Elastic Energy Theory

Elastic Energy Savings

Elastic cloaking theory

Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress i...

Minimal energy for elastic inclusions

We consider a variant of the isoperimetric problem with a nonlocal term representing elastic energy. More precisely, our aim is to analyse the optimal energy of an inclusion of fixed volume whose energy is determined by surface and elastic energy. This problem has been studied extensively in the physical/metallurgical literature; however, the analysis has mainly been either (i) numerical, or (i...

Elastic bars with cohesive energy

Most quasi-static variational models of fracture are based on the splitting of the energy functional into the sum of two terms: bulk, depending on the displacement gradient, and surface, depending on the displacement discontinuities. In this paper we consider the simplest one-dimensional problem of this type, a bar stretched by a given axial displacement, and systematically compare two alternat...

Energy Theorems and Critical Load Approximations in the General Theory of Elastic Stability