I. Potekaev. "Asymmetric deformation of linear elastic cylindrical shape material." Letters on Materials 4, no. 1 (2014): 62–67. http://dx.doi.org/10.22226/2410-3535-2014-1-62-67.

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Schapery, R. A. "Linear Elastic and Viscoelastic Deformation Behavior of Ice." Journal of Cold Regions Engineering 11, no. 4 (December 1997): 271–90. http://dx.doi.org/10.1061/(asce)0887-381x(1997)11:4(271).

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Szatmary, Alex C., and Charles D. Eggleton. "Elastic capsule deformation in general irrotational linear flows." Fluid Dynamics Research 44, no. 5 (July 5, 2012): 055503. http://dx.doi.org/10.1088/0169-5983/44/5/055503.

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15

Chhillar, Ajay, and Rajender Singh. "An Investigation for Evaluating Distinct Test Functions for Predicting Elastic Deformations of Metal Parts Using." International Journal of Advance Research and Innovation 3, no. 3 (2015): 54–65. http://dx.doi.org/10.51976/ijari.331508.

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Elastic deformation of metal parts has been a matter of great concern for investigation of researchers in academia and research institutions all over the world. Literature reveals that earlier researchers have applied efforts for evaluating Gaussian and spline test functions only for predicting elastic deformations. However few research efforts have been reported in literature for predicting elastic deformation through modified meshless method using exponential test functions. This paper presents an investigation for evaluating distinct test function for predicting elastic deformations of metal parts using modified meshless method. In present work, a modified meshless method has been implemented with three distinct test functions namely Gaussian, Exponential and Spline both with linear and quadratic basis function. Results of investigation reveal that Gaussian test function provides accurate results followed by exponential and spline functions. Effect of choosing different geometrical parameters affecting the solution for prediction of elastic deformation in case of exponential test function has also been presented here. Moreover, the present investigation for evaluating distinct test functions for predicting elastic deformations of metal parts using modified meshless method helps to observe that computational results with higher order basis functions are almost ten times better when compared with lower order basis functions.

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Bortnowski, Piotr, Lech Gladysiewicz, Robert Krol, and Maksymilian Ozdoba. "Tests of Belt Linear Speed for Identification of Frictional Contact Phenomena." Sensors 20, no. 20 (October 14, 2020): 5816. http://dx.doi.org/10.3390/s20205816.

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In the locations where driving forces are transmitted, the changing tensile forces cause rapid elastic deformations of the belt. The deformation changes the belt speed. Measurement of the belt speed on the friction contact sections is essential to identify elastic slippage. However, the scale of the phenomenon is small, so it is necessary to use precise measuring equipment. The article presents measurements of the linear belt speed with the use of various sensors and measuring devices. A measurement error was determined for each of the presented measurement methods. The method with the highest accuracy was used to identify the elastic slippage on the drive pulley.

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Xiao, B., and J. Feng. "Higher order elastic tensors of crystal structure under non-linear deformation." Journal of Micromechanics and Molecular Physics 04, no. 04 (December 2019): 1950007. http://dx.doi.org/10.1142/s2424913019500073.

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The higher-order elastic tensors can be used to characterize the linear and non-linear mechanical properties of crystals at ultra-high pressures. Besides the widely studied second-order elastic constants, the third- and fourth-order elastic constants are sixth and eighth tensors, respectively. The independent tensor components of them are completely determined by the symmetry of the crystal. Using the relations between elastic constants and sound velocity in solid, the independent elastic constants can be measured experimentally. The anisotropy in elasticity of crystal structures is directly determined by the independent elastic constants.

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Pfeiffer, Steffen, and Martin Franz-Xaver Wagner. "Elastic deformation of twinned microstructures." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2204 (August 2017): 20170330. http://dx.doi.org/10.1098/rspa.2017.0330.

