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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…
We outline a phenomenological model to assess friction at the interface between two bodies in mutual contact. Although the approach is general, the application inspiring the approach is the Discrete Element Method. The kinematics of the…
We formulate and analyze a Nitsche-type algorithm for frictional contact problems. The method is derived from, and analyzed as, a stabilized finite element method and shown to be quasi-optimal, as well as suitable as an adaptive scheme…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
A method to treat frictional contact problems along embedded surfaces in the finite element framework is developed. Arbitrarily shaped embedded surfaces, cutting through finite element meshes, are handled by the X-FEM. The frictional…
Contact algorithm between different bodies plays an important role in solving collision problems. Usually it is not easy to be treated very well. Several ones for material point method were proposed by Bardenhangen, Brackbill, and…
We study the frictional adhesive contact of a rigid insulating sphere sliding past a multiferroic coating deposed onto a rigid substrate, based on the hybrid element method (HEM). The adhesion behavior is described based on the…
Design optimization problems, e.g., shape optimization, that involve deformable bodies in unilateral contact are challenging as they require robust contact solvers, complex optimization methods that are typically gradient-based, and…
This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the…
In this paper we review the simulation method of the non-smooth contact dynamics. This technique was designed to solve the unilateral and frictional contact problem for a large number of rigid bodies and has proved to be especially valuable…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an…
In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact…
In this work, we analyse a simplified frictional contact problem and its variational formulation that has a form of the elliptic variational inequality of the second kind. For this problem, we consider a numerical approximation based on…
With the increasing demand for the accuracy of numerical simulation of pavement mechanics, the variational inequality model and its induced finite element method which can simulate the interlayer contact state becomes a potential solution.…
In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Accurately handling contact with friction remains a core bottleneck for Material Point Method (MPM), from reliable contact point detection to enforcing frictional contact laws (non-penetration, Coulomb friction, and maximum dissipation…
A fractured poroelastic body is considered where the opening of the fractures is governed by a nonpenetration law while slip is described by a Coulomb-type friction law. This physical model results in a nonlinear variational inequality…
Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact problem on the internal interfaces can be computationally…