Stress analysis linear elastic assumption

Most of the crack problems that have been solved are based on two-dimensional, linear elasticity (i.e., the infinitesimal or small strain theory for elasticity). Some three-dimensional problems have also been solved however, they are limited principally to axisymmetric cases. Complex variable techniques have served well in the solution of these problems. To gain a better appreciation of the problems of fracture and crack growth, it is important to understand the basic assumptions and ramifications that underlie the stress analysis of cracks. 

In Section 5.3 we have based the mechanical analysis on linear elasticity theory. In particular, we have assumed that the actuation-induced stress is proportional to the swelling/deswelling caused by ion transport, as represented by (5.8). While this is a reasonable assumption when the deformation is small, experimental evidences have indicated that the relationship... 

The stresses in an adhesive joint depend, once a constitutive model is chosen, on the geometry, boundary conditions, the assumed mechanical properties of the regions involved, and the type and distribution of loads acting on the joint. In practice, most adhesives exhibit, depending on the stress levels, nonlinear-viscoelastic behavior, and the adhetends exhibit elastoplastic behavior. Most theoretical studies conducted to date on the stress analysis of adhesively bonded joints have made simplifying assumptions of linear and elastic and/or viscoelastic behavior in the interest of tracking solutions. 

For the