Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation
ISSN: 0264-4401
Article publication date: 6 September 2021
Issue publication date: 4 March 2022
Abstract
Purpose
The aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.
Design/methodology/approach
The cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.
Findings
When compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.
Originality/value
This work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.
Keywords
Acknowledgements
The authors gratefully acknowledge the important support of the Brazilian research agencies CAPES (in Portuguese “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior”), FAPEMIG (in Portuguese “Fundação de Amparo à Pesquisa de Minas Gerais” - Grant APQ-01656-18) and CNPq (in Portuguese “Conselho Nacional de Desenvolvimento Científico e Tecnológico”) - Grants 304211/2019-2, 437639/2018-5 and 311663/2017-6.
Citation
Campos, B.C., Barros, F.B. and Penna, S.S. (2022), "Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation", Engineering Computations, Vol. 39 No. 3, pp. 1134-1160. https://doi.org/10.1108/EC-01-2021-0029
Publisher
:Emerald Publishing Limited
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