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Many crystalline materials exhibit twinned microstructures, where well-defined orientation relationships define the special symmetry between different, elastically anisotropic twin variants. When such twins are subjected to external loading, additional internal stresses necessarily occur at the twin boundaries in order to maintain compatibility. These compatibility stresses are constant inside each variant in repeating stacks of twins and considerably affect the local stress state. In this paper, we use anisotropic linear elasticity to derive general analytical solutions for compatibility stresses in a stack of twin variants in arbitrary materials, for arbitrary variant volume fractions and twin types, subjected to arbitrary applied stresses. By considering two examples, growth twins in electrodeposited Cu and B19′ martensite twins in the shape memory alloy NiTi, we further demonstrate that compatibility stresses can considerably alter the preferred slip systems for dislocation plasticity as well as the effective macroscopic behaviour of twinned microstructures.

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Nho, In-Sik, Jong-Man Kim, and Jeong-Seok Kwak. "Non-linear Large Deformation Analysis of Elastic Rubber Mount." Journal of the Society of Naval Architects of Korea 45, no. 2 (April 20, 2008): 186–91. http://dx.doi.org/10.3744/snak.2008.45.2.186.

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Bao, L., M. Takatera, and A. Shinohara. "Analysis of Large Non-linear Elastic Deformation of Fabrics." Journal of The Textile Institute 93, no. 4 (January 2002): 410–19. http://dx.doi.org/10.1080/00405000.2002.12027748.

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Li, D. S., and M. R. Wisnom. "Non-linear stress-strain behaviour of unidirectional silicon carbide fibre reinforced aluminium alloy." Journal of Strain Analysis for Engineering Design 27, no. 3 (July 1, 1992): 137–44. http://dx.doi.org/10.1243/03093247v273137.

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Longitudinal tensile tests have been conducted on unidirectional SiC fibre reinforced 6061 aluminium matrix composites in the annealed and as-manufactured conditions. The results are presented in terms of stress-strain curves and tangent modulus-strain relations, which show considerable non-linearity. Corresponding micromechanical finite element modelling is performed including the effects of the manufacturing process on the matrix in-situ properties. The analysis shows that the non-linear behaviour of the composite is caused by the elastic-plastic deformation of the matrix alloy. The matrix fully yields during the cooldown from manufacturing. Residual stress relaxation plays an important role in the stress-strain characteristics of the annealed aluminium matrix composite by introducing some initial elastic deformation. The amount of elastic deformation for the as-manufactured condition is greater because of subsequent age hardening. However, more linear elastic deformation was observed than predicted in the as-manufactured specimens, which is believed to be due to higher precipitation hardening caused by metallurgical effects induced in the manufacturing process.

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Chen, Xiao Liang, Zuan Tian, and Jian Ping Ding. "Mechanical Analysis of Three Kinds of Beams on Non-Linear Elastic Foundation Materials." Materials Science Forum 867 (August 2016): 147–51. http://dx.doi.org/10.4028/www.scientific.net/msf.867.147.

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The deformation and internal forces of beams on non-linear elastic foundation materials were studied. The reaction force between the beam and the foundation was fitted as a cubic polynomial about the deflection of beams by experimental data, and the corresponding control equations were derived by the finite difference method. MATLAB program with the Newton iteration method was used to obtain numerical results. Results of the numerical example show the deformation and internal force of short non-linear and linear elastic Winkler beams are same, but the relative errors can reach 10%-20% for moderate and long beams, so the non-linear foundation effect on the settlement of beams should be considered in engineering; the relative errors of the deformation and internal force between moderate non-linear and linear elastic Winkler beams vary with the length of beams, but keep invariant for long beams.

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Kumar, Sandeep, and David M. Parks. "On the hyperelastic softening and elastic instabilities in graphene." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140567. http://dx.doi.org/10.1098/rspa.2014.0567.

