| In recent years, problems involving the mechanical contact between deformable bodies have received increasing attention from the computational solid mechanics community. Such problems, usually called contact problems, are particularly challenging in the presence of large deformations and inelastic response, as are found, for example, in dynamic impacts between bodies, metal forming applications, mechanical (hardness) testing, and post buckling response. The introduction of friction is an additional complication which has important consequences, both in the underlying mathematical structure of the problem and in the design of efficient solution algorithms.; In this work, a new comprehensive approach is presented which enables the solution of frictional contact problems within a Lagrangian framework. The approach is suitable for the solution of static or low frequency dynamic problems using implicit time integration. Novel features of the work include: (1) a continuum basis for the formulation, making it suitable for arbitrary discretizations and two or three spatial dimensions; (2) the presence of an exact linearization for the discrete global equations, such that optimal convergence properties are attained when using a Newton-Raphson strategy for solving the nonlinear equation system; and (3) penalty and augmented Lagrangian enforcement of constraints, leading to efficient solution of the global equations while circumventing ill-conditioning. The augmented Lagrangian treatment presented includes a reliable algorithmic symmetrization of the frictional response, lending the formulation a high level of compatibility with existing structural and solid mechanics finite element codes.; In presenting the proposed formulation, many details of the discretization process are given, including explicit expressions for the contact contributions to the global equation system. A full set of numerical simulations, demonstrating the utility of the proposed methodology, is also presented. |
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