New Inequality and Functional for Contact with Friction: The Implicit Standard Material Approach∗
New Inequality and Functional for Contact with Friction: The Implicit Standard Material Approach∗
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DOI：
10.1080/08905459108905146
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
G. Saxcé;Zhi-Qiang Feng
中科院分区：
文献类型：
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作者：
G. Saxcé;Zhi-Qiang Feng
本文主要研究具有库仑摩擦、准静力平衡和小位移的二维或三维弹性接触问题。经典的方法是基于两个最小原则，或变分不等式：第一个是单边接触，第二个是摩擦。在实际应用中，这导致算法交替求解两个问题，直到达到收敛。提出了一种仅使用一个原理或一个不等式的耦合方法。这种新方法基于一种称为隐式标准的材料模型，允许将正态性定律的概念扩展到具有非相关流动规则（如表面摩擦）的耗散行为。对于这些规律的数值时间积分，采用莫罗隐式方法。利用增广拉格朗日技术对不可微势进行正则化。本文报道了采用有限元方法的离散化公式及其数值应用。
Abstract This paper is devoted to the analysis of the two- or three-dimensional elastic contact problem with Coulomb friction, quasi-static equilibrium, and small displacements. The classical approach is based on two minimum principles, or variational inequalities: the first for unilateral contact and the second for friction. In practical applications, this leads to an algorithm of alternately solving the two problems until convergence is achieved. A coupled approach using one principle or one inequality only is presented. This new approach, based on a model of material called implicit standard, allows for extension of the notion of a normality law to dissipative behavior with a nonassociated flow rule, such as surface friction. For numerical time integration of the laws, Moreau's implicit method is considered. Nondifferentiable potentials are regularized by means of the augmented Lagrangian technique. A discretized formulation using the finite element method and numerical applications are reported in a s...