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An Adaptive h-Refinement Algorithm for Local Damage Models
Department of Engineering Science and Mechanics, The Pennsylvania State University, 212 EES Building, University Park, PA 16802, USA
* Author to whom correspondence should be addressed.
Received: 30 April 2009; in revised form: 18 September 2009 / Accepted: 28 September 2009 / Published: 6 October 2009
Abstract: An adaptive mesh refinement strategy is proposed for local damage models that often arise from internal state variable based continuum damage models. The proposed algorithm employs both the finite element method and the finite difference method to integrate the equations of motion of a linear elastic material with simple isotropic microcracking. The challenges of this problem include the time integration of coupled partial differential equations with time-dependent coefficients, and the proper choice of solution spaces to yield a stable finite element formulation. Discontinuous elements are used for the representation of the damage field, as it is believed that this reduction in regularity is more consistent with the physical nature of evolving microcracking. The adaptive mesh refinement algorithm relies on custom refinement indicators, two of which are presented and compared. The two refinement indicators we explore are based on the time rate of change of the damage field and on the energy release rate, respectively, where the energy release rate measures the energy per unit volume available for damage to evolve. We observe the performance of the proposed algorithm and refinement indicators by comparing the predicted damage morphology on different meshes, hence judging the capability of the proposed technique to address, but not eliminate, the mesh dependency present in the solutions of the damage field.
Keywords: adaptive mesh refinement; damage-based refinement indicators; dynamic fracture; discontinuous-Galerkin finite element methods; continuum damage mechanics
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Pitt, J.S.; Costanzo, F. An Adaptive h-Refinement Algorithm for Local Damage Models. Algorithms 2009, 2, 1281-1300.
Pitt JS, Costanzo F. An Adaptive h-Refinement Algorithm for Local Damage Models. Algorithms. 2009; 2(4):1281-1300.
Pitt, Jonathan S.; Costanzo, Francesco. 2009. "An Adaptive h-Refinement Algorithm for Local Damage Models." Algorithms 2, no. 4: 1281-1300.