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Elastic material instabilities are precursors to failure in defect-free graphene single crystals. Elastic instabilities originate from softening in the material response (decay of tangent moduli) induced by dilatant mechanical deformation. Here, we characterize the softening in the constitutive response of graphene within the framework of hyperelasticity based on symmetry-invariants of the two-dimensional logarithmic strain tensor E (0) . The use of symmetry-invariants provides significant functional simplification in representation of the strain energy function of graphene; ab initio calculations of deformation energy are well-fit using half the number of elastic constants of previous formulations. For a set of large homogeneous deformations comprising uniaxial stretch/stress along the armchair and the zigzag directions, and equi-biaxial tension, stress values predicted by the model compare well with those directly calculated from ab initio solutions. Using acoustic tensor analysis, we show that the constitutive model accurately captures elastic stability limits for a number of biaxial deformation modes, providing results that compare well with independent phonon calculations carried out using linear response density functional perturbation theory. In the case of equi-biaxial deformation, an elastic shearing instability is identified which occurs prior to the configuration of maximum true stress. Potential implications of the present results on the interpretation of limiting deformations achieved in nanoindentation experiments are briefly noted.

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Luo, J. J., and I. M. Daniel. "Deformation of Inhomogeneous Elastic Solids With Two-Dimensional Damage." Journal of Applied Mechanics 68, no. 4 (January 1, 2001): 528–36. http://dx.doi.org/10.1115/1.1380384.

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A general correlation is derived between macroscopic stresses/strains and microscopic deformation on the damage surfaces for inhomogeneous elastic solids with two-dimensional damage. Assuming linear elastic behavior for the undamaged materials, the macroscopic deformation associated with nonlinear strains, or damage strains, is shown to be the weighted sum of the microscopic deformations on the damage surfaces. For inhomogeneous materials with periodic structures (laminated composites, for example) and various identifiable damage modes, simple relations are derived between the macroscopic deformation and microscopic damage. When the number of identifiable damage modes is less than or equal to the number of relevant measurable macroscopic strains, the correlation can be used to evaluate the damage progression from simple macroscopic stress and strain measurements. The simple case of a unidirectional fiber-reinforced composite under longitudinal load is used to show how the results can help detect and characterize the damage using macroscopic measurements, without resorting to assumptions of detailed microscopic deformation mechanisms.

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SZABÓ, DÉNES, and MIKLÓS ZRÍNYI. "NONHOMOGENEOUS, NON-LINEAR DEFORMATION OF POLYMER GELS SWOLLEN WITH MAGNETO-RHEOLOGICAL SUSPENSIONS." International Journal of Modern Physics B 16, no. 17n18 (July 20, 2002): 2616–21. http://dx.doi.org/10.1142/s0217979202012748.

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Polymer gels swollen with a magneto-rheological suspension are highly elastic materials with considerable magnetic susceptibility. In this work the magnetic field induced deformation and motion of these magnetic polymer systems is discussed. We present a continuum material model by introducing magnetic equations into non-linear elasticity theory. The material properties of these magnetic rubber-like substances are characterized with a Langevin type magnetization and a neo-Hookean strain energy function. The non-linear character of the equations that describe the material properties and the nonhomogeneity of the deformation lead to a unique deformation mechanism. In order to demonstrate the characteristics of the magnetic field induced deformations we present numerical and finite element calculations and compare them with experimental results.

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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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Li, Xiang, and Qing Xiao. "A Numerical Study on an Oscillating Water Column Wave Energy Converter with Hyper-Elastic Material." Energies 15, no. 22 (November 8, 2022): 8345. http://dx.doi.org/10.3390/en15228345.

