Exact corotational shell for finite strains and fracture

Engineering Fracture Mechanics

Dias-da-Costa

2013

Self Cite

214

Please cite this article as: Areias, P., Rabczuk, T., Dias-da-Costa, D., Element-wise fracture algorithm based on rotation of edges, Engineering Fracture Mechanics (2013), doi: http://dx.doi.org/10.1016/j.engfracmech. 2013.06.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Element-wise fracture algorithm based on rotation of edges AbstractWe propose an alternative, simpler algorithm for FEM-based computational fracture in brittle, quasibrittle and ductile materials based on edge rotations. Rotation axes are the crack front edges (respectively nodes in surface discretizations) and each rotated edge affects the position of only one or two nodes. Modified positions of the entities minimize the difference between the predicted crack path (which depends on the specific propagation theory in use) and the edge or face orientation. The construction of all many-to-many relations between geometrical entities in a finite element code motivates operations on existing entities retaining most of the relations, in contrast with remeshing (even tip remeshing) and enrichment which alter the structure of the relations and introduce additional entities to the relation graph (in the case of XFEM, enriched elements which can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding). In this sense, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives and the approach is independent of the underlying element used for discretization. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, two prototype models are used: tip energy dissipation (LEFM) and cohesive-zone approaches. The Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/deflection accuracy. Nomenclature

Section: Principle Of Virtual Power For Cracked Bodies With Cohesive mentioning

confidence: 99%

“…Units correspond, in the original paper, to the British Imperial System but for uniformity we indicate them as "consistent". Our recent corotational shell element is adopted [11] with multiplicative plasticity (cf. [10]).…”

Section: Pressure Vessel Fracture With Slotmentioning

confidence: 99%

Element-wise fracture algorithm based on rotation of edges

Engineering Fracture Mechanics

Dias-da-Costa

2013

Self Cite

214

“…The second variation of a present in (3) is determined by the previous quantities (9) and (10). Using index notation, it results…”

Section: Independent Constraintsmentioning

confidence: 99%

“…Both T %l and b %l are sparse, but with different properties: in the sparse T % -matrices there are 1's for degrees-of-freedom that remain active and in the sparse b % -vectors these will be 0. This perspective of interconnected 9 constraints is motivated by classical static analysis. Fill-in (or profile) concerns during Gauss decomposition are described in earlier works [1,38,17] but can now be attenuated 10 with the Approximate Minimum Degree (AMD) [3] and, in a lesser extent, with profile compressors (such as the one of Kumfert and Pothen [28]).…”

Section: Interconnected Constraintsmentioning

confidence: 99%

See 1 more Smart Citation

Implicit solutions with consistent additive and multiplicative components

Finite Elements in Analysis and Design

Dias-da-Costa

et al. 2012

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a b s t r a c tThis work describes an algorithm and corresponding software for incorporating general nonlinear multiple-point equality constraints in a implicit sparse direct solver. It is shown that direct addressing of sparse matrices is possible in general circumstances, circumventing the traditional linear or binary search for introducing (generalized) constituents to a sparse matrix. Nested and arbitrarily interconnected multiple-point constraints are introduced by processing of multiplicative constituents with a built-in topological ordering of the resulting directed graph. A classification of discretization methods is performed and some re-classified problems are described and solved under this proposed perspective. The dependence relations between solution methods, algorithms and constituents becomes apparent. Fracture algorithms can be naturally casted in this framework. Solutions based on control equations are also directly incorporated as equality constraints. We show that arbitrary constituents can be used as long as the resulting directed graph is acyclic. It is also shown that graph partitions and orderings should be performed in the innermost part of the algorithm, a fact with some peculiar consequences. The core of our implicit code is described, specifically new algorithms for direct access of sparse matrices (by means of the clique structure) and general constituent processing. It is demonstrated that the graph structure of the second derivatives of the equality constraints are cliques (or pseudoelements) and are naturally included as such. A complete algorithm is presented which allows a complete automation of equality constraints, avoiding the need of pre-sorting. Verification applications in four distinct areas are shown: single and multiple rigid body dynamics, solution control and computational fracture.

Finite strain fracture of plates and shells with configurational forces and edge rotations

Numerical Meth Engineering

2013

Self Cite

231

SUMMARYWe propose a simple and efficient algorithm for FEM‐based computational fracture of plates and shells with both brittle and ductile materials on the basis of edge rotation and load control. Rotation axes are the crack front nodes, and each crack front edge in surface discretizations affects the position of only one or two nodes. Modified positions of the entities maximize the modified mesh quality complying with the predicted crack path (which depends on the specific propagation theory in use). Compared with extended FEM or with classical tip remeshing, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives, and the approach is independent of the underlying element used for discretization. For history‐dependent materials, there are still some transfer of relevant quantities between elements. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, three prototype models are used: tip energy dissipation linear elastic fracture mechanics (LEFM), cohesive‐zone approaches, and ductile fracture. Both the Sutton crack path criterion and the path estimated by the Eshelby tensor are employed. Traditional fracture benchmarks, including one with plastic hinges, and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load ∕ deflection accuracy. Copyright © 2013 John Wiley & Sons, Ltd.