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1
Vena, P. "A Computational Model of Viscoelastic Composite Materials for Ligament or Tendon Prostheses." Advanced Composites Letters 9, no. 3 (May 2000): 096369350000900. http://dx.doi.org/10.1177/096369350000900302.
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A constitutive model and a finite element formulation for viscoelastic anisotropic materials subject to finite strains is expounded in this paper. The composite material is conceived as a matrix reinforced with stiff fibres. The constitutive relations are obtained by defining a strain energy function and a relaxation function for each constituent. By means of this approach, the viscoelastic properties of the material constituents can be taken into account and therefore different time dependent behaviour can be assigned to the matrix and to the reinforcing fibres. The response provided by this kind of constitutive formulation allows for the description of mechanical behaviour for either natural anisotropic tissues (such as tendons and ligaments) and for the composite materials which are currently adopted for tissue reconstruction. The main features of those mechanical properties observed in an ideal uniaxial test are: a non linear stress-strain response and a time dependent response which is observed in relaxation of stresses for a prescribed constant stretch and in a moderate strain rate dependence of the measured response.
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WANG, Y., Y. L. HE, T. S. ZHAO, G. H. TANG, and W. Q. TAO. "IMPLICIT-EXPLICIT FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD FOR COMPRESSIBLE FLOWS." International Journal of Modern Physics C 18, no. 12 (December 2007): 1961–83. http://dx.doi.org/10.1142/s0129183107011868.
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We propose an implicit-explicit finite-difference lattice Boltzmann method for compressible flows in this work. The implicit-explicit Runge–Kutta scheme, which solves the relaxation term of the discrete velocity Boltzmann equation implicitly and other terms explicitly, is adopted for the time discretization. Owing to the characteristic of the collision invariants in the lattice Boltzmann method, the implicitness can be completely eliminated, and thus no iteration is needed in practice. In this fashion, problems (no matter stiff or not) can be integrated quickly with large Courant–Friedriche–Lewy numbers. As a result, with our implicit-explicit finite-difference scheme the computational convergence rate can be significantly improved compared with previous finite-difference and standard lattice Boltzmann methods. Numerical simulations of the Riemann problem, Taylor vortex flow, Couette flow, and oscillatory compressible flows with shock waves show that our implicit-explicit finite-difference lattice Boltzmann method is accurate and efficient. In addition, it is demonstrated that with the proposed scheme non-uniform meshes can also be implemented with ease.
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Boscarino, S., G. Russo, and M. Semplice. "High order finite volume schemes for balance laws with stiff relaxation." Computers & Fluids 169 (June 2018): 155–68. http://dx.doi.org/10.1016/j.compfluid.2017.10.009.
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Abreu, Eduardo, Abel Bustos, and Wanderson Lambert. "A unsplitting finite volume method for models with stiff relaxation source terms." Bulletin of the Brazilian Mathematical Society, New Series 47, no. 1 (March 2016): 5–20. http://dx.doi.org/10.1007/s00574-016-0118-1.
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Boscheri, Walter, and Raphaël Loubère. "High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms." Communications in Computational Physics 21, no. 1 (December 5, 2016): 271–312. http://dx.doi.org/10.4208/cicp.oa-2015-0024.
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AbstractIn this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms. This scheme is constructed with a single stencil polynomial reconstruction operator, a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources, a nodal solver with relaxation to determine the mesh motion, a path-conservative integration technique for the treatment of non-conservative products and ana posterioristabilization procedure derived from the so-called Multidimensional Optimal Order Detection (MOOD) paradigm. In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff. The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study. Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D. The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.
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Nshimiyimana, J. D., F. Plumier, C. Ndagije, J. Gyselinck, and C. Geuzain. "High Order Relaxation Methods for Co-simulation of Finite Element and Circuit Solvers." Advanced Electromagnetics 9, no. 1 (March 20, 2020): 49–58. http://dx.doi.org/10.7716/aem.v9i1.1245.
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Coupled problems result in very stiff problems whose char- acteristic parameters differ with several orders in magni- tude. For such complex problems, solving them monolithi- cally becomes prohibitive. Since nowadays there are op- timized solvers for particular problems, solving uncoupled problems becomes easy since each can be solved indepen- dently with its dedicated optimized tools. Therefore the co-simulation of the sub-problems solvers is encouraged. The design of the transmission coupling conditions between solvers plays a fundamental role. The current paper ap- plies the waveform relaxation methods for co-simulation of the finite element and circuit solvers by also investigating the contribution of higher order integration methods. The method is illustrated on a coupled finite element inductor and a boost converter and focuses on the comparison of the transmission coupling conditions based on the waveform iteration numbers between the two sub-solvers. We demon- strate that for lightly coupled systems the dynamic iterations between the sub-solvers depends much on the inter- nal integrators in individual sub-solvers whereas for tightly coupled systems it depends also to the kind of transmission coupling conditions.
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Busto, Saray, Michael Dumbser, and Laura Río-Martín. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows." Mathematics 9, no. 22 (November 21, 2021): 2972. http://dx.doi.org/10.3390/math9222972.
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This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.
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Saxena, Nishank, and Gary Mavko. "Effects of fluid-shear resistance and squirt flow on velocity dispersion in rocks." GEOPHYSICS 80, no. 2 (March 1, 2015): D99—D110. http://dx.doi.org/10.1190/geo2014-0304.1.
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Laboratory measurements of rocks saturated with high-viscosity fluids (such as heavy-oil, bitumen, magma, kerogen, etc.) often exhibit considerable seismic velocity dispersion, which is usually underestimated by the Biot theory. Over the years, grain-scale dispersion mechanisms such as squirt (local-flow) and shear relaxation (nonzero shear stress in the pore fluid) have been more successful in explaining the measured dispersion. We developed a new method to quantify the combined high-frequency effects of squirt and shear dispersion on the effective moduli of rocks saturated with viscous fluids. Viscous fluid at high frequencies was idealized as an elastic solid of finite shear modulus, hydraulically locked in stiff and soft pores. This method entailed performing solid substitution in stiff pores of a dry rock frame, which itself was unrelaxed due to solid-filled soft pores. The unrelaxed frame stiffness solutions required information on the pressure dependency of the rock stiffness and porosity. This method did not have any adjustable parameters, and all required inputs can be directly measured. With various laboratory and numerical examples, we noted that accounting for combined effects of squirt and shear relaxation was necessary to explain laboratory-measured velocities of rocks saturated with fluids of high viscosity. Predictions of the new method were in good agreement with the laboratory data.
