A plasticity formulation for the Hybrid Virtual Element Method (HVEM) is presented. The main features include the use of an energy norm for the VE projection, a high-order divergence-free interpolation for stresses and a piecewise constant interpolation for plastic multipliers within element subdomains. The HVEM does not require any stabilization term, unlike classical VEM formulations which are affected by the choice of stabilization parameters. The algorithmic tangent matrix is derived consistently and analytically. A standard strain-driven formulation and a Backward-Euler time integration scheme are adopted. The return mapping process for the stress evaluation is formulated at the element level to preserve the stress interpolation as plasticity evolves. Even though general constitutive laws can be readily considered, to test the robustness of HVEM, an elastic-perfectly plastic behavior is adopted. In such a case, the return mapping process is efficiently solved using a Sequential Quadratic Programming Algorithm. The solution is free from volumetric locking and from spurious hardening effects that are observed in stabilized VEM. The numerical results confirm the accuracy of HVEM for rough meshes and high rate of convergence in recovering the collapse load.

中文翻译：

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用于准确分析 2D 弹塑性问题的无稳定混合虚拟元公式


提出了混合虚拟元法 （HVEM） 的塑性公式。其主要特点包括对 VE 投影使用能量模，对应力进行高阶无发散插值，对单元子域内塑性乘数进行分段常数插值。HVEM 不需要任何稳定项，这与经典的 VEM 公式不同，后者受稳定参数选择的影响。算法切线矩阵是一致且分析地推导的。采用标准的应变驱动公式和 Backward-Euler 时间积分方案。应力评估的返回映射过程是在单元级别制定的，以便在塑性演变时保持应力插值。尽管可以很容易地考虑一般的本构定律，但为了测试 HVEM 的稳健性，采用了弹性完美塑性行为。在这种情况下，使用 Sequential Quadratic Programming Algorithm 可以有效地解决 return mapping 过程。该解决方案没有在稳定的 VEM 中观察到的体积锁定和虚假硬化效应。数值结果证实了 HVEM 对粗网格的准确性和恢复塌陷载荷的高收敛率。