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Hybrid-mixed stress finite element models in elastoplastic analysis

机译：弹塑性分析中的混合混合应力有限元模型

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摘要

A hybrid-mixed stress finite element formulation for the elastoplastic analysis of stretching plates is presented. This model is characterized by the simultaneous and independent approximation of both the stress and the displacement fields in the domain and of the displacement field on the static boundary. To model the local phenomena associated with plasticity, the plastic parameter increments are also directly approximated. The plastic flow and the kinematic boundary conditions are locally satisfied. The remaining fundamental equations are enforced in a weighted residual form so designed as to ensure that the discrete model presents all relevant properties of the continuous system, namely the static-kinematic duality, elastic reciprocity and associated plasticity. The orthogonal Legendre polynomials are used as approximation functions for the stress and the displacements fields. Dirac functions and non-negative polynomial functions are used to model the plastic parameter increments. The model presented here assumes a quasi-static and geometrically linear response. The elastoplastic constitutive relations are uncoupled into elastic and plastic deformation modes and both the Von Mises and the Drucker-Prager yield criteria have been implemented. The non-linear governing system is solved using the Newton-Raphson method. To validate the hybrid-mixed stress model and to assess its performance and accuracy, a set of numerical test cases is presented and discussed.
机译：提出了用于拉伸板弹塑性分析的混合混合应力有限元公式。该模型的特征是在区域内的应力和位移场以及静态边界上的位移场同时且独立地近似。为了模拟与可塑性相关的局部现象，可塑性参数的增量也可以直接估算出来。塑性流动和运动学边界条件是局部满足的。其余的基本方程式以加权残差形式执行，以确保离散模型显示连续系统的所有相关属性，即静态运动对偶性，弹性互易性和相关可塑性。正交勒让德多项式被用作应力场和位移场的近似函数。 Dirac函数和非负多项式函数用于对塑性参数增量进行建模。这里介绍的模型假定为准静态和几何线性响应。弹塑性本构关系解耦为弹性和塑性变形模式，并且已经实现了冯·米塞斯（Von Mises）和德鲁克-普拉格（Drucker-Prager）屈服准则。使用牛顿-拉夫森法求解非线性控制系统。为了验证混合混合应力模型并评估其性能和准确性，提出并讨论了一组数值测试案例。

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