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Mendonça da Silveira, Francisco Eugenio. "TEARING MODES GROWTH RATE AMPLIFICATION DUE TO FINITE CURRENT RELAXATION." Acta Polytechnica 57, no. 1 (February 28, 2017): 32–37. http://dx.doi.org/10.14311/ap.2017.57.0032.
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In this work, we explore the influence of perturbative wavelengths, shorter than those usually considered, on the growth rate γ of the tearing modes. Thus, we adopt an extended form of Ohm’s law, which includes a finite relaxation time for the current density, due to inertial effects of charged species. In the long wavelength limit, we observe the standard γ of the tearing modes. However, in the short wavelength limit, we show that γ does not depend on the fluid resistivity any longer. Actually, we find out that γ now scales with the electron number density n<sub>e</sub> as γ ~ n<sub>e</sub><sup>−3/2</sup>. Therefore, through a suitable combination of both limiting results, we show that the standard γ can be substantially amplificated, even by moderate shortenings of perturbative wavelengths. Further developments of our theory may contribute to the explanation of the fast magnetic reconnection of field lines, as observed in astrophysical plasmas.
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Condat, C. A. "Solution to the Glarum model with a finite relaxation rate." Zeitschrift f�r Physik B Condensed Matter 77, no. 2 (June 1989): 313–20. http://dx.doi.org/10.1007/bf01313675.
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Suh, Jun-Kyo, and Robert L. Spilker. "Indentation Analysis of Biphasic Articular Cartilage: Nonlinear Phenomena Under Finite Deformation." Journal of Biomechanical Engineering 116, no. 1 (February 1, 1994): 1–9. http://dx.doi.org/10.1115/1.2895700.
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The nonlinear indentation response of hydrated articular cartilage at phsiologically relevant rates of mechanical loading is studied using a two-phase continuum model of the tissue based on the theory of mixtures under finite deformation. The matrix equations corresponding to the governing mixture equations for this nonlinear problem are derived using a total Lagrangian penalty finite element method, and solved using a predictor-corrector iteration within a modified Newton-Raphson scheme. The stress relaxation indentation problem is examined using either a porous (free draining) indenter or solid (impermeable) indenter under fast and slow compression rates. The creep indentation problem is studied using a porous indenter. We examine the finite deformation response and compare with the response obtained using the linear infinitesimal response. Differences between the finite deformation response and the linear response are shown to be significant when the compression rate is fast or when the indenter is impermeable. The finite deformation model has a larger ratio of peak-to-equilibrium reaction force, and higher relaxation rate than the linear model during the early relaxation period, but a similar relaxation time. The finite deformation model predicts a slower creep rate than the linear model, as well as a smaller equilibrium creep displacement. The pressure distribution below the indenter, particularly near the loaded surface is also larger with the finite deformation model.
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Zaporozhets, T. V., and Andriy Gusak. "Role of Finite Vacancy Relaxation Rate at SHS Reactions in Nanosized Multilayers." Defect and Diffusion Forum 309-310 (March 2011): 215–22. http://dx.doi.org/10.4028/www.scientific.net/ddf.309-310.215.
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Rate of SHS (self-propagating high-tеmperature synthesis) reactions in solid nano-sized multilayers is controlled by the time and temperature dependent vacancy concentration. The increase of reaction temperature is typically faster than the rate of vacancy generation. Therefore, the finite relaxation rate of vacancies leads to drastic slowing down of SHS. On the other hand, as-prepared vacancy supersaturation due to fast deposition on the cold substrate may lead to a certain acceleration of SHS. Influence of (1) vacancy mean free path and (2) initial vacancy supersaturation on the SHS rate is investigated numerically. In wide region of parameters the front velocity appears to be inversely proportional to the square root of vacancy mean free path length.
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Flory, A., and G. B. McKenna. "Finite Step Rate Corrections in Stress Relaxation Experiments: A Comparison of Two Methods." Mechanics of Time-Dependent Materials 8, no. 1 (March 2004): 17–37. http://dx.doi.org/10.1023/b:mtdm.0000027681.86865.4a.
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SAPOVAL, B., S. RUSS, J. P. KORB, and D. PETIT. "NUCLEAR RELAXATION IN IRREGULAR OR FRACTAL PORES." Fractals 04, no. 03 (September 1996): 305. http://dx.doi.org/10.1142/s0218348x96000418.
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We apply a fractal description of pore surface irregularity to study the nuclear relaxation of a liquid confined in an irregular pore. Our calculation on a pre-fractal volume with infinite surface relaxation rate shows that the long time relaxation behavior is dominated by an exponential mode characterizing a free diffusive volume. At short time, the calculated magnetization follows closely the power-law behavior previously proposed by de Gennes. For finite surface relaxation rate, we extend our studies of the efficiency of exchange on fractal membranes to nuclear relaxation in the same geometry. We predict a decay involving two characteristic times. For very slow surface relaxation, there will exist exponential relaxation governed by the surface relaxation. These laws show that the pore surface irregularities may play an important role in nuclear relaxation.
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SAPOVAL, B., S. RUSS, J. P. KORB, and D. PETIT. "NUCLEAR RELAXATION IN IRREGULAR OR FRACTAL PORES." Fractals 04, no. 04 (December 1996): 453–62. http://dx.doi.org/10.1142/s0218348x9600056x.
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We apply a fractal description of pore surface irregularity to study the nuclear relaxation of a liquid confined in an irregular pore. Our calculation on a pre-fractal volume with infinite surface relaxation rate shows that the long time relaxation behavior is dominated by an exponential mode characterizing a free diffusive volume. At short time, the calculated magnetization follows closely the power-law behavior previously proposed by de Gennes. For finite surface relaxation rate, we extend our studies of the efficiency of exchange on fractal membranes to nuclear relaxation in the same geometry. We predict a decay involving two characteristic times. For very slow surface relaxation, there will exist exponential relaxation governed by the surface relaxation. These laws show that the pore surface irregularities may play an important role in nuclear relaxation.
