Sharif Digital Repository

In Hypo-elastic constitutive models an objective rate of the Cauchy stress tensor is expressed in terms of the current state of the stress and the deformation rate tensor D in a way that the dependency on the latter is a homogeneously linear one. In this work, a type of grade-one hypo-elastic models (i.e. models with linear dependency of the hypo-elasticity tensor on the stress) is considered for isotropic materials based on the objective corotational rates of stress. A positive real parameter denoted by n is involved in the considered type. Different values can be selected for this parameter, each selection leads to a specific model within the class of grade-one hypo-elasticity. The spin of... 

In this paper, some basis-free expressions for the material time derivative of Lagrangian stress tensors are presented which are generally valid in all cases of coalescent principal stretches. The material is assumed to be elastic and isotropic  

In this paper, an analysis of kinematics of the isotropic elastic Cosserat continuum is presented in infinitesimal and finite deformations. Emphasis is given on the applicability of corotational stress rates for hypoelasticity in micro-polar continua. A non-linear finite element analysis is performed with an explicit formulation of tangent stiffness matrices in the case of Truesdell stress and couple stress rates. A comprehensive path-dependent procedure is employed based on the arc-length method to calculate the stability points and handle the snap-back problem. Finally, the accuracy and efficiency of method are illustrated by numerical examples