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A model different from the traditional WEC, known as the flexible wave energy converter (fWEC), is numerically modeled in this paper. The fWEC is believed to be more efficient and has a greater range of operation when compared with the conventionally rigid WEC. A fully coupled fluid–structure interaction (FSI) tool is developed for the research performed in this paper. This tool is able to accommodate the dynamic interaction between the flexible membrane structure of the fWEC and the surrounding fluid. In this research, both linear-elastic and hyper-elastic materials are examined for their use in the fWEC. The fluid flow surrounding the fWEC is solved by a computational fluid dynamics (CFD) method. The deformation of the hyper-elastic structure within the fWEC is modeled using a finite element analysis method (FEA). Both the hyper-elastic material of the fWEC and the free surface wave contribute to the overall nonlinearity of the numerical simulation. To tackle this problem, a robust coupling scheme is implemented by an advanced coupling library. With this tool, the flexible deformations within the fWEC structure can be accurately captured. The degree of these deformations can then further be examined, allowing the overall effects on the fWEC energy output to be determined. The simulation results show that the peak deformation of the hyper-elastic material is four times that of the linear-elastic material. This suggests that the fWEC would perform better and generate greater power using the hyper-elastic material compared with the linear-elastic material. Additionally, because a wide range of wave conditions are studied, it can be concluded that unlike conventional WECs, the efficiency of energy harvesting of such an fWEC is not sensitive to certain wave periods. Such findings are supported by both the detailed flow fields captured and the structural stress–strain analysis results from this simulation.

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Recabov, Ilqar Saleh, and Mahammadali Nuraddin Nuriyev. "Evaluation of Deformation Properties of Elastic Fibres in Threads." Fibres and Textiles in Eastern Europe 29, no. 5(149) (October 31, 2021): 34–36. http://dx.doi.org/10.5604/01.3001.0014.9293.

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In the article, the change in the linear dimensions of tissues is analysed by the closure of the elastane threads in the tissue system under the influence of wet processing. It is found that standard techniques cover changes in linear dimensions only in the direction of the base and utka. However, for clothing design, it is necessary to know the change in linear dimensions in arbitrary directions. The empirical models used to calculate these dimensions do not have the required accuracy. The article proposes a model for calculating the change in linear dimensions in an arbitrary direction based on the analysis of the geometry of the fabric and describing the process of tissue shrinkage under the influence of wet processing, which allows to obtain results with sufficient accuracy.

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Imam, A., and G. C. Johnson. "Decomposition of the Deformation Gradient in Thermoelasticity." Journal of Applied Mechanics 65, no. 2 (June 1, 1998): 362–66. http://dx.doi.org/10.1115/1.2789063.

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The deformation gradient of a thermoelastic solid undergoing large deformations is decomposed into elastic and thermal components, corresponding to an intermediate configuration which is assumed to be stress-free. This decomposition is shown to be unique only to within a rigid-body motion of the intermediate configuration. An alternate decomposition is proposed in which this arbitrariness is removed. The thermoelastic theory developed on the basis of these decompositions is linearized, resulting in familiar expressions of linear thermoelasticity. The stress response function is further specialized for the particular case of isotropic linear solids.

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Wang, Ru Bin, Wei Ya Xu, and Jiu Chang Zhang. "Modeling Coupled Flow-Stress-Damage during Creep Deformation." Applied Mechanics and Materials 204-208 (October 2012): 3294–98. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.3294.

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In order to reflect the tertiary rheological characteristics of hard rocks at the high stress states, a new nonlinear visco-elastic-plastic model is proposed on the basis of linear visco-elastic-plastic model and nonlinear visco-elastic-plasticity. And then the corresponding constitutive model are deduced, which can be used for describing rocks’ long-term strength characteristics and their creep deformational behavior and time-dependent damage under interaction of coupled seepage-stress field in rock engineering. At last, considering the time effect of rock damage in the process of tertiary creep, a coupled seepage -stress creep damage model for investigating the whole creep deformation behavior, including tertiary creep failure process is established, and the related equations governing the evolution of stress, creep damage and rock permeability along with the creep deformation of rock is introduced.

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Prado, Jose Manuel. "The Elastic Behaviour of Metal Powder Compacts." Materials Science Forum 534-536 (January 2007): 325–28. http://dx.doi.org/10.4028/www.scientific.net/msf.534-536.325.