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YUE, HONGZHI, JIANXIN DENG, JUN ZHOU, YAN LI, FUQIAN CHEN, and LIHONG LI. "BIOMECHANICS OF PORCINE BRAIN TISSUE UNDER FINITE COMPRESSION." Journal of Mechanics in Medicine and Biology 17, no. 01 (February 2017): 1750001. http://dx.doi.org/10.1142/s0219519417500014.
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While the developments in finite element method have made it possible to simulate the complex problems in biomechanics, building an accurate constitutive model of living tissues is a major factor in getting reliable finite element analysis (FEA) results. In this study, a set of experiments were performed to test the properties of porcine brain tissue under unconfined uniaxial compression with 20[Formula: see text]s hold time at varied strain levels (10–50%) and strain rates (0.1–1[Formula: see text]s[Formula: see text]). A novel method was developed to build a quasi-linear viscoelasticity (QLV) model. The elastic function and the relaxation function were calculated separately. An Odgen model was adopted to characterize the elastic behavior, while the relaxation response was modeled at six decay rates. A standard to choose the visco parameters was discussed and carried out. The disparity of parameter values in previous models was discussed and explained. It is suggested that this model should be used in the tested loading conditions (relaxation time, strain rate, strain levels).
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Bersten, A. D., D. R. G. Williams, and G. D. Phillips. "Central Venous Catheter Stiffness and its Relation to Vascular Perforation." Anaesthesia and Intensive Care 16, no. 3 (August 1988): 342–51. http://dx.doi.org/10.1177/0310057x8801600317.
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Delayed central venous perforation is an uncommon but serious complication of central venous catheter insertion. An increase in catheter stiffness may have been responsible for our association of venous perforation with use of a guidewire insertion technique. A bench model was used to investigate the stiffness characteristics of thirty-four different types of catheters. The initial stiffness is poorly described by material or catheter gauge. A large range of values is seen between apparently similar catheters — the 16 gauge polyethylene catheter associated with two perforations at our institution had an initial stiffness value 7.5 Nm 2 X 10 -5 at 37°C in comparison with our previous standard—the 16 gauge Deseret Intracath with an initial stiffness of 2 Nm2 X 10 -5. Multilumen catheters had a similar range of stiffness to single lumen catheters, while paediatric catheters in general were less stiff. Dialysis catheters were up to five times as stiff as the stiffest central venous catheter. Stiffness decayed at a rate and to an extent which differed from catheter to catheter. Absorption of water by the catheter appears to be one factor involved in stress relaxation.
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Choi, Han-Yong. "Finite bandwidth effects on the transition temperature and NMR relaxation rate of impure superconductors." Physical Review B 53, no. 13 (April 1, 1996): 8591–98. http://dx.doi.org/10.1103/physrevb.53.8591.
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Candler, Graham V. "Rate Effects in Hypersonic Flows." Annual Review of Fluid Mechanics 51, no. 1 (January 5, 2019): 379–402. http://dx.doi.org/10.1146/annurev-fluid-010518-040258.
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Hypersonic flows are energetic and result in regions of high temperature, causing internal energy excitation, chemical reactions, ionization, and gas-surface interactions. At typical flight conditions, the rates of these processes are often similar to the rate of fluid motion. Thus, the gas state is out of local thermodynamic equilibrium and must be described by conservation equations for the internal energy and chemical state. Examples illustrate how competition between rates in hypersonic flows can affect aerodynamic performance, convective heating, boundary layer transition, and ablation. The conservation equations are outlined, and the most widely used models for internal energy relaxation, reaction rates, and transport properties are reviewed. Gas-surface boundary conditions are described, including finite-rate catalysis and slip effects. Recent progress in the use of first-principles calculations to understand and quantify critical gas-phase reactions is discussed. An advanced finite-rate carbon ablation model is introduced and is used to illustrate the role of rate processes at hypersonic conditions.
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Biasiori-Poulanges, L., and K. Schmidmayer. "A phenomenological analysis of droplet shock-induced cavitation using a multiphase modeling approach." Physics of Fluids 35, no. 1 (January 2023): 013312. http://dx.doi.org/10.1063/5.0127105.
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Investigations of shock-induced cavitation within a droplet are highly challenged by the multiphase nature of the mechanisms involved. Within the context of heterogeneous nucleation, we introduce a thermodynamically well-posed multiphase numerical model accounting for phase compression and expansion, which relies on a finite pressure-relaxation rate formulation. We simulate (i) the spherical collapse of a bubble in a free field, (ii) the interaction of a cylindrical water droplet with a planar shock wave, and (iii) the high-speed impact of a gelatin droplet onto a solid surface. The determination of the finite pressure-relaxation rate is done by comparing the numerical results with the Keller–Miksis model, and the corresponding experiments of Sembian et al. and Field et al., respectively. For the latter two, the pressure-relaxation rate is found to be [Formula: see text] and [Formula: see text], respectively. Upon the validation of the determined pressure-relaxation rate, we run parametric simulations to elucidate the critical Mach number from which cavitation is likely to occur. Complementing simulations with a geometrical acoustic model, we provide a phenomenological description of the shock-induced cavitation within a droplet, as well as a discussion on the bubble-cloud growth effect on the droplet flow field. The usual prediction of the bubble cloud center, given in the literature, is eventually modified to account for the expansion wave magnitude.
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Peddireddy, Karthik R., Ryan Clairmont, and Rae M. Robertson-Anderson. "Polymer threadings and rigidity dictate the viscoelasticity of entangled ring-linear blends and their composites with rigid rod microtubules." Journal of Rheology 67, no. 1 (January 2023): 125–38. http://dx.doi.org/10.1122/8.0000529.
