scholarly journals Second‐order constitutive relations for transversely isotropic piezoelectric porous materials

1995 ◽  
Vol 97 (4) ◽  
pp. 2595-2598 ◽  
Author(s):  
R. C. Batra ◽  
J. S. Yang
Keyword(s):  
Porous Materials ◽  
Constitutive Relations ◽  
Transversely Isotropic ◽  
Second Order

On Constitutive Relations and Finite Deformations of Passive Cardiac Tissue: I. A Pseudostrain-Energy Function

1987 ◽  
Vol 109 (4) ◽  
pp. 298-304 ◽  
Author(s):  
J. D. Humphrey ◽  
F. C. P. Yin
Keyword(s):  
Energy Function ◽  
Cardiac Tissue ◽  
Functional Form ◽  
Structural Information ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Limited Range ◽  
Material Parameters ◽  
Data Result

A three-dimensional constitutive relation for passive cardiac tissue is formulated in terms of a structurally motivated pseudostrain-energy function, W, while the mathematical simplicity of phenomenological approaches is preserved. A specific functional form of W is proposed on the basis of limited structural information and multiaxial experimental data. The material parameters are determined in a least-squared sense from both uniaxial and biaxial data. Our results suggest that (1) multiaxially-loaded cardiac tissue is nearly transversely-isotropic with respect to local muscle fiber directions, at least for a limited range of strain histories, (2) material parameters determined from uniaxial papillary muscle data result in gross underestimates of the stresses in multiaxially-loaded specimens, and (3) material parameters determined from equibiaxial tests predict the behavior of the tissue under various nonequibiaxial stretching protocols reasonably well.

AN ELASTOPLASTIC CONSTITUTIVE MODEL FOR POROUS MATERIALS

2013 ◽  
Vol 05 (03) ◽  
pp. 1350035 ◽  
Author(s):  
ZHUPING HUANG ◽  
YONGQIANG CHEN ◽  
SHU-LIN BAI
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Porous Materials ◽  
Constitutive Relations ◽  
Matrix Material ◽  
Three Dimensional ◽  
Porous Solids ◽  
Additional Material ◽  
Prediction Of Mechanical Properties ◽  
Elastoplastic Constitutive Model

A micromechanics-based elastoplastic constitutive model for porous materials is proposed. With an assumption of modified three-dimensional Ramberg–Osgood equation for the compressible matrix material, the variational principle based on a linear comparison composite is applied to study the effective mechanical properties of the porous materials. Analytical expressions of elastoplastic constitutive relations are derived by means of micromechanics principles and homogenization procedures. It is demonstrated that the derived expressions do not involve any additional material constants to be fitted with experimental data. The model can be useful in the prediction of mechanical properties of elastoplastic porous solids.

On the thermodynamics of nonlinear constitutive relations in gasdynamics

1980 ◽  
Vol 101 (2) ◽  
pp. 225-241 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Final Section ◽  
Constitutive Relations ◽  
Second Law Of Thermodynamics ◽  
Second Order ◽  
Irreversible Processes ◽  
Burnett Equations ◽  
Necessary Constraints ◽  
Nonlinear Constitutive Relations ◽  
Monatomic Gas ◽  
General Method

The thermodynamics of irreversible processes is normally limited to processes that can be adequately described by linear constitutive relations, like those of Fourier and Newton in a simple gas. In this paper we use thermodynamic arguments to derive the (nonlinear) Burnett equations for a monatomic gas, thus avoiding the complicated kinetic theory by which the equations were discovered and which somewhat obscures the origin of the various terms in the equations. Expressions are given for the entropy, its flux and its production rate correct to second-order in Knudsen number. The theory involves five phenomenological parameters, and as there are eleven coefficients in the second-order terms of Burnett's equations, we are able to deduce several necessary constraints between these coefficients. Compact forms for the equations are found that clarify their physical significance. The general method we have developed is applicable to media other than simple gases.In a final section we use our theory of Burnett's equations to draw some general conclusions concerning the second law of thermodynamics. It is shown that the Clausius-Duhem inequality holds only for the linear theory of constitutive relations; and that axiomatic generalizations of the inequality to nonlinear processes – common in continuum mechanics–fail because the vital distinction between reversible and irreversible processes is not made.

On the instability in second-order systems for acoustic VTI and TTI media

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. T171-T186 ◽  
Author(s):  
Kenneth P. Bube ◽  
Tamas Nemeth ◽  
Joseph P. Stefani ◽  
Ray Ergas ◽  
Wei Liu ◽  
...  
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Differential Equations ◽  
Shear Wave ◽  
Transversely Isotropic ◽  
Second Order ◽  
Wave Speeds ◽  
Tti Media ◽  
Second Order Systems ◽  
Vti Media

We studied second-order wave propagation systems for vertical transversely isotropic (VTI) and tilted transversely isotropic (TTI) acoustic media with variable axes of symmetry that have their shear-wave speeds set to zero. Acoustic TTI systems are commonly used in reverse-time migration, but these second-order systems are susceptible to instablities appearing as nonphysical stationary noise growing linearly in time, particularly in variable-tilt TTI media. We found an explanation of the cause of this phenomenon. The instabilities are not caused only by the numerical schemes; they are inherent to the differential equations. These instabilities are present even in homogeneous VTI media. These instabilities are caused by zero wave speeds at a wide variety of wavenumbers — a direct consequence of setting the shear-wave speeds to zero — coupled with the second time derivative in these systems. Although the second-order isotropic wave equation allows smooth time-growing solutions, a larger class of time-growing solutions exists for the second-order acoustic TI systems, including nonsmooth solutions. Boundary conditions appear to be less effective in controlling these time-growing solutions than they are for the isotropic wave equation. These systems conserve an incomplete energy that does not prevent the instabilities. The corresponding steady-state systems are no longer elliptic differential equations and can have nonsmooth solutions that are related to the instabilities. We started initially with homogeneous VTI media, and then extended these results to heterogeneous variable-tilt TTI media. We also developed a second-order acoustic system for heterogeneous variable-tilt TTI media derived directly from the full-elastic system for heterogeneous variable-tilt TTI media. All second-order systems with a dispersion relation obtained by setting the shear-wave speeds to zero in the elastic dispersion relation allowed these nonphysical time-growing solutions; however, knowing the cause of these instabilities, it may be possible to prevent or control the activation of these solutions.

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