Sharif Digital Repository

In this paper the torsion problem of a circular bar with fixed ends is solved using a finite deformation constitutive model based on the corotational rates of the logarithmic strain. The logarithmic, Green-Naghdi and Eulerian corotational rates of the logarithmic strain are used in the model. The solution is based on a von Mises type yield function that incorporates isotropic and kinematic hardenings. For the kinematic hardening, a modified Armstrong-Fredrick hardening model with the corotational rate of the logarithmic strain is used. Assuming incompressible behavior, the fixed-end torsion problem is simplified to the simple shear problem. Solving the problem, the stress components are... 

In this paper a finite deformation constitutive model for rigid plastic hardening materials based on the logarithmic strain tensor is introduced. The flow rule of this constitutive model relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. The evolution equation for the kinematic hardening of this model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. Using Jaumann, Green-Naghdi, Eulerian and logarithmic corotational rates in the proposed constitutive model, stress-strain responses and subsequent yield surfaces are determined for rigid... 

The hot working behavior of a low carbon resulfurized free-cutting steel was studied by hot compression tests at temperature range of 1000-1200°C with strain rates of 0.001 to 1s-1. The conventional parameters such as activation energy of deformation and relationships between flow stress/strain and Zener-Hollomon parameter were determined. Both the critical stress and strain for initiation of dynamic recrystallization (DRX) were determined using: (1) strain hardening rate versus stress curve, (2) the natural logarithm of strain hardening rate versus strain curve, and (3) the constitutive equations. In summary, for low carbon resulfurized free - cutting steels, the activation energy of... 

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, employing the logarithmic (or Hencky) strain as a more physical measure of strain, the time-dependent response of compressible viscoelastic materials is investigated. In this regard, we present a phenomenological finite strain viscoelastic constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The formulation is based on the multiplicative decomposition of the deformation gradient into elastic and viscoelastic parts, together with the use of the isotropic property of the Helmholtz strain energy function. Making use of a logarithmic mapping, we present an appropriate form of the proposed constitutive equations in the... 

The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g.; the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We... 

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...