A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly precise virtual elements using a generalization to virtual elements of the node-based uniform strain approach for finite elements. The averaged strain is then used to sample the weak form at the nodes of the mesh leading to a method in which all the field variables, including state and history-dependent variables, are related to the nodes and thus they are tracked only at these locations during the nonlinear computations. Through various elastoplastic benchmark problems, we demonstrate that the NVEM is locking-free while enabling linearly precise virtual elements to solve elastoplastic solids with accuracy.

翻译：本文将最近提出的基于节点的均匀应变虚拟单元法（NVEM）扩展至小应变弹塑性固体。在该方法中，应变通过将有限元中基于节点的均匀应变方法推广至虚拟单元，从周围线性精确虚拟单元的应变在节点处进行平均。随后，平均应变用于在网格节点处对弱形式进行采样，从而形成一种所有场变量（包括状态变量和历史相关变量）均与节点相关的方法，因此在非线性计算过程中仅需在这些位置进行跟踪。通过多种弹塑性基准问题，我们证明NVEM在无锁定的同时，能够使线性精确虚拟单元准确求解弹塑性固体问题。