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A continuation method for rigid‐cohesive fracture in a discontinuous Galerkin finite element setting
Author(s) -
Hirmand M. Reza,
Papoulia Katerina D.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5819
Subject(s) - finite element method , discontinuous galerkin method , discretization , mathematics , robustness (evolution) , lagrange multiplier , minification , energy minimization , penalty method , mathematical optimization , extended finite element method , quasistatic process , mixed finite element method , galerkin method , weak formulation , mathematical analysis , boundary value problem , structural engineering , engineering , physics , biochemistry , chemistry , quantum mechanics , gene
Summary An energy minimization formulation of initially rigid cohesive fracture is introduced within a discontinuous Galerkin finite element setting with Nitsche flux. The finite element discretization is directly applied to an energy functional, whose term representing the energy stored in the interfaces is nondifferentiable at the origin. Unlike finite element implementations of extrinsic cohesive models that do not operate directly on the energy potential, activation of interfaces happens automatically when a certain level of stress encoded in the interface potential is reached. Thus, numerical issues associated with an external activation criterion observed in the previous literature are effectively avoided. Use of the Nitsche flux avoids the introduction of Lagrange multipliers as additional unknowns. Implicit time stepping is performed using the Newmark scheme, for which a dynamic potential is developed to properly incorporate momentum. A continuation strategy is employed for the treatment of nondifferentiability and the resulting sequence of smooth nonconvex problems is solved using the trust region minimization algorithm. Robustness of the proposed method and its capabilities in modeling quasistatic and dynamic problems are shown through several numerical examples.