The evaluation of structural integrity involves the determination of a limit state. If there is plasticity, limit analysis theory takes place. The aim of this paper is to present a limit analysis formulation considering friction at the contact interface. The deduction of this formulation involves the study of contact mechanics, unilateral conditions at normal direction and a slipping rule for the tangential direction. Concerning the contact between a rigid and a deformable body, at limit state there is permanent contact between the bodies and the contact length is supposed known. These hypotheses enable the development of a limit analysis formulation considering friction dissipation. The solution of a limit analysis problem is based on duality between the static, kinematic, mixed and the set of optimum conditions and its relation with the solution of a non-linear programming optimization problem with constraints. The solution is based on Newton method with contraction and relaxation techniques, associated with condensation technique to solve the linear complementarity problem at contact. As an application, the influence of friction coefficient at tool-specimen interface on the wedge indentation is evaluated.

中文翻译：

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极限分析和摩擦接触：公式和数值解

结构完整性的评估涉及极限状态的确定。如果存在可塑性，就会产生极限分析理论。本文的目的是提出一个考虑接触界面摩擦的极限分析公式。该公式的推导涉及接触力学、法向单边条件和切向滑动规则的研究。关于刚性物体和可变形物体之间的接触，在极限状态下，物体之间存在永久接触，并且接触长度应该是已知的。这些假设有助于开发考虑摩擦耗散的极限分析公式。极限分析问题的解决方案基于静态、运动、混合和最佳条件集及其与具有约束的非线性规划优化问题的解决方案的关系。该解决方案基于牛顿法，采用收缩和松弛技术，结合缩合技术来解决接触时的线性互补问题。作为应用，评估了工具-试样界面处的摩擦系数对楔形压痕的影响。