对数应变框架下有限弹塑性变形的混合高阶方法
A Hybrid High-Order method for finite elastoplastic deformations within a logarithmic strain framework
AI总结：
针对对数应变框架下的有限塑性变形问题，提出一种支持多面体网格且无体积锁定的混合高阶（HHO）方法，通过局部静凝消除多余未知量以保证对称切线矩阵，经多组基准测试验证了其有效性与工业软件对比的一致性。
摘要：
我们设计并数值评估了一种用于对数应变框架内有限塑性的混合高阶（HHO）方法。HHO方法使用网格骨架上阶数为$k\ge1$的分段多项式作为离散未知量，连同可通过静凝在局部消除的基于单元的多项式。HHO方法导出原初公式，支持具有非匹配界面的多面体网格，无体积锁定，本构定律的积分仅在基于单元的求积节点上执行，且Newton法中的切线矩阵是对称的。此外，虚功原理在局部通过平衡牵引力得到满足。展示了各种二维和三维基准测试，并与使用协调和混合有限元的工业软件的已知解进行了比较。
英文摘要：
We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The HHO method leads to a primal formulation, supports polyhedral meshes with non-matching interfaces, is free of volumetric locking, the integration of the behavior law is performed only at cell-based quadrature nodes, and the tangent matrix in Newton's method is symmetric. Moreover, the principle of virtual work is satisfied locally with equilibrated tractions. Various two- and three-dimensional benchmarks are presented, as well as comparison against known solutions with an industrial software using conforming and mixed finite elements.
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