On the construction of effective constitutive relations for porous elastic materials subjected to finite deformations including the case of their superposition

2002 ◽  
Vol 47 (2) ◽  
pp. 136-140 ◽  
Author(s):  
V. A. Levin ◽  
K. M. Zingerman
Keyword(s):  
Constitutive Relations ◽  
Finite Deformations ◽  
Elastic Materials

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.

Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains

2003 ◽  
Vol 70 (6) ◽  
pp. 809-816 ◽  
Author(s):  
V. A. Levin ◽  
K. M. Zingermann
Keyword(s):  
Plane Strain ◽  
Constitutive Equations ◽  
Rigid Motion ◽  
Finite Deformations ◽  
Finite Strains ◽  
Effective Characteristics ◽  
Elastic Materials ◽  
Preliminary Loading ◽  
Nonlinear Elastic

A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.

scholarly journals Reciprocity, passivity and causality in Willis materials

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160604 ◽  
Author(s):  
Michael B. Muhlestein ◽  
Caleb F. Sieck ◽  
Andrea Alù ◽  
Michael R. Haberman
Keyword(s):  
Elastic Material ◽  
Time Domain ◽  
Material Properties ◽  
Constitutive Equations ◽  
Wave Motion ◽  
Constitutive Relations ◽  
Alternative Formulation ◽  
Elastic Materials ◽  
Order Dispersion ◽  
Insight Into

Materials that require coupling between the stress–strain and momentum–velocity constitutive relations were first proposed by Willis (Willis 1981 Wave Motion 3 , 1–11. ( doi:10.1016/0165-2125(81)90008-1 )) and are now known as elastic materials of the Willis type, or simply Willis materials. As coupling between these two constitutive equations is a generalization of standard elastodynamic theory, restrictions on the physically admissible material properties for Willis materials should be similarly generalized. This paper derives restrictions imposed on the material properties of Willis materials when they are assumed to be reciprocal, passive and causal. Considerations of causality and low-order dispersion suggest an alternative formulation of the standard Willis equations. The alternative formulation provides improved insight into the subwavelength physical behaviour leading to Willis material properties and is amenable to time-domain analyses. Finally, the results initially obtained for a generally elastic material are specialized to the acoustic limit.

Numerical Method for Solving the Problem of Thermomechanics of Polymeric Environment in Conditions of Phase Transition

2015 ◽  
Vol 243 ◽  
pp. 139-145
Author(s):  
R.G. Kulikov ◽  
T.G. Kulikova ◽  
Nikolai A. Trufanov
Keyword(s):  
Constitutive Relations ◽  
Numerical Procedure ◽  
Numerical Algorithms ◽  
Finite Deformations ◽  
Problem Statement ◽  
Time Step ◽  
Boundary Problems ◽  
Galerkin Approach ◽  
Small Deformations ◽  
Elastic Polymer

A methodology and a numerical algorithm of solving boundary problems of mechanics of deformable crystallizing elastic polymer media have been developed. A class of problems describing processes taking place in polymer products during their manufacturing is considered. Due to the significance of shrinking deformations the problem is considered within finite deformations theory. Constitutive relations are built on base of Peng-Landel potential. A ‘weak’ variation problem statement based on Galerkin approach is used. The offered algorithm is based on linearization methodology when small deformations are applied to finite ones. Deformation process is considered as a sequence of transitions through intermediate configurations. This approach makes possible to bring the received solution to the sequence of linearized boundary problems for which effective numerical algorithms have been designed. Numerical procedure is based on the technology of finite element method. Increments of displacements on the considered time step are taken to be nodal unknowns. The offered algorithm is applied to solution of the problem concerning the polyethylene pipe deformation during its manufacturing. Main advantages of the proposed algorithm have been defined.

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