Relation Between Eshelbyan Mechanics and Topological Derivative Concept
The Pólya-Szegö polarization tensor, introduced in 1951, naturally appears on the famous Eshelby problem, also referred to as Eshelby theorem. This problem, formulated by Eshelby in 1957 and 1959, forms the basis to the theory of elasticity involving the determination of effective elastic properties of materials with multiple inhomogeneities (inclusions, pores, defects, cracks, etc.). This important result represents one of the major advances in the continuum mechanics theory of the twentieth century. In this work, a relation between Eshelby Mechanics and the modern concept of topological derivative is discussed. 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, cavities, inclusions,...
- Delfour MC, Zolésio JP (2001) Shapes and geometries. In: Advances in design and control. Society for Industrial and Applied Mathematics (SIAM), PhiladelphiaGoogle Scholar
- Gurtin ME (2000) Configurational forces as basic concept of continuum physics. Applied mathematical sciences, vol 137. Springer, New YorkGoogle Scholar