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Critical friction for wedged configurations

机译：楔形结构的临界摩擦

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A wedged configuration with Coulomb friction is a nontrivial equilibrium state of a linear elastic body in a frictional unilateral contact with a rigid body under vanishing external loads. We analyze here the relation between the geometry of the elastic body and the friction coefficient for which wedged configurations exist in a 3-D context. The critical friction coefficient, mu(w), is defined as the infimum of a supremal functional defined on the set of admissible normal displacement and tangential stresses. For friction coefficients mu with mu > mu(w) the wedged problem has at least a solution and for mu < mu(w) there exits no wedged configurations. For the in-plane problem we discuss the link between the critical friction and the smallest real eigenvalue mu(s) which is related to the loss of uniqueness. The wedged problem is stated in a discrete framework using a mixed finite element approach and the (discrete) critical friction coefficient mu(w)(h) is introduced as the solution of a global minimization problem involving a non differentiable and non-convex functional. The existence of Phi(*)(h), the displacement field of a critical wedged state, is proved and a specific numerical method, based on a genetic algorithm, was developed to compute the critical wedged configurations. Some techniques to handle the discontinuities of the normal vector on the contact surface are presented and the analysis is illustrated with three numerical simulations. (c) 2007 Elsevier Ltd. All rights reserved.
机译：具有库仑摩擦的楔形结构是线性弹性体在消失的外部载荷下与刚体的摩擦单侧接触的非平凡平衡状态。我们在这里分析弹性体的几何形状与摩擦系数之间的关系，对于该摩擦系数，在3-D环境中存在楔形构造。临界摩擦系数mu（w）定义为在允许的法向位移和切向应力集合上定义的最高功能的最小值。对于mu> mu（w）的摩擦系数mu，楔形问题至少具有一个解，对于mu

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