1/27/2024 0 Comments Finite element scilab![]() ![]() The constitutive models listed above are available in practically every software which is utilized for engineering analysis, e.g. Furthermore, a group of mixed-hardening models exists which combine the two aforementioned behaviors. The so-called backstress variable which defines the translation of the yield surface center is, in the simplest case, taken to evolve according to the linear equation proposed by Prager . A slightly more sophisticated approach assumes the usage of kinematic hardening rule, i.e., the translation of the yield surface which occurs during straining. Linear, piecewise linear and nonlinear relations are used to describe the evolution of the yield stress. One of the simplest versions of this theory assumes the so-called isotropic hardening rule, i.e., the expansion of the yield surface in the stress space which occurs during the plastic straining. ![]() This theory is based on the Huber–von Mises–Hencky (HMH) yield criterion and is most commonly utilized to capture the mechanical properties of metals, e.g. The classical small strain plasticity theory finds a wide range of applications in the engineering analysis. A number of numerical simulations were conducted in order to verify the performance of the developed UMAT code. A developed user material subroutine (UMAT) which allows one to use the viscoplastic models under consideration in the FEM program CalculiX is attached in the appendix section. The consistent tangent operator was derived for the considered class of models and is presented in the paper. For that purpose, the radial-return mapping algorithm was utilized. The general form of the generalized constitutive model obtained this way was subsequently implemented into the finite element method (FEM). What is more, the backstress evolution equation which was proposed by Marquis was modified so that any equivalent plastic strain function can be used in the recovery term now. Furthermore, the presented model formulation enables one to use an arbitrary equivalent plastic strain function to describe the isotropic hardening behavior. The viscoplastic model which was proposed by Marquis is generalized by allowing multiple terms describing the isotropic and the kinematic hardening. In this paper a selected type of elasto-viscoplastic constitutive equations is considered.
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