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Mixtures of polymers of varying topologies and stiffnesses display complex emergent rheological properties that often cannot be predicted from their single-component counterparts. For example, entangled blends of ring and linear polymers have been shown to exhibit enhanced shear thinning and viscosity, as well as prolonged relaxation timescales, compared to pure solutions of rings or linear chains. These emergent properties arise in part from the synergistic threading of rings by linear polymers. Topology has also been shown to play an important role in composites of flexible (e.g., DNA) and stiff (e.g., microtubules) polymers, whereby rings promote mixing while linear polymers induce demixing and flocculation of stiff polymers, with these topology-dependent interactions giving rise to highly distinct rheological signatures. To shed light on these intriguing phenomena, we use optical tweezers microrheology to measure the linear and nonlinear rheological properties of entangled ring-linear DNA blends and their composites with rigid microtubules. We show that linear viscoelasticity is primarily dictated by microtubules at lower frequencies, but their contributions become frozen out at frequencies above the DNA entanglement rate. In the nonlinear regime, we reveal that mechanical response features, such as shear thinning and stress softening, are mediated by entropic stretching, threading, and flow alignment of entangled DNA, as well as forced dethreading, disentanglement, and clustering. The contributions of each of these mechanisms depend on the strain rate as well as the entanglement density and stiffness of the polymers, leading to nonmonotonic rate dependences of mechanical properties that are most pronounced for highly concentrated ring-linear blends rather than DNA-microtubule composites.
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Zhang, Lihong, Tianyun Liu, and Qingbin Li. "A Robust and Efficient Composite Time Integration Algorithm for Nonlinear Structural Dynamic Analysis." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/907023.
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This paper presents a new robust and efficient time integration algorithm suitable for various complex nonlinear structural dynamic finite element problems. Based on the idea of composition, the three-point backward difference formula and a generalized central difference formula are combined to constitute the implicit algorithm. Theoretical analysis indicates that the composite algorithm is a single-solver algorithm with satisfactory accuracy, unconditional stability, and second-order convergence rate. Moreover, without any additional parameters, the composite algorithm maintains a symmetric effective stiffness matrix and the computational cost is the same as that of the trapezoidal rule. And more merits of the proposed algorithm are revealed through several representative finite element examples by comparing with analytical solutions or solutions provided by other numerical techniques. Results show that not only the linear stiff problem but also the nonlinear problems involving nonlinearities of geometry, contact, and material can be solved efficiently and successfully by this composite algorithm. Thus the prospect of its implementation in existing finite element codes can be foreseen.
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Roeleveld, K., R. V. Baratta, M. Solomonow, A. G. van Soest, and P. A. Huijing. "Role of tendon properties on the dynamic performance of different isometric muscles." Journal of Applied Physiology 74, no. 3 (March 1, 1993): 1348–55. http://dx.doi.org/10.1152/jappl.1993.74.3.1348.
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The effect of the tendon's viscoelastic stiffness on the dynamic performance of muscles with different architecture was determined using the cat's medial gastrocnemius and extensor digitorum longus. Dynamic response models were derived under sinusoidal contraction-relaxation in the range of 0.4 (556.0 Hz and between 20 and 80% of the muscles' maximal isometric tension, manipulated by orderly recruitment-derecruitment of motor units together with firing rate increase-decrease. It was shown that, for isometric contractions at the muscle's optimum length, the dynamic response of the muscles was not significantly different before and after dissection of the tendon. Therefore the conclusion that under these conditions the tendon acts like a stiff force transmitter without significantly modifying the muscle's performance was confirmed and extended to muscles with different architecture.
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Shen, Wenfei, Chi Zhang, Liwen Zhang, Yang Yang, and Zhi Zhu. "Stress Relaxation Behaviour and Creep Constitutive Equations of SA302Gr.C Low-Alloy Steel." High Temperature Materials and Processes 37, no. 9-10 (October 25, 2018): 857–62. http://dx.doi.org/10.1515/htmp-2017-0090.
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AbstractIn order to study the stress relaxation behaviour of SA302Gr.C low-alloy steel, the stress relaxation experiments were performed at the temperatures of 400, 500 and 620 °C with the constant strain of 0.5 %. Based on the experimental stress relaxation curves, the relationship between creep strain rate and stress were derived and the creep strain rate–stress curves at different temperatures were obtained. Then, the creep constitutive equations at different conditions were developed and the constants in the equations were determined. In order to verify the developed creep constitutive equations, the finite-element (FE) model of stress relaxation of SA302Gr.C low-alloy steel was established with the FE software MSC.Marc. The comparison results show that the simulated stress relaxation curves agree with the experimental ones, which illustrates that the developed creep constitutive equations are appropriate for the tested steel.
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Tzou, D. Y. "Thermal Control in Solids With Rapid Relaxation." Journal of Dynamic Systems, Measurement, and Control 125, no. 4 (December 1, 2003): 563–68. http://dx.doi.org/10.1115/1.1636196.
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Feedback control of temperature in solids with a finite speed of heat propagation is investigated in this work. The emphases are placed on the effect of rapid thermal relaxation in high-rate heating and the possible delay during the short-time operations. Fundamental characteristics and dominating parameters are identified for effective feedback control in proportional heating. Transient instability, including the intrinsic transition from the desirable stability, neutral stability, to the ultimate unstable response are investigated in a wide spectrum of heating rates. Delayed heating is found to have a destabilizing effect during the short-time transient.
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Nemat-Nasser, Sia, and Luqun Ni. "Effective constitutive algorithms in elastoplasticity and elastoviscoplasticity." European Journal of Applied Mathematics 5, no. 3 (September 1994): 313–35. http://dx.doi.org/10.1017/s0956792500001480.
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The basic constitutive relations for elastoplasticity and elastoviscoplasticity are shown to form a typical boundary layer-type stiff system of ordinary differential equations. Three numerical algorithms are discussed: (i) The singular perturbation method (O'Malley, 1971a, b; Hoppensteadt, 1971; Miranker, 1981; Smith, 1985), which yields accurate results for both the rate-independent and rate-dependent cases, where in the former case, the algorithm is explicit, whereas in the latter case, it is implicit and requires the solution of a nonlinear equation; therefore it is impractical as a constitutive algorithm for large-scale finite-element applications, where the constitutive algorithm is used a great number of times at each finite-element node. (ii) The new constitutive algorithm (Nemat-Nasser, 1991; Nemat-Nasser & Chung, 1989, 1992) which is explicit and accurate for both the rate-independent and rate-dependent cases; the underlying mathematical feature of this new method is investigated, and it is shown that it can be classified as a simplified perturbation method; computable error bounds for this algorithm are obtained, and when the flow rule is given by the commonly used power law, it is shown that the errors are very small, (iii) A modified outer-solution method, which combines the above two techniques, and is simple, explicit, and accurate.