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In this work the elastic behaviour of metallic powder compacts is studied. Cylindrical specimens with different levels of density have been submitted to uniaxial compression tests with loading and unloading cycles. The analysis of the elastic loadings shows a non linear elasticity which can be mathematically represented by means of a potential law. Results are explained by assuming that the total elastic strain is the contribution of two terms one deriving from the hertzian deformation of the contacts among particles and another that takes into account the linear elastic deformation of the powder skeleton. A simple model based in a one pore unit cell is presented to support the mathematical model.

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Kubiak, Przemyslaw, Ewa Sys, Lukasz Goslawski, Maria Manko, Jacek Gralewski, Mateusz Krukowski, Ricardo Alves de Sousa, Adam Mrowicki, Tigran Soghabatyan, and Tiefang Zou. "Nonlinear method of determining the vehicle pre-crash speed based on B-spline with propabilistic weights - subcompact car class." Archives of Automotive Engineering – Archiwum Motoryzacji 85, no. 3 (September 30, 2019): 5–18. http://dx.doi.org/10.14669/am.vol85.art1.

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A new non-linear method utilizing the work W of car deformation is considered in this study. The car deformation is defined as an algebraic function of deformation ratio Cs. The method of variable correlation is exploited in order to develop experimental data. To determinate mathematical model parameters, data from the NHTSA database including frontal crash tests are used. Such database is comprised of substantial number of crash cases and main focus was put on frontal impacts. In the non-linear method used so far, the so-called energetic approach, collisions are considered non-elastic. The speed threshold defining the elastic collision was set to be 11 km/h. This simplistic approach is used to determine the linear relation of energy loss during deformation on deformation coefficient Cs. Deformation points C1-C6 are taken into account while calculating a mean value that defines this coefficient. A more accurate non-linear method as well as more complex form of deformation coefficient is suggested to determine the work of deformation in this paper. The focus of those methods is to establish the value of nonlinear coefficient b_k which is the slope factor of precrash velocity Vt and deformation ratio Cs function.

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Sivák, Peter, Peter Frankovský, Ingrid Delyová, Jozef Bocko, Ján Kostka, and Barbara Schürger. "Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading." Materials 13, no. 23 (November 24, 2020): 5323. http://dx.doi.org/10.3390/ma13235323.

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In exact analyses of bodies in the elastic–plastic regime, the behavior of the material above critical stress values plays a key role. In addition, under cyclic stress, important phenomena to be taken into account are the various types of hardening and the design of the material or structure. In this process, it is important to define several groups of characteristics. These include, for instance, the initial area of plasticity or load which defines the interface between elastic and plastic deformation area. The characteristics also include the relevant law of plastic deformation which specifies the velocity direction of plastic deformation during plastic deformation. In the hardening condition, it is also important to determine the position, size and shape of the subsequent loading area. The elasto-plastic theory was used for the analysis of special compliant mechanisms that are applied for positioning of extremely precise members of the Compact Linear Collider (CLIC), e.g., cryomagnets, laser equipment, etc. Different types of deformation hardening were used to simulate the behavior of particular structural elements in the elastic–plastic regime. Obtained values of stresses and deformations may be used in further practical applications or as default values in other strain hardening model simulations.

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Simpson, B. "Anisotropic linear elastic materials subject to undrained plane strain deformation." Géotechnique 67, no. 8 (August 2017): 728–32. http://dx.doi.org/10.1680/jgeot.16.p.057.

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Bjo¨rklund, S. "A Random Model for Micro-Slip Between Nominally Flat Surfaces." Journal of Tribology 119, no. 4 (October 1, 1997): 726–32. http://dx.doi.org/10.1115/1.2833877.

