We present a B-bar formulation of the virtual element method (VEM) for the analysis of both nearly incompressible and compressible materials. The material stiffness is decomposed into dilatational and deviatoric parts, and only the deviatoric part of the material stiffness is utilized for stabilization of the element stiffness matrix. A feature of the formulation is that locking behavior for nearly incompressible materials is successfully removed by the spectral decomposition of the material stiffness. The eigenvalue analysis demonstrates that the method eliminates higher energy modes associated with locking behavior for nearly incompressible materials, while capturing constant strain energy modes for both compressible and nearly incompressible materials. The convergence and accuracy of the B-bar VEM are discussed using 2D and 3D examples with various element shapes (convex and non-convex).

中文翻译：

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几乎不可压缩和可压缩材料的B-bar虚拟单元法

我们提出了虚拟元法 (VEM) 的 B-bar 公式，用于分析几乎不可压缩和可压缩的材料。材料刚度分解为膨胀部分和偏部分，仅利用材料刚度的偏部分来稳定单元刚度矩阵。该公式的一个特点是几乎不可压缩材料的锁定行为可以通过材料刚度的谱分解成功消除。特征值分析表明，该方法消除了与几乎不可压缩材料的锁定行为相关的较高能量模式，同时捕获了可压缩和几乎不可压缩材料的恒定应变能量模式。