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We present a barrier method for treating frictional contact on interfaces embedded in finite elements. The barrier treatment has several attractive features, including: (i) it does not introduce any additional degrees of freedom or iterative steps, (ii) it is free of inter-penetration, (iii) it avoids an ill-conditioned matrix system, and (iv) it allows one to control the solution accuracy directly. We derive the contact pressure from a smooth barrier energy function that is designed to satisfy the non-penetration constraint. Likewise, we make use of a smoothed friction law in which the stick-slip transition is described by a continuous function of the slip displacement. We discretize the formulation using the extended finite element method to embed interfaces inside elements, and devise an averaged surface integration scheme that effectively provides stable solutions without traction oscillations. Subsequently, we develop a way to tailor the parameters of the barrier method to embedded interfaces, such that the method can be used without parameter tuning. We verify and investigate the proposed method through numerical examples with various levels of complexity. The numerical results demonstrate that the proposed method is remarkably robust for challenging frictional contact problems, while requiring low cost comparable to that of the penalty method.
We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent arbitrary crack ge
Simulation of contact mechanics in fractured media is of paramount important in the scope of computational mechanics. In this work, a preconditioned mixed-finite element scheme with Lagrange multipliers is proposed in the framework of constrained var
We develop a stable finite difference method for the elastic wave equations in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equations are discretized in second order form by a fourth or sixth o
We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the capillary surf
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved interfaces.