Prechtel M, Leugering G, Steinmann P, Stingl M (2013)
Publication Type: Journal article, Original article
Publication year: 2013
Publisher: American Institute of Mathematical Sciences (AIMS)
Book Volume: 12
Pages Range: 1705-1729
Journal Issue: 4
DOI: 10.3934/cpaa.2013.12.1705
We investigate the propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. As we take cohesive effects along the crack path into account and impose a non-penetration condition, inequalities appear in the constitutive equations describing the elastic behavior of a domain with crack. In contrast to existing approaches, we consider cohesive effects arising from crack opening in normal as well as in tangential direction. We establish a constrained energy minimization problem and show that the solution of this problem satisfies the set of constitutive equations. In order to solve the energy minimization problem numerically, we apply a finite element discretization using a combination of standard continuous finite elements with so-called cohesive elements. A particular strength of our method is that the crack path is a result of the minimization process. We conclude the article by numerical experiments and compare our results to results given in the literature.
APA:
Prechtel, M., Leugering, G., Steinmann, P., & Stingl, M. (2013). A cohesive crack propagation model: Mathematical theory and numerical solution. Communications on Pure and Applied Analysis, 12(4), 1705-1729. https://doi.org/10.3934/cpaa.2013.12.1705
MLA:
Prechtel, Marina, et al. "A cohesive crack propagation model: Mathematical theory and numerical solution." Communications on Pure and Applied Analysis 12.4 (2013): 1705-1729.
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