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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 study, a pure Lagrangian algorithm for numerical simulation of fluid-structure interaction problems is proposed based on the Smoothed Particle Hydrodynamics (SPH) method. A new treatment of boundary conditions at the interfaces is introduced that provides the possibility of simultaneous integration of governing equations for all particles, regardless of its material type. The proposed algorithm is capable of dealing with large deformations of hypo elastic solids. The method is validated by comparison of numerical results with other numerical simulations and also examining the consistent behaviors of the algorithm for different parameters  

In this paper, the concept of hypo-elasticity is generalized to the micropolar continuum theory, and the general forms of the constitutive equations of the micropolar hypo-elastic materials are presented. A new co-rotational objective rate whose spin is the micropolar gyration tensor is introduced which describes the deformation of the material in view of an observer attached to the micro-structure. As special case, simplified versions of the proposed constitutive equations are given in which the same fourth-order elasticity tensors are used as in the micropolar linear elasticity. A 2-D finite element formulation for large elastic deformation of micropolar hypo-elastic media based on the... 

In this paper, updated Lagrangian finite element formulations for large elastic deformation of micropolar hypo-elastic materials are presented. Using representation theorems of tensor functions, the general form of the constitutive equations for the micropolar hypo-elastic materials model are presented. The finite element formulations are based on the general form of the micropolar hypo-elastic constitutive equations in conjunction with Jaumann rate and a new rate called gyration rate. Gyration rate describes the deformation of the material in view of an observer attached to the micro-structure. An incrementally objective stress and couple stress update procedure is developed and its...