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Giona, Massimiliano, Andrea Cairoli, Davide Cocco, and Rainer Klages. "Spectral Properties of Stochastic Processes Possessing Finite Propagation Velocity." Entropy 24, no. 2 (January 28, 2022): 201. http://dx.doi.org/10.3390/e24020201.
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This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson–Kac processes and Lévy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower boundedness of the real part of the eigenvalue spectrum that corresponds to an upper limit of the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We also analyze Generalized Poisson–Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there is a critical value for the wave vector, above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case, and in fact, it represents a simple and clear example of a sub-quantum dynamics with hidden variables.
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Li, J., and G. J. Weng. "Strain-Rate Sensitivity, Relaxation Behavior, and Complex Moduli of a Class of Isotropic Viscoelastic Composites." Journal of Engineering Materials and Technology 116, no. 4 (October 1, 1994): 495–504. http://dx.doi.org/10.1115/1.2904319.
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A micromechanical principle is developed to determine the strain-rate sensitivity, relaxation behavior, and complex moduli of a linear viscoelastic composite comprised of randomly oriented spheroidal inclusions. First, by taking both the matrix and inclusions as Maxwell or Voigt solids, it is found possible to construct a Maxwell or a Voigt composite when the Poisson ratios of both phases remain constant and the ratios of their shear modulus to shear viscosity (or their bulk counterparts) are equal; such a specialized composite can never be attained if either phase is purely elastic. In order to shed some light for the obtained theoretical structure, explicit results are derived next with the Maxwell matrix reinforced with spherical particles and randomly oriented disks. General calculations are performed for the glass/ED-6 system, the matrix being represented by a four-parameter model. It is found that, under the strain rates of 10−7/hr and 10−6/hr, randomly oriented disks and needles at 20 percent of concentration both give rise to a very stiff, almost linear, stress-strain behavior, whereas inclusions with an aspect ratio lying between 0.1 and 10 all lead to a softer nonlinear response. The relaxation behavior of the composite reinforced with spherical particles is found to be more pronounced than those reinforced with other inclusion shapes, with disks giving rise to the least stress relaxation. The real and imaginary parts of the overall complex moduli are also established, and found that, as the frequency increases, the real part of the complex bulk and shear moduli would approach their elastic counterparts, whereas for the imaginary part, the increase shows two maxima, and then drops to zero as the frequency continues to increase. Finally, the complex bulk modulus is examined in light of the Gibiansky and Milton bounds, and it is found that, for all inclusion shapes considered, this modulus always lies on or within the bounds.
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Kiselev, Alexei D., Ranim Ali, and Andrei V. Rybin. "Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems." Entropy 23, no. 11 (October 27, 2021): 1409. http://dx.doi.org/10.3390/e23111409.
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In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.
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Nishiguchi, I., T. L. Sham, and E. Krempl. "A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part I—Constitutive Equations." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 548–52. http://dx.doi.org/10.1115/1.2897057.
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The viscoplasticity theory based on overstress (VBO) is extended to finite deformation (FVBO). Yield surfaces and loading/unloading conditions are not part of this theory which represents creep, relaxation, and rate sensitivity in a “unified” way. Additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed. For the elastic part, the hypoelastic relation is used. For the inelastic part, the flow law of VBO is augmented by a term quadratic in the overstress together with a modified Jaumann stress rate which jointly or separately allow the modeling of second-order effects.
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SILVEIRA, FRANCISCO E. M. "Hydromagnetic waves and current relaxation: Damping at short wavelengths and small conductivity." Journal of Plasma Physics 79, no. 1 (July 17, 2012): 45–49. http://dx.doi.org/10.1017/s0022377812000670.
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AbstractInertial and diffusive effects on the propagation of hydromagnetic waves in plasmas of finite conductivity are explored by assuming a finite relaxation time for the current density. The domain of validity of the hydromagnetic approximation is determined by defining a lower limit for the perturbative wavelength. Three independent dispersion relations are obtained. At short wavelengths, it is found that the longitudinal component of the perturbative magnetic field damps out at a finite rate, which is determined fully by the relaxation time of the current density. In the same limit, it is shown that Alfvén waves can propagate through conductive plasmas with a null group speed. It is also shown that strong inertial and diffusive effects on magnetosonic waves can be discussed by defining suitably a perturbative parameter with the dimension of speed. It is argued that relevant corrections to space and time scales describing the reconnection of magnetic field lines are expected by applying the results presented here at sufficiently high frequencies.
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Zheng, J., M. S. Hossain, and D. Wang. "Prediction of spudcan penetration resistance profile in stiff-over-soft clays." Canadian Geotechnical Journal 53, no. 12 (December 2016): 1978–90. http://dx.doi.org/10.1139/cgj-2015-0339.
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Spudcan punch-through during installation and preloading process is one of the key concerns for the jack-up industry. This incident occurs in layered deposits, with new design approaches for spudcan penetration in sand-over-clay deposits reported recently. This paper reports a novel design approach for spudcan penetration in stiff-over-soft clay deposits. Large-deformation finite element (LDFE) analyses were carried out using the Coupled Eulerian–Lagrangian (CEL) approach. The clay was modelled using the extended elastic – perfectly plastic Tresca soil model allowing strain softening and rate dependency of the undrained shear strength. A detailed parametric study was undertaken, varying the strength ratio between bottom and top soil layers, the thickness of the top layer relative to the spudcan diameter, and degree of nonhomogeneity of the bottom layer. Existing data from centrifuge model tests were first used to validate the LDFE results, and then the measured and computed datasets were used to develop the formulas in the proposed design approach. The approach accounts for the soil plug in the bottom layer, and the corresponding additional resistance. Where there is the potential for punch-through, the approach provides estimations of the depth and bearing capacity at punch-through, the bearing capacity at the stiff–soft layer interface, and the bearing capacity in the bottom layer. Comparison shows that the punch-through method suggested in ISO standard 19905-1 provides a conservative estimate of the bearing capacity at punch-through, with guidelines provided to improve the method.
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Rani, Luxmi, Pankaj Bhalla, and Navinder Singh. "Nonequilibrium electron relaxation in graphene." International Journal of Modern Physics B 33, no. 17 (July 10, 2019): 1950183. http://dx.doi.org/10.1142/s0217979219501832.
