ON CORRECTNESS OF VISCO-ELASTO-PLASTICITY MODELS WITH NON-NEWTONIAN VISCOSITY
M. A. Guseva, V. N. Sofronov
VANT. Ser.: Mat. Mod. Fiz. Proc 2016. Вып.1. С. 3-15.
Problems arising in the numerical implementation of visco-elasto-plasticity models are considered. In this type of models, von Mises model has been taken for a plastic component and non-Newtonian medium has been taken for a viscous component, for which the viscosity coefficient depends not only on the thermodynamic parameters, but on the reduced velocity of shear strains as well. An attempt has been made to give an answer to the question concerning the extent of arbitrariness of such dependence.
The thermodynamic research of correctness is based on constructing the plastic and viscous dissipation functions. There is a common requirement of convexity of these functions relative to fluxes. The conditions (limits on the model parameters), under which the viscous dissipation function is strictly convex for the given form of viscosity, have been identified. For the plastic potential, this requirement is always met, if an ideal plasticity model is used. The condition of evolutionary development (correctness of the Cauchy problem for appropriate differential equations) has been found, this condition coincides with the requirement of convexity of the viscous dissipation function.
The conditions (limits on the model parameters and parameters of shock waves) under which the solution for the given form of viscosity exists in the form of a stationary wave have been identified. It is shown that the requirement of convexity of the viscous dissipation function is also a sufficient condition of the structure existence.
The visco-elasto-plastic model has been used for the numerical simulation of Barker experiments, in which the shock wave front structure has been identified using the laser interferometry method. Two parameter sets of the viscosity model (both with the met and not met requirement of convexity of the dissipation function) have been used to take into account the viscousity properties of a given material. In the first case, a good agreement of the calculated and experimental results is observed. In the second case, there is no passage to the limit with the computational grid refinement Δm > 0 and the shock wave front structure does not agree with that obtained experimentally. So, the results allow concluding that the model parameters should ensure that the dissipation function convexity requirement is met. Keywords: visco-elasto-plasticity models, non-Newtonian models of viscosity, dissipation functions, condition of evolutionary development, steady-state structures.
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