Constitutive relations for finite deformations of transversely isotropic piezoelectric porous materials

1995 ◽  
Author(s):  
Romesh C. Batra ◽  
J. S. Yang
Keyword(s):  
Porous Materials ◽  
Constitutive Relations ◽  
Transversely Isotropic ◽  
Finite Deformations

Constitutive Relations and Parameter Estimation for Finite Deformations of Viscoelastic Adhesives

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
G. O. Antoine ◽  
R. C. Batra
Keyword(s):  
Constitutive Relation ◽  
Axial Strain ◽  
Constitutive Relations ◽  
Finite Deformations ◽  
Low Velocity Impact ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Cauchy Stress ◽  
Peak Strain ◽  
Material Parameters

We propose a constitutive relation for finite deformations of nearly incompressible isotropic viscoelastic rubbery adhesives assuming that the Cauchy stress tensor can be written as the sum of elastic and viscoelastic parts. The former is derived from a stored energy function and the latter from a hereditary type integral. Using Ogden’s expression for the strain energy density and the Prony series for the viscoelastic shear modulus, values of material parameters are estimated by using experimental data for uniaxial tensile and compressive cyclic deformations at different constant engineering axial strain rates. It is found that values of material parameters using the loading part of the first cycle, the complete first cycle, and the complete two loading cycles are quite different. Furthermore, the constitutive relation with values of material parameters determined from the monotonic loading during the first cycle of deformations cannot well predict even deformations during the unloading portion of the first cycle. The developed constitutive relation is used to study low-velocity impact of polymethylmethacrylate (PMMA)/adhesive/polycarbonate (PC) laminate. The three sets of values of material parameters for the adhesive seem to have a negligible effect on the overall deformations of the laminate. It is attributed to the fact that peak strain rates in the severely deforming regions are large, and the corresponding stresses are essentially unaffected by the long time response of the adhesive.

Nonisothermic Finite Deformations of Hypoelastic Bodies

2016 ◽  
Vol 08 (08) ◽  
pp. 1650099 ◽  
Author(s):  
Yuri Astapov ◽  
Glagolev Vadim ◽  
Khristich Dmitrii ◽  
Markin Alexey ◽  
Sokolova Marina
Keyword(s):  
Variational Formulation ◽  
Deformation Process ◽  
Strain State ◽  
Constitutive Relations ◽  
Finite Deformations ◽  
Reference Configuration ◽  
Deformation Characteristics ◽  
Equilibrium Flow ◽  
Variational Form ◽  
Axisymmetric Bodies

Variational formulation of a coupled thermomechanical problem of anisotropic solids for the case of nonisothermal finite deformations in a reference configuration is shown. The formulation of the problem includes: a condition of equilibrium flow of a deformation process in the reference configuration; an equation of a coupled heat conductivity in a variational form, in which an influence of deformation characteristics of a process on the temperature field is taken into account; constitutive relations for a thermohypoelastic material; kinematic and evolutional relations; initial and boundary conditions. The obtained solutions show the development of stress–strain state and temperature changing in axisymmetric bodies in the case of finite deformations.

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.

Sign in / Sign up

Export Citation Format

Share Document