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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用于精确分析二维弹塑性问题的无稳定化混合虚拟单元公式


提出了混合虚拟元法 (HVEM) 的塑性公式。主要特征包括使用 VE 投影的能量范数、应力的高阶无散插值以及单元子域内塑性乘数的分段常数插值。与受稳定参数选择影响的经典 VEM 公式不同，HVEM 不需要任何稳定项。算法正切矩阵是通过一致和分析得出的。采用标准应变驱动公式和后向欧拉时间积分方案。应力评估的返回映射过程是在单元级别制定的，以随着塑性的变化保留应力插值。尽管可以很容易地考虑一般本构定律，但为了测试 HVEM 的鲁棒性，采用了完美弹塑性行为。在这种情况下，可以使用顺序二次规划算法有效地解决返回映射过程。该解决方案不会出现在稳定 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 对于粗糙网格的准确性以及恢复崩溃载荷的高收敛率。