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We apply memory function formalism to investigate nonequilibrium electron relaxation in graphene. Within the premises of two-temperature model (TTM), explicit expressions of the imaginary part of the memory function or generalized Drude scattering rate (1/[Formula: see text]) are obtained. In the DC limit and in equilibrium case where electron temperature (Te) is equal to phonon temperature (T), we reproduce the known results (i.e., 1/[Formula: see text][Formula: see text]T4 when T[Formula: see text][Formula: see text] and 1/[Formula: see text][Formula: see text]T when T[Formula: see text][Formula: see text], where [Formula: see text] is the Bloch–Grüneisen temperature). We report several new results for 1/[Formula: see text] where T[Formula: see text][Formula: see text][Formula: see text]Te relevant in pump–probe spectroscopic experiments. In the finite-frequency regime we find that 1/[Formula: see text] when [Formula: see text], and for [Formula: see text] it is [Formula: see text]-independent. These results can be verified in a typical pump–probe experimental setting for graphene.
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Kumar, Pramod. "Evaluation of Damping for Glass Fiber Reinforced Composite Materials." Advanced Materials Research 488-489 (March 2012): 654–58. http://dx.doi.org/10.4028/www.scientific.net/amr.488-489.654.
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A structural composite is a material system consisting of two or more phases on macroscopic scale whose mechanical performance and properties are designed to be superior to those of the constituent materials acting independently. One of the phases is stiffer and stronger and is called reinforcement and less stiff and weaker phase is known as matrix. This paper presents an experimental analysis of the dynamic characteristics of the unidirectional fiber composite as functions of fiber orientation, temperature, frequency and ramp rate. Dynamic characteristics of glass fiber composite are measured using dynamic machine analyzer (Triton 2000) in three point flexure bending. Micromechanical finite element model is modeled in NISA FEM software and damping of composite material is predicted and results are compared with experimental result.
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CASTELLA, F., and E. DUMAS. "HIGH FREQUENCY BEHAVIOR OF THE MAXWELL–BLOCH MODEL WITH RELAXATION: CONVERGENCE TO THE SCHRÖDINGER-RATE SYSTEM." Journal of Hyperbolic Differential Equations 09, no. 03 (September 2012): 355–401. http://dx.doi.org/10.1142/s0219891612500129.
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We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.
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Majid, Yudi Abdul. "PENGARUH TERAPI RELAKSASI GUIDED IMAGERY TERHADAP TEKANAN DARAH PADA LANSIA PENDERITA HIPERTENSI." Masker Medika 9, no. 2 (February 1, 2022): 542–50. http://dx.doi.org/10.52523/maskermedika.v9i2.468.
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Background: The elderly are individuals aged 60 years and over who experience physical, mental, psychosocial changes. One of the thysical changes in the cardiovaskular system where the heart valves thicken and become stiff so that the aortic wall decreases. The heartꞌs ability to pump blood decreases resulting in loss of elasticity of blood vessels which can cause blood pressure which is at risk for several degenerative disease including hypertension. Hypertension is a condition in which a person experiences an increase in blood pressure above normal. One of the non-farmakological treatments is guided imagery relaxation theraphy, guided imagery relaxation theraphy is a techique that uses a personꞌs imagination by imagining good or happy things, fun and calming. Research Objectives: The aim in this study was to analyze the effect of guided imagery relaxation theraphy on blood pressure in the elderly with hypertension. Research Methods: This study uses a literature review by analyzing articels related to the research. Data were obtained from electronic databases, namely Goggle Scholar, Pubmed, Proques, with the keywords elderly, guided imagery, and hypertension published in 2015-2020. Results: Based on the results of the analysis of 10 research articles reviewed, it was found that area there was a significant effect of guided imagey relaxation theraphy on changes in blood pressure in the elderly with hypertension, because by stimulating the brain through imagination, a response in the nervouse system can arise which makes the body relax. It is felt by the body so that endorphins are released into the blood vessels so that the blood vessels experience vasodilation and the blood supply is fulfilled which can cause a decrease in blood pressure and heart rate. Conclussion: Guided imagery relaxation theraphy can reduce blood pressure in elderly patients with hypertension.
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Johnson, A. R., and C. J. Quigley. "A Viscohyperelastic Maxwell Model for Rubber Viscoelasticity." Rubber Chemistry and Technology 65, no. 1 (March 1, 1992): 137–53. http://dx.doi.org/10.5254/1.3538596.
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Abstract A new viscoelaslic model for rubber is presented. It is similar in a Maxwell internal solid model in which all the solids are hyperelastic. A key feature of this model is its ability to accurately predict step-strain relaxation test data for very large strains. A method to obtain the constitutive models for the solids is presented for the three legged version and is used with existing data in the literature to compute variable-rate uniaxial pull tests. The finite-element implementation of this theory is given. Computations are made for a uniaxial constant-strain-rate test using a nearly incompressible axisymmetric version of the finite-element method.
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Li, Fu Lin, and Fang Le Peng. "FEM Simulation of Earth Pressure on Geosynthetic-Reinforced Soil Retaining Wall under Variable Rate Loading." Advanced Materials Research 594-597 (November 2012): 266–69. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.266.
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On the basis of the Dynamic Relaxation method, a nonlinear finite element method (FEM) analysis procedure was developed for the geosynthetic-reinforced soil retaining wall. The FEM procedure technique incorporated the unified three-component elasto-viscoplastic constitutive model which can consider the rate-dependent behavior of both the backfill soil and the geosynthitic reinforcement. A simulation was performed on a physical model test on geosynthetic-reinforced soil retaining wall to validate the presented FEM. Extensive finite-element analyses were carried out to investigate the earth pressure distributions from the back of retaining wall under variable rate loading. It is shown that this FEM can well simulate the rate-dependent behavior and the earth pressure of geosynthetic-reinforced soil retaining wall.
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Liu, Hailiang. "Asymptotic decay to relaxation shock fronts in two dimensions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 6 (December 2001): 1385–410. http://dx.doi.org/10.1017/s0308210500001451.