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A random surface model has been developed for the deformations of contacting surfaces subjected to both normal and tangential load. The model is restricted to nominally flat (rough) elastic surfaces in contact with perfectly flat (smooth) elastic surfaces. The deformations of the asperities are assumed to be independent of each other and the heights of the asperities are assumed to be randomly distributed. Depending on the height of an asperity, it will either slip or stick. The relation between tangential deformation and load will consequently be non-linear and this effect is often named micro-slip. Results are presented for two types of deformation laws for the individual asperities, with three different asperity height distributions. The results show typical micro-slip behaviour, independent of both the individual asperity deformation and the type of asperity height distribution. The influence of the standard deviation of asperity heights is strong and is an important factor when determining the micro-slip of nominally flat surfaces in contact.

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Mihai, L. Angela, and Alain Goriely. "How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2207 (November 2017): 20170607. http://dx.doi.org/10.1098/rspa.2017.0607.

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The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.

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Flores, Fernando G. "A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis." Journal of Applied Mechanics 73, no. 6 (December 19, 2005): 970–76. http://dx.doi.org/10.1115/1.2173674.

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An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

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Schmidt, R., and J. N. Reddy. "A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells." Journal of Applied Mechanics 55, no. 3 (September 1, 1988): 611–17. http://dx.doi.org/10.1115/1.3125837.

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A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Ka´rma´n type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

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HOANG, VIET HA. "Stress–elastic strain relation for a two-phase isotropic strain gradient plastic composite." European Journal of Applied Mathematics 20, no. 4 (August 2009): 319–42. http://dx.doi.org/10.1017/s0956792509007815.

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The stress–elastic strain relationship is studied for a composite under a plastic deformation. The constitutive law of each component is described by a deformation theory of strain gradient plasticity which introduces an internal length scale. The conventional deformation plastic theory is obtained when the internal length scale tends to 0. The Hashin–Shtrikman upper bound for a two-phase composite governed by a power law is derived. It is predicted, by differentiating the bounds, that in most cases, the stress and the elastic strain follow a non-linear relation immediately after the elastic range. However, for some particular values of the ratio of the internal length scale and the micro-scale of the composite, this relation is linear. The prediction is illustrated by various numerical examples.

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Balbi, Valentina, Tom Shearer, and William J. Parnell. "A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2217 (September 2018): 20180231. http://dx.doi.org/10.1098/rspa.2018.0231.

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The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

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KOENEMANN, FALK H. "LINEAR ELASTICITY AND POTENTIAL THEORY: A COMMENT ON GURTIN (1972)." International Journal of Modern Physics B 22, no. 28 (November 10, 2008): 5035–39. http://dx.doi.org/10.1142/s0217979208049224.

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In an exhaustive presentation of the linear theory of elasticity by Gurtin [The Linear Theory of Elasticity (Springer-Verlag, 1972)], the author included a chapter on the relation of the theory of elasticity to the theory of potentials. Potential theory distinguishes two fundamental physical categories: divergence-free and divergence-involving problems. From the criteria given in the source quoted by the author, it is evident that elastic deformation of solids falls into the latter category. It is documented in this short note that the author presented volume-constant elastic deformation as a divergence-free physical process, systematically ignoring all the information that was available to him that this is not so.

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Kim, Chun Il, and Zhe Liu. "Mechanics of Lipid Membranes under the Influence of Intramembrane Viscosity." Mathematical Problems in Engineering 2019 (April 7, 2019): 1–13. http://dx.doi.org/10.1155/2019/3412129.

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We discuss a continuum-based model describing the deformations of lipid membranes subjected to intramembrane viscosity. Within the frame work of the theory of an elastic surface, the membrane equilibrium equations and the expressions of viscous stress are obtained. The corresponding deformation energy of the membrane is computed via the first and second fundamental form of surface. A compatible linear model is also formulated within the prescription of superposed incremental deformations through which the deformation profiles of the membrane is obtained. It is shown that the intramembrane viscous flow gives rise to straining effects on the membranes. Further, the corresponding dynamic edge conditions reduce to purely elastic boundary conditions in the limit of vanishing viscous effects. Lastly, admissible sets of velocity fields are also examined and are used to formulate membrane shape equations and the associated dynamic boundary conditions.

