报告人：曾宪乙 (Department of Mathematics, University of Texas, El Paso)

题目：A dynamic variational multiscale method for elastic and inelastic solid dynamics using linear tetrahedral elements

时间：2017年6月1日11:00 - 12:00

地点：华中科技大学恩明楼813

摘要：

We present a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly/fully incompressible transient solid dynamics computations. Our method is based on a mixed formulation for isotropic elasticity, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized by a variational multiscale (VMS) approach to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics.

We then extend the methodology to incompressible viscoelastic materials, for which we notice that the physical dissipation is usually insufficient to suppress the pressure oscillations. The constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Extension of the VMS stabilization incorporates the viscoelastic dissipation that is determined from internal state variables.

We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations, and close the talk by the numerical simulation of the interaction between a blast wave and viscoelastic gel.