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A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities. (English) Zbl 1126.74050
Summary: We introduce a discontinuous finite element method for computational modelling of strong and weak discontinuities in geometrically nonlinear elasticity. The location of the interface is independent of the mesh structure, and therefore discontinuous elements are introduced to capture the jump in the deformation map or its gradient, respectively. To model strong discontinuities, the cohesive crack concept is adopted. The inelastic material behaviour is covered by a cohesive constitutive law, which associates the cohesive tractions, acting on the crack surfaces, with the jump in the deformation map. In the case of weak discontinuities an extended Nitsche’s method is applied, which ensures the continuity of deformation map in a weak sense. The applicability of the proposed method is highlighted by means of numerical examples, dealing with both crack propagation and material interfaces.
74S05Finite element methods in solid mechanics
74R10Brittle fracture
74B20Nonlinear elasticity