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Block coordinate descent energy minimization for dynamic cohesive fracture
- Source :
- Computer Methods in Applied Mechanics and Engineering. 354:663-688
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- A block coordinate descent algorithm within a discontinuous Galerkin finite element formulation is proposed for both explicit and implicit energy minimization in solid bodies in which rigid-cohesive fractures initiate and propagate. The crack opening dependent Barenblatt type surface cohesive energy function is non-differentiable at the origin. In each iteration or each explicit update, the algorithm minimizes the potential with respect to each crack opening displacement unknown and with respect to the block of deformation unknowns, sequentially. This decomposes minimization of the full non-differentiable problem into a number of “small” non-differentiable sub-problems that must be solved locally at the inter-element boundaries of the finite element mesh and an “easy” differentiable sub-problem that characterizes global equilibrium. As a result, non-differentiability is effectively treated locally and the algorithm can be easily incorporated into standard finite element codes. On the basis of a convexity analysis of the proposed non-differentiable energy functional, we obtain a minimum cohesive process zone resolution criterion, known empirically in the previous literature as a requirement for capturing the amount of dissipated fracture energy correctly. The method is free of any regularization parameters and preserves the discrete nature of fracture without introducing a stress discontinuity at initiation of decohesion. Robustness of the method is shown through several numerical examples of fragmentation and branching and through comparisons with existing numerical and experimental results.
- Subjects :
- Computer science
Mechanical Engineering
Computational Mechanics
General Physics and Astronomy
Fracture mechanics
02 engineering and technology
Energy minimization
01 natural sciences
Convexity
Finite element method
Computer Science Applications
010101 applied mathematics
020303 mechanical engineering & transports
0203 mechanical engineering
Mechanics of Materials
Discontinuous Galerkin method
Applied mathematics
Differentiable function
0101 mathematics
Coordinate descent
Energy functional
Subjects
Details
- ISSN :
- 00457825
- Volume :
- 354
- Database :
- OpenAIRE
- Journal :
- Computer Methods in Applied Mechanics and Engineering
- Accession number :
- edsair.doi...........1b97d5eaec55605499527971e18c0891