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We prove nonlinear stability of planar shock fronts for certain relaxation systems in two spatial dimensions. If the subcharacteristic condition is assumed and the initial perturbation is sufficiently small and the mass carried by the perturbations is not necessarily finite, then the solution converges to a shifted planar shock front solution as time t ↑ ∞. The asymptotic phase shift of shock fronts is, in general, non-zero and governed by a similarity solution to the heat equation. The asymptotic decay rate to the shock front is proved to be t−1/4 in L∞(R2) without imposing extra decay rates in space for the initial perturbations. The proofs are based on an elementary weighted energy analysis to the error equation.
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Khajehsaeid, Hesam. "A Comparison Between Fractional-Order and Integer-Order Differential Finite Deformation Viscoelastic Models: Effects of Filler Content and Loading Rate on Material Parameters." International Journal of Applied Mechanics 10, no. 09 (November 2018): 1850099. http://dx.doi.org/10.1142/s1758825118500990.
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Elastomers or rubber-like materials exhibit nonlinear viscoelastic behavior such as creep and relaxation upon mechanical loading. Differential constitutive models and hereditary integrals are the main frameworks followed in the literature for modeling the viscoelastic behavior at finite deformations. Regular differential operators can be replaced by fractional-order derivatives in the standard models in order to make fractional viscoelastic models. In the present paper, the relaxation behavior of elastomers is formulated both in terms of ordinary (integer-order) and fractional differential viscoelastic models. The derived constitutive equations are fitted to several experimental data to compare their efficiency in modeling the stress relaxation phenomenon. Specifically, a fractional viscoelastic model with one fractional dashpot (FD) is compared with two ordinary models including respectively one and two ordinary dashpots (OD). The models are compared in fitting accuracy, number of required material parameters and also variation of parameters from one compound to another to clarify the effects of filler content and deformation rate. It is shown that, the results of the ordinary model with one OD is not good at all. The fractional model with one FD and the ordinary model with two ODs provide good fittings for all compounds whereas the former uses only three parameters and the latter uses five material parameters. For the fractional model, the order of the Maxwell element and the associated relaxation time approximately remain the same for different compounds of each material at certain loading rates, but it is not the case for the ordinary differential models.
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Yin, Dong Hui, Xiao Gui Wang, Bao Xiang Qiu, and Zeng Liang Gao. "Fatigue Crack Growth Rate of 16mnr Steel with Effect of Stress Ratio." Advanced Materials Research 118-120 (June 2010): 278–82. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.278.
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Fatigue crack growth was simulated by using a newly developed unified model on the fatigue initiation and crack growth based on an incremental multiaxial fatigue criterion. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue crack growth rates with respect to three different stress ratios were selected as the benchmark to check the unified model. The predicted results agreed with the experimental data very well. The insensitivity of the crack growth rate to the stress ratio is due to the fast mean stress relaxation.
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NGUYEN, TRUNG DUNG, YUANTONG GU, ADEKUNLE OLOYEDE, and WIJITHA SENADEERA. "ANALYSIS OF STRAIN-RATE DEPENDENT MECHANICAL BEHAVIOR OF SINGLE CHONDROCYTE: A FINITE ELEMENT STUDY." International Journal of Computational Methods 11, supp01 (November 2014): 1344005. http://dx.doi.org/10.1142/s0219876213440052.
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Various studies have been conducted to investigate the effects of impact loading on cartilage damage and chondrocyte death. These have shown that the rate and magnitude of the applied strain significantly influence chondrocyte death, and that cell death occurred mostly in the superficial zone of cartilage suggesting the need to further understand the fundamental mechanisms underlying the chondrocytes death induced at certain levels of strain-rate. To date there is no comprehensive study providing insight on this phenomenon. The aim of this study is to examine the strain-rate dependent behavior of a single chondrocyte using a computational approach based on finite element method (FEM). An FEM model was developed using various mechanical models, which were standard Neo-Hookean solid (SnHS), porohyperelastic (PHE) and poroviscohyperelastic (PVHE) to simulate atomic force microscopy (AFM) experiments of chondrocyte. The PVHE showed, it can capture both relaxation and loading rate dependent behaviors of chondrocytes, accurately compared to other models.
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XU, JIANG. "ENERGY-TRANSPORT LIMIT OF THE HYDRODYNAMIC MODEL FOR SEMICONDUCTORS." Mathematical Models and Methods in Applied Sciences 20, no. 06 (June 2010): 937–54. http://dx.doi.org/10.1142/s0218202510004489.
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This paper is mainly devoted to study the energy-transport limit of a non-isentropic hydrodynamic model with momentum relaxation time τ and energy relaxation time σ. Inspired by the Maxwell iteration, we construct a new approximation under the assumption τσ = 1, and show that periodic initial-value problems of a certain scaled hydrodynamic model have unique smooth solutions in a finite time interval independent of τ. Furthermore, it is also obtained that as τ tends to zero, the smooth solutions converge to the smooth solutions of energy-transport models at the rate of τ2. The proof of these results is based on a continuation principle.
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Agoritsas, Elisabeth, and Kirsten Martens. "Non-trivial rheological exponents in sheared yield stress fluids." Soft Matter 13, no. 26 (2017): 4653–60. http://dx.doi.org/10.1039/c6sm02702d.
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In this work we discuss possible physical origins of non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. Within a mean-field description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel–Bulkley-type rheological response of exponent 1/2.
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Li, Fu Lin, and Fang Le Peng. "FEM Analysis on Tensile Force of Geosynthetic Reinforcement Arranged in GRS-RW Considering Variable Loading Rate." Applied Mechanics and Materials 188 (June 2012): 60–65. http://dx.doi.org/10.4028/www.scientific.net/amm.188.60.
Full textAbstract:
The combined effects of the rate-dependent behavior of both the backfill soil and the geosynthetic reinforcement have been investigated, which should be attributed to the viscous property of material. A nonlinear finite element method (FEM) analysis procedure based on the Dynamic Relaxation method was developed for the geosynthetic-reinforced soil retaining wall (GRS-RW). In the numerical analysis, both the viscous properties of the backfill and the reinforcement were considered through the unified nonlinear three-component elastic-viscoplastic model. The FEM procedure was validated against a physical model test on geosynthetic-reinforced soil retaining wall with granular backfill. Extensive finite-element analyses were carried out to investigate the tensile force distributions in geosynthetic reinforcement of geosynthetic-reinforced soil retaining wall under the change of loading rate. It is found from the analyses that the presented FEM can well simulate the rate-dependent behavior of geosynthetic-reinforced soil retaining wall and the tensile force of geosynthetic reinforcement arranged in retaining wall.
