Towards optimization of crack resistance of composite materials by adjustment of fiber shapes

Prechtel, M., Leugering, G., Steinmann, P. and Stingl, M. (2011) Towards optimization of crack resistance of composite materials by adjustment of fiber shapes. Engineering Fracture Mechanics, 78(6), pp. 944-960. (doi: 10.1016/j.engfracmech.2011.01.007)

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Abstract

We investigate the evolution and propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. In addition to the classical variational formulation, where the standard potential energy is minimized over the cracked domain under physical conditions characterizing the behavior of the material close to the crack (e.g. non-penetration conditions), we include a ‘cohesive traction term’ in the energy expression. In this way we obtain a mathematically concise set of partial differential equations with non-linear boundary conditions at the crack interfaces. We perform a finite element discretization using a combination of standard continuous finite elements and so-called cohesive elements. During the simulation process cohesive elements are adaptively inserted at positions where a certain stress bound is exceeded. In our numerical studies we consider domains consisting of a matrix material with fiber inclusions. Beyond pure crack path simulation, our ultimate goal is to determine an optimal shape of the fibers resulting in a crack path that releases for a given load scenario as much energy as possible without destroying the specimen completely. We develop a corresponding optimization model and propose a solution algorithm for the same. The article is concluded by numerical results.

Item Type:Articles
Additional Information:The authors gratefully acknowledge the funding of the German Research Council (DFG), which, within the framework of its ‘Excellence Initiative’ supports the Cluster of Excellence ‘Engineering of Advanced Materials’ at the University of Erlangen-Nuremberg.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Prechtel, M., Leugering, G., Steinmann, P., and Stingl, M.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Engineering Fracture Mechanics
Publisher:Elsevier
ISSN:0013-7944
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