residual stress

In this paper we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems.

This paper is dedicated to the memory of my friend Professor Bill Klug whose life was tragically cut short on June 1, 2016.

We formulate a geometric theory of nonlinear morphoelastic shells that can model the time evolution of residual stresses induced by bulk growth. We consider a thin body and idealize it by a representative orientable surface. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell (material manifold). We consider the evolution of both the first and second fundamental forms in the material manifold by considering them as dynamical variables in the variational problem.

Strained multilayer structures are extensively investigated because of their applications in microelectromechanical/nano-elecromechanical systems. Here we employ a finite element method (FEM) to study the bending and twisting of multilayer structures subjected to misfit strains or residual stresses. This method is first validated by comparing the simulation results with analytic predictions for the bending radius of a bilayer strip with given misfit strains.

The geometric formulation of continuum mechanics provides a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects, or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometric structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space.

I’ll present this below without the answer, in case you want to enjoy a little brain teaser. It is a solid and experimental mechanics problem that, while not terribly practical, I found very interesting:

A part fractures cleanly in two by brittle fracture (no plasticity) under the action of residual and applied stresses. You only have the broken part in front of you, no prior information.

 What were the original residual stresses on the fracture plane?