Sharif Digital Repository

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is... 

In this paper, decomposition of the total strain into elastic and plastic parts is investigated for extension of elastic-type constitutive models to finite deformation elastoplasticity. In order to model the elastic behavior, a Hookean-type constitutive equation based on the logarithmic strain is considered. Based on this constitutive equation and assuming the deformation theory of Hencky as well as the yield criteria of von Mises, the elastic-plastic behavior of materials at finite deformation is modeled in the case of the proportional loading. Moreover, this elastoplastic model is applied in order to determine the stress distribution in thick-walled cylindrical pressure vessels at finite... 

In this paper, using the multiplicative decomposition of the deformation gradient into mechanical and thermal parts, both kinematic and kinetic aspects of finite deformation thermoelasticity are considered. At first, the kinematics of the thermoelastic continua in the purely thermal process of nonisothermal deformation is investigated for finite deformation thermoelasticity. Also, a linear relation between the thermal expansion tensor and the rate of the thermal deformation tensor is presented. In order to model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the... 

In this paper, two corotational modeling for elastic-plastic, mixed hardening materials at finite deformations are introduced. In these models, the additive decomposition of the strain rate tensor as well as the multiplicative decomposition of the deformation gradient tensor is used. For this purpose, corotational constitutive equations are derived for elastic-plastic hardening materials with the non-linear Armstrong-Frederick kinematic hardening and isotropic hardening models. As an application of the proposed constitutive modeling, the governing equations are solved numerically for the simple shear problem with different corotational rates and the stress components are plotted versus the... 

In this paper based on the multiplicative decomposition of the deformation gradient, the plastic spin tensor and the plastic spin corotational rate are introduced. Using this rate (and also lograte), an elastic-plastic constitutive model for hardening materials are proposed. In this model, the Armstrong-Frederick kinematic hardening and the isotropic hardening equations are used. The proposed model is solved for the simple shear problem with the material properties of the stainless steel SUS 304. The results are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the results of proposed theoretical model and the experimental data. As... 

In many engineering applications, shape memory polymers (SMPs) usually undergo arbitrary thermomechanical loadings at finite deformation. Thus, development of 3D constitutive models for SMPs within the finite deformation regime has attracted a great deal of interest. In this paper, based on the classical framework of thermodynamics of irreversible processes, employing the logarithmic (or Hencky) strain as a more physical measure of strain, a 3D large-strain macromechanical model is presented. In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts. In addition, employing the averaging scheme, the logarithmic... 

We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green-Lagrange strain without omission of higher order terms. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed theory, however, is applicable to problems that also exhibit material nonlinearity. For the rod model, we... 

In this paper, a deformation measure is introduced which leads to a class of strain measures in the Lagrangian and Eulerian descriptions. In order to develop a constitutive equation, a second-order constitutive relation based on these strain measures is considered for modeling the mechanical behavior of solids at finite deformation. For this purpose and performance evaluation of the proposed strains, a Hookean-type constitutive equation is considered and the uniaxial loading as well as simple shear and pure shear tests are examined. It is shown that the constitutive modeling based on the proposed strains give results which are in good agreement with the experimental data  

The behavior of foams is typically rate-dependent and viscoelastic. In this paper, multiplicative decomposition of the deformation gradient and the second law of thermodynamics are employed to develop the differential constitutive equations for isotropic viscoelastic foams experiencing finite deformations, from a phenomenological point of view, i.e. without referring to micro-structural viewpoint. A model containing an equilibrium hyperelastic spring which is parallel to a Maxwell model has been utilized for introducing constitutive formulation. The deformation gradient tensor is decomposed into two parts: elastic deformation gradient tensor and viscoelastic deformation gradient tensor. A... 

We derive the exact dispersion relations for flexural elastic wave motion in a beam under finite deformation. We employ the Euler-Bernoulli kinematic hypothesis. Focusing on homogeneous waveguides with constant cross-section, we utilize the exact strain tensor and retain all high order terms. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to the small strain assumption. We show that incorporation of finite deformation shifts the frequency dispersion curves downwards. Furthermore, the group velocity increases with wavenumber but this trend reverses at high wavenumbers when the wave amplitude is sufficiently high. At... 

Strain and stress concentrations are studied for elastomers at finite deformations. Effects of strain-induced crystallization, filler reinforcement and deformation rate are also investigated, and micromechanical descriptions are provided for the observed results. A simple problem is subjected to finite element simulations to show the results evidently. Material parameters are obtained from experimental tests conducted on standard tensile samples of filled and unfilled natural rubber (NR) as well as styrene–butadiene rubber (SBR) as crystallizing and non-crystallizing rubbers, respectively. In all simulations, the strain concentration factor KE is shown to decrease monotonically where the... 

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good... 

The macroscopic constitutive law for a heterogeneous solid containing two dissimilar nonlinear elastic phases undergoing finite deformation is obtained. Attention is restricted to the case of spherical symmetry such that only the materials consisting of an irregular suspension of perfectly spherical particles experiencing all-round uniform loading are considered which leads to a one-dimensional modeling. For the homogenization procedure, a strain-energy based scheme which utilizes Hashin's composite sphere is employed to obtain the macroscopic stress-deformation relation added by the initial volume fraction of the particles. As applications of the procedure, the closed-form macroscopic... 

In this paper, formulation and implementation of finite element analysis within an Arbitrary Lagrangian Eulerian (ALE) description is presented for large deformation analysis of elasto-viscoplastic materials. The rate effects are included using a consistent procedure. An implicit algorithm with backward Euler integration scheme is used to integrate the elasto-viscoplastic constitutive equations. Also, the closed form of the consistent tangent operator is derived using the momentum balance equation to reduce the computation time. A fully coupled ALE procedure is used which includes dynamic effects. The proposed algorithm is implemented in an ALE code and its effectiveness and efficiency is... 

In this paper, the method of additive plasticity at finite deformations is generalized to the micropolar continuous media. It is shown that the non-symmetric rate of deformation tensor and gradient of gyration vector could be decomposed into elastic and plastic parts. For the finite elastic deformation, themicropolar hypo-elastic constitutive equations for isotropicmicropolar materials are considered.Concerning the additive decomposition and the micropolar hypo-elasticity as the basic tools, an elastic-plastic formulation consisting of an arbitrary number of internal variables and arbitrary form of plastic flow rule is derived. The localization conditions for the micropolar material obeying... 

Exact solutions for nonlinear composites undergoing finite deformation are in general difficult to find. In this article, such a solution is obtained for a two-phase composite reinforced with elliptic fibers under anti-plane shear. The analysis is based on the theory of hyperelasticity with both phases characterized by incompressible neo-Hookean strain energies, and is carried out when the composite elliptic cylinder assemblage carries a confocal microgeometry. The problem for a class of compressible neo-Hookean materials is also studied. The analytical results for the stress and strain distributions are verified with finite element calculations where excellent agreement is found. We then...