The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. VEM applied to linear elasticity problems is now well established. Nonlinear problems involving plasticity and hyperelasticity have also been explored by researchers using VEM. Clearly, techniques for extending the method to nonlinear problems are attractive. In this work a novel first order consistent virtual element method is applied within a static co-rotational framework. To the author's knowledge this has not appeared before in the literature with virtual elements. The formulation allows for large displacements and large rotations in a small strain setting. For some problems avoiding the complexity of finite strains, and alternative stress measures, is warranted. Furthermore, small strain plasticity is easily incorporated. The basic method, VEM specific implementation details for co-rotation, and representative benchmark problems are illustrated. Consequently, this research demonstrates that the co-rotational VEM formulation successfully solves certain classes of nonlinear solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.

翻译：虚拟单元法（VEM）允许在二维问题域中使用多边形进行离散。这些多边形可具有任意数量的边，且可为凹形或凸形。这些特性尤其适用于复杂几何的网格划分。目前，VEM在线弹性问题中的应用已相当成熟。研究者们也已利用VEM探索了涉及塑性和超弹性的非线性问题。显然，将VEM扩展至非线性问题的技术具有重要吸引力。本文首次将一阶一致虚拟单元法应用于静态共旋框架内。据作者所知，此前文献中尚未出现虚拟单元与此框架的结合。该公式允许在小应变条件下处理大位移与大转动。针对某些问题，避免有限应变复杂性及替代应力度量是合理的。此外，小应变塑性可轻松整合。本文详细阐述了基础方法、共旋框架下的VEM特定实现细节，并展示了代表性基准测试问题。研究结果表明，共旋VEM公式成功求解了某类非线性固体力学问题。最后，本文讨论了当前公式的结果及未来研究方向。