Extended mortar method for contact and mesh-tying applications

Abstract : In this work we develop a set of methods to handle tying and contact problems along real and virtual (embedded) surfaces in the framework of the finite element method. The first objective is to elaborate an efficient and fully consistent three-dimensional mortar formulation using the monolithicaugmented Lagrangian method (ALM) to treat frictional contact problems. Variousaspects of the numerical treatment of contact are discussed: detection, discretization, accurate evaluation of mortar integrals (projections, clipping, triangulation), the parallelization on distributedmemory architectures and optimization of convergence for problems involving both contact and material non-linearities. With mortar methods being drawn from the domain decomposition methods, the mesh tying problems for the class on non-matching interfaces is also presented.A new two-dimensional MorteX framework, which combines features of the extended finite element method (X-FEM) and the classical mortar methods is elaborated. Within this framework, mesh tying between overlapping domains and contact between embedded (virtual) boundaries can be treated. However, in this setting, severe manifestation of mesh locking phenomenon can take place under specific problem settings both for tying and contact. Stabilization techniques such as automatic triangulation of blending elements and coarse-grained Lagrange multiplier spaces are proposed to overcome these adverse effects. In addition, the coarse graining of Lagrange multipliers was proven to be useful for classical mortar methods, which is illustrated with relevant numericalexamples.The MorteX framework is used to treat frictional wear problems. Within this framework the contact surface evolution as a result of material removal due to wear is modeled as an evolving virtual surface. Use of MorteX method circumvents the need for complex remeshing techniques to account for contact surface evolution. The proposed methods are developed and implemented in the in-house finite element suite Z-set. Numerous numerical examples are considered to validate the implementation and demonstrate the robustness, performance and accuracy of the proposed methods.
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Basava Raju Akula. Extended mortar method for contact and mesh-tying applications. Mechanics of materials [physics.class-ph]. PSL Research University, 2019. English. ⟨NNT : 2019PSLEM003⟩. ⟨tel-02200516⟩

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