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Микенина, Ольга Александровна, and Александр Филиппович Ревуженко. "Linear elasticity theory free from diffeomorphism: plane deformation." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 162–67. http://dx.doi.org/10.37972/chgpu.2020.60.58.016.

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Строится плоская модель линейно упругого тела, в которой постулат о диффеоморфизме (предположение о гладкости поля перемещений) значительно ослаблен. Вместо одного поля перемещений, которое фигурирует в классической модели, вводятся два гладких поля перемещений. Рассмотрены постановки краевых задач, доказана теорема единственности. The authors create a two-dimensional model of a linearly elastic body at considerably weakened postulate of diffeomorphism-supposed smoothness of field of displacements. One field of displacements as in the classical model is replaced by two smooth fields of displacements. The authors discuss formulations of boundary value problem and prove the unicity theorem

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44

Микенина, Ольга Александровна, and Александр Филиппович Ревуженко. "Linear elasticity theory free from diffeomorphism: plane deformation." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 162–67. http://dx.doi.org/10.37972/chgpu.2020.60.58.016.

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Строится плоская модель линейно упругого тела, в которой постулат о диффеоморфизме (предположение о гладкости поля перемещений) значительно ослаблен. Вместо одного поля перемещений, которое фигурирует в классической модели, вводятся два гладких поля перемещений. Рассмотрены постановки краевых задач, доказана теорема единственности. The authors create a two-dimensional model of a linearly elastic body at considerably weakened postulate of diffeomorphism-supposed smoothness of field of displacements. One field of displacements as in the classical model is replaced by two smooth fields of displacements. The authors discuss formulations of boundary value problem and prove the unicity theorem

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45

Balymov, K. G., E. V. Kudyukov, N. A. Kulesh, V. N. Lepalovskij, and V. O. Vas’kovskiy. "Elastomagnetoresistive Properties of Films of 3d-Metalls Alloys." KnE Materials Science 1, no. 1 (October 12, 2016): 11. http://dx.doi.org/10.18502/kms.v1i1.555.

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Magnetoresistive properties of 3d-metals alloys magnetostrictive films under application of elastic deformations were investigated. Linear stress was shown to have a significant effect on magnetoresistive effect in the films through the rotation of the easy magnetization axis. Dependencies of the relative change of resistivity were obtained in a cyclic deformation regime for films of different compositions.

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Starovoitov, Eduard I., and Alina V. Nesterovich. "The non-axisymmetric loading of an elastoplastic three-layer plate in its plane." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (August 1, 2022): 57–69. http://dx.doi.org/10.33581/2520-6508-2022-2-57-69.

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The statement of the boundary value problem on the deformation of a circular three-layer plate in its plane under the action of a non-axisymmetric load is herein presented. The materials of thin carrier layers obey the hypotheses of the theory of small elastoplastic deformations. The relatively thick filler is physically non-linearly elastic. A system of non-linear differential equilibrium equations in partial derivatives is obtained. A general technique for solving the problem in displacements based on the Fourier method and Ilyushin’s method of elastic solutions is proposed. The case of an external cosine load is considered. An iterative solution of a boundary value problem for a physically non-linear plate is obtained. The corresponding solution of the elastic problem is written out in the final form. The obtained solution is numerically tested.

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Recrosi, Filippo, Rodolfo Repetto, Amabile Tatone, and Giovanna Guidoboni. "Thermodynamic derivation of a non-linear poroelastic model describing hemodynamicsmechanics interplay in the lamina cribrosa." Modeling and Artificial Intelligence in Ophthalmology 2, no. 2 (June 18, 2018): 80–85. http://dx.doi.org/10.35119/maio.v2i2.78.

