论文标题
弹性动力学的交错显式时间消化
Staggered explicit-implicit time-discretization for elastodynamics with dissipative internal variables
论文作者
论文摘要
提出了将线性弹性动力学以应力形式形式的两步分配时间离散化扩展到涉及可能非线性耗散演化的内部变量的系统。因此，对于内部变量的另一个步骤，它通常是隐式的，尽管如果不涉及内部变量的空间梯度，则可以显式。使用抽象的Banach空间公式，A-Priori估计值和收敛性在CFL条件下得到证明。开发的三步方案在小应变下找到了连续力学的各种问题的应用。在这里，我们特别考虑了可塑性，粘弹性（蠕变），毛弹性介质的扩散和损害。
An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is thus enhanced by another step for the internal variables which, in general, is implicit, although even this step might be explicit if no spatial gradients of the internal variables are involved. Using an abstract Banach-space formulation, a-priori estimates and convergence are proved under a CFL condition. The developed three-step scheme finds applications in various problems of continuum mechanics at small strain. Here, we consider in particular plasticity, viscoelasticity (creep), diffusion in poroelastic media, and damage.
