发表机构
IMDEA Materials Institute; Universidad Politécnica de Madrid（IMDEA材料研究所; 马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种变分一致、稳定的节点应变有限元方法，适用于小变形和有限应变，通过混合变分原理和假定应变算子实现纯原始公式，并证明其在频繁重网格和非弹性材料问题中能最小化内部变量扩散。
AI 中文摘要
本文介绍了使用变分一致、稳定的节点应变有限元公式对小变形和有限应变力学进行离散化。我们证明了这些方法源于一个混合变分原理，该原理对原始变量和对偶变量使用不同的网格。我们证明，对于这两种力学问题，节点应变有限元可以写成带有假定应变算子的纯原始公式。稳定性项被证明是必要的，并为有限应变范围提出了一类新的、通用的稳定函数。由此产生的公式可以被解释为纯粒子方法，因为所有运动学和材料信息都存储在节点上。这一观点解释了节点应变方法在需要频繁重网格且涉及非弹性材料的问题中所具有的有利特性。在这些情况下，内部变量的扩散被保持在最低限度。所提供的数值示例验证了这些论断。
英文摘要
We present in this article the discretization of small and finite strain mechanics using variationally consistent, stabilized, nodal strain finite element formulations. We prove that these methods derive from a mixed variational principle that uses different meshes for the primal and dual variables. We demonstrate that, for both mechanical problems, nodal strain finite elements can be written as pure primal formulations with assumed strain operators. The stabilization terms are shown to be necessary and a new, general class of stabilizing functions is proposed for the finite strain regime. The ensuing formulations can be interpreted as pure particle methods because all kinematic and material information is stored at the nodes. This point of view explains the favorable properties of nodal strain methods when employed in problems that require frequent remeshing and involve inelastic materials. In these cases, the diffusion of internal variables is kept to a minimum. The numerical examples presented validate the claims.