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Sakaki, T., T. Kuroki, and K. Sugimoto. "Creep of a Hollow Sphere." Journal of Applied Mechanics 57, no. 2 (June 1, 1990): 276–81. http://dx.doi.org/10.1115/1.2891985.
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Using internal stress arising from a spherically symmetric, finite plastic strain, creep of a hollow sphere subjected to inner and outer pressures, and also thermal stress, is discussed. If computer-aided numerical calculation method is used, creep is easily followed up to a finite plastic strain range including initial transient creep, whatever type of creep law is employed. If assumed in a steady state, creep rate, stress, small plastic strain leading to a stress state in steady creep, and another small plastic strain relaxing thermal stress are analytically obtained. Numerical method is also applicable to creep relaxation. Further, the origin of residual stress after unloading is clarified.
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Koprowski-Theiss, N., M. Johlitz, and S. Diebels. "CHARACTERIZING THE TIME DEPENDENCE OF FILLED EPDM." Rubber Chemistry and Technology 84, no. 2 (June 1, 2011): 147–65. http://dx.doi.org/10.5254/1.3570527.
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Abstract The mechanical properties of a carbon black filled rubber are investigated. The main focus lays on the theoretical modeling of the basic elasticity and the viscoelastic behavior. Therefore, uniaxial tension tests at different feedrates are performed. The occurring Mullins effect can be neglected due to adequate pretreatment of the specimens. Healing effects are also verified and investigated in the examined material. The constitutive model for the basic elasticity is based on the Yeoh model, while the theory of finite viscoelasticity with an intermediate configuration is used to describe the rate dependent behavior. The healing effects are constituted with large relaxation times and not with an additional structural parameter. As the material has a strong nonlinear behavior with respect to the deformation rate, nonlinearity in the relaxation time with respect to this behavior is introduced. The material parameters of the model are estimated using a stochastic identification algorithm.
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Massa, Luca, and Prashaanth Ravindran. "On the effects of finite-rate carbon/oxygen chemistry on supersonic jet instability." Journal of Fluid Mechanics 713 (October 17, 2012): 330–61. http://dx.doi.org/10.1017/jfm.2012.459.
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AbstractThe instability of high-temperature jets is studied because of its importance to the analysis of gas-turbine engine exhaust flow, shock–shock interaction and bypass transition. The focus is on fluid–chemistry coupling, where the chemical time scales are supported by both reactive and inelastic molecular processes. The former are associated with dissociation/exchange reactions, while the latter are associated with transfers of vibrational quanta. The interaction affects both the instability growth rate and acoustic feedback by sustaining thermo-acoustic damping. Resonance conditions are identified as those that yield the maximum damping against the Damköhler number. The main results of the present study are the explanation of the dichotomy between vortical and acoustic modes in relation to the thermo-acoustic damping, and the analysis of the resonance condition as it depends on the physico-chemical properties of carbon/oxygen mixtures. The ability of a mode to support thermo-acoustic damping is related to the local convective Mach number of its most amplified frequency, and thus to the phenomenon of acoustic trapping in the jet core. Regarding the second issue, carbon dioxide acts as the best damper at low jet temperatures ${T}_{j} \approx 1000~\mathrm{K} $, where the vibrational relaxation is the main chemical scale, and up to ${T}_{j} = 3500~\mathrm{K} $ because its reactive chemistry resonates with the fluid fluctuation at a lower temperature than the dissociation of ${\mathrm{O} }_{2} $. At higher temperatures, oxygen is the best damper because of the larger endothermicity of the reactions it supports.
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Hou, Wanting, Li-Yun Fu, José M. Carcione, Zhiwei Wang, and Jia Wei. "Simulation of thermoelastic waves based on the Lord-Shulman theory." GEOPHYSICS 86, no. 3 (April 8, 2021): T155—T164. http://dx.doi.org/10.1190/geo2020-0515.1.
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Thermoelasticity is important in seismic propagation due to the effects related to wave attenuation and velocity dispersion. We have applied a novel finite-difference (FD) solver of the Lord-Shulman thermoelasticity equations to compute synthetic seismograms that include the effects of the thermal properties (expansion coefficient, thermal conductivity, and specific heat) compared with the classic forward-modeling codes. We use a time splitting method because the presence of a slow quasistatic mode (the thermal mode) makes the differential equations stiff and unstable for explicit time-stepping methods. The spatial derivatives are computed with a rotated staggered-grid FD method, and an unsplit convolutional perfectly matched layer is used to absorb the waves at the boundaries, with an optimal performance at the grazing incidence. The stability condition of the modeling algorithm is examined. The numerical experiments illustrate the effects of the thermoelasticity properties on the attenuation of the fast P-wave (or E-wave) and the slow thermal P-wave (or T-wave). These propagation modes have characteristics similar to the fast and slow P-waves of poroelasticity, respectively. The thermal expansion coefficient has a significant effect on the velocity dispersion and attenuation of the elastic waves, and the thermal conductivity affects the relaxation time of the thermal diffusion process, with the T mode becoming wave-like at high thermal conductivities and high frequencies.
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Wang, Wei, and D. V. Griffiths. "Case study of slope failure during construction of an open pit mine in Indonesia." Canadian Geotechnical Journal 56, no. 5 (May 2019): 636–48. http://dx.doi.org/10.1139/cgj-2017-0662.
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This paper presents back-analyses of a failed slope at an open pit lignite mine in Muara Enim, Indonesia. The slope, which was being raised by the dumping of excavated material, failed at a dump height of 24 m, well before reaching the design height of 80 m. The primary cause of failure was determined to be the presence of a previously unknown weak layer in the foundation, combined with high excess pore pressures generated by a relatively fast dumping rate. The failure resulted in significant disruption of the mining operation, in addition to environmental problems and a high cost of remediation. Finite element analyses were performed to gain a better understanding of the influence of the weak layer at the time of the failure. The case history emphasizes the need for a thorough site investigation and the risks associated with fast dumping on saturated weak clay overlain by a stiff residual soil layer with low permeability.