Topological Sensitivity Analysis: Theory and Applications

Abstract

The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks (Novotny A.A. and Sokolowski J., Topological Derivatives in Shape Optimization. Interaction of Mechanics and Mathematics Series. Springer, 2013). This relatively new concept has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In this talk, the topological derivative concept is presented, together with a portfolio of applications in the context of topology optimization, inverse problems and fracture mechanics.