A cohesive crack propagation model: Mathematical theory and numerical solution

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Prechtel M, Leugering G, Steinmann P, Stingl M
Zeitschrift: Communications on Pure and Applied Analysis
Verlag: American Institute of Mathematical Sciences (AIMS)
Jahr der Veröffentlichung: 2013
Band: 12
Heftnummer: 4
Seitenbereich: 1705-1729
ISSN: 1534-0392


Abstract


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.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Prechtel, Marina Dr.
Graduiertenzentrum der FAU
Steinmann, Paul Prof. Dr.-Ing.
Lehrstuhl für Technische Mechanik
Stingl, Michael Prof. Dr.
Professur für Angewandte Mathematik (Kontinuierliche Optimierung)


Zusätzliche Organisationseinheit(en)
Exzellenz-Cluster Engineering of Advanced Materials


Forschungsbereiche

A3 Multiscale Modeling and Simulation
Exzellenz-Cluster Engineering of Advanced Materials


Zitierweisen

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://dx.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.

BibTeX: 

Zuletzt aktualisiert 2018-17-10 um 20:10