small strain

Recently, a very general and novel class of implicit bodies has been developed to describe the elastic response of solids. It contains as a special subclass the classical Cauchy and Green elastic bodies. Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress. Such an approximation is not possible within classical theories of Cauchy and Green elasticity, where the process of linearization will only lead to the classical linearized elastic body.

Hi,

I was wondering if someone knows literature related to "Inverse eigenstrain analysis based on residual strains in the case of small strain geometric nonlinearity"? (elongated bodies)

In the case of lineralized elasticity I guess one could postulate an eigenstrain distribution as the sum of a finite set of basic eigenstrain distribution and minimize the difference between the predicted and the actual residual strain distribution (retrieved from a synchroton mapping for example).

As done in the paper:

Consider a ridig pillar ontop of a elastic substrate. Applying a moment to the pillar will lead to elastic deformation of the substrate. If the pillar is infinitly large in diameter, then this problem is the same as an infinitely sharp crack, considering the symmetry of the crack problem, i.e. there are square root singularities. However, the infinitly large diameter assumtion does not hold if the global rotation of the substrate under the pillar is of interest, because the both sides of the pillar interact.