Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity
Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity
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DOI：
10.1016/j.cma.2014.11.040
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发表时间：
2015-03-01
影响因子：
7.2
通讯作者：
Codina, R.
中科院分区：
文献类型：
--
作者：
Cervera, M.;Chiumenti, M.;Codina, R.
本文提出了一种稳定的混合应变/位移有限元列式的应用，用于解决涉及可压缩和不可压缩塑性的非线性固体力学问题。引入变分多尺度稳定允许使用等阶插值在一个一致的方式。当与标准的、基于位移的、不可约的公式相比时，这样的公式呈现两个优点：（a）它提供应变（和应力）场的增强的收敛速率，以及（B）它能够处理不可压缩的情况。第一个优点也适用于与混合压力/位移公式的比较。本文研究了改进的应变和应力场的影响，涉及应变软化和局部化导致失败的问题，使用低阶有限元连续应变和位移场（P1 P1三角形或四面体和Q1 Q1四边形，六面体，三棱柱）结合关联摩擦Drucker-Prager塑性模型。可压缩和几乎不可压缩的变形模式下的应变/位移制剂的性能进行评估，并与以前提出的压力/位移制剂。基准数值算例表明，混合配方的能力，正确预测故障机制与局部模式的应变，几乎没有任何依赖的网格方向偏差。不需要辅助裂纹跟踪技术。(c)2014爱思唯尔有限公司版权所有。
This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) field and (b) it is able to deal with incompressible situations. The first advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the effect of the improved strain and stress fields in problems involving strain softening and localization leading to failure, using low order finite elements with continuous strain and displacement fields (P1P1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker-Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary. (c) 2014 Elsevier B.V. All rights reserved.