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.
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Austria (AT)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.
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