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In this paper we formulate a poroelastic model starting from a model of species diffusion in an elastic material. The model is applied to study the mechanics of the lamina cribrosa (LC) in the eye. The LC is a porous tissue at the head of the optic nerve. Deformation of this tissue and impairment of blood flow induced by tissue deformation are considered to be related to the pathogenesis of glaucoma.The governing equations are derived from general thermomechanical principles. We carefully revise the role of the energy-stress Eshelby tensor, mutuated from the framework of tissue growth, in describing the hemo-mechanical behaviour of the tissue.The model accounts for non-linear deformations of the solid matrix and deformation-induced changes in porosity and permeability. The model provides a qualitative better undertanding of the phatophysiology and pathogenesis of glaucoma in terms of coupling between tissue deformation and the resulting impaired hemodynamics inside the LC.

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Iwatsubo, T., and B. S. Yang. "The Effects of Elastic Deformation on Seal Dynamics." Journal of Vibration and Acoustics 110, no. 1 (January 1, 1988): 59–64. http://dx.doi.org/10.1115/1.3269481.

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The dynamic characteristics and stability of the annular pressure seal employed in pumps have been theoretically deduced with consideration of the effects of elastic deformation due to the high pressure difference. Turbulent flow is assumed in both circumferential and axial direction, and the deformation of the seal and the shaft is governed by the linear theory of elasticity. The results derived herein considering the elastic deformation are compared with the previously published author’s results [3] in the stiffness, damping, and add mass coefficients.

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Bakushev, S. V. "LINEAR THEORY OF ELASTICITY WITH QUADRATIC SUMMAND." STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS 303, no. 4 (February 28, 2022): 29–36. http://dx.doi.org/10.37538/0039-2383.2022.1.29.36.

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We suggest a linear theory version based on Taylor decompositions for stresses and power-series for quadratic summand deformations. Thus, static equations of equilibrium in stresses are written in the form of the second-order partial derivatives differential equations. The resolving equations of equilibrium in displacements are represented in the form of the third order partial derivatives differential equations. The physical equations in this version of the linear theory of elasticity are written in the same way as in the classical linear theory of elasticity. Equilibrium equations, along with other parameters – physical constants of the medium – contain minor parameters dx, dy, dz, the value of which, as shown by numerical modelling, has little effect on the nature of the stress-strain state. It is suggested to use experimental data to determine them. Along with the formulating of the basic equations of the three-dimensional theory of elasticity, particular cases of the stress-strain state of elastic continuous medium are considered: uniaxial stressed state; uniaxial deformed state; flat deformation; generalized plane stress state. Determination of the stressed and deformed state of a thin elastic bar by integrating the resolving equations in stresses and displacements is considered as examples. The suggested version of the linear theory of elasticity, due to the quadratic summand in Taylor decompositions for stresses and in power-series for deformations, expands the classical linear theory of elasticity and, with an appropriate experimental justification, can lead to new qualitative effects in the calculation of elastic deformable bodies.

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El Ghoche, Hayssam. "Linearization of a Viscoelastic Model for Light-Weight Embankment." Advanced Materials Research 324 (August 2011): 368–71. http://dx.doi.org/10.4028/www.scientific.net/amr.324.368.

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A new process of light-weight embankment by using parallelepipedal blocks which made up of plastic films in order to obtain a density of 0.4, 0.5 or 0.6. The experimental and theoretical studies of this material enabled us to elaborate a nonlinear viscoelastic model. It shows clearly the real behavior, but it needs the identification of a great number of parameters. The purpose of this paper is to simplify the model by linearzing it. This linearization was carried out for a specific density (0.6) in two ways: - Adoption of linear forms of the elastic and delayed deformations according to the stress. - Adoption of a linear form of the elastic deformation and a constant delayed one (linear viscoelasticity). The comparison between experience and theory shows that the linear model describes the reality in a field of stresses which can reach 200 kPa.

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Journal articles on the topic 'Linear elastic deformation'

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