A shape-topological control problem for nonlinear crack-defect interaction: The antiplane variational model

Leugering G, Kovtunenko V (2016)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2016

Journal

Publisher: Society for Industrial and Applied Mathematics Publications

Book Volume: 54

Pages Range: 1329-1351

Journal Issue: 3

DOI: 10.1137/151003209

Abstract

We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a micro-object (defect) and a macro-object (crack) modeled in two dimensions. The corresponding nonlinear optimization problem subject to inequality constraints at the crack is considered within a general variational framework. For the reason of asymptotic analysis, singular perturbation theory is applied, resulting in the topological sensitivity of an objective function representing the release rate of the strain energy. In the vicinity of the nonlinear crack, the antiplane strain energy release rate is expressed by means of the mode-III stress intensity factor that is examined with respect to small defects such as microcracks, holes, and inclusions of varying stiffiness. The result of shape-topological control is useful either for arrests or rise of crack growth.

Authors with CRIS profile

Additional Organisation(s)

Involved external institutions

How to cite

APA:

Leugering, G., & Kovtunenko, V. (2016). A shape-topological control problem for nonlinear crack-defect interaction: The antiplane variational model. SIAM Journal on Control and Optimization, 54(3), 1329-1351. https://doi.org/10.1137/151003209

MLA:

Leugering, Günter, and Viktor Kovtunenko. "A shape-topological control problem for nonlinear crack-defect interaction: The antiplane variational model." SIAM Journal on Control and Optimization 54.3 (2016): 1329-1351.

BibTeX: Download