Smoothing methods for convex inequalities and linear complementarity problems
Mathematical Programming: Series A and B
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
A damage model for ductile crack initiation and propagation
Computational Mechanics
Exact corotational shell for finite strains and fracture
Computational Mechanics
A new semi-implicit formulation for multiple-surface flow rules in multiplicative plasticity
Computational Mechanics
Damage-based fracture with electro-magnetic coupling
Computational Mechanics
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We propose alternative methods for performing FE-based computational fracture: a mixed mode extrinsic cohesive law and crack evolution by edge rotations and nodal reposition. Extrinsic plastic cohesive laws combined with the discrete version of equilibrium form a nonlinear complementarity problem. The complementarity conditions are smoothed with the Chen-Mangasarian replacement functions which naturally turn the cohesive forces into Lagrange multipliers. Results can be made as close as desired to the pristine strict complementarity case, at the cost of convergence radius. The smoothed problem is equivalent to a mixed formulation (with displacements and cohesive forces as unknowns). In terms of geometry, our recently proposed edge-based crack algorithm is adopted. Linear control is adopted to determine the displacement/load parameter. Classical benchmarks in computational fracture as well as newly proposed tests are used in assessment with accurate results. In this sense, the proposed solution has algorithmic and accuracy advantages, at a slight penalty in the computational cost. The Sutton crack path criterion is employed in a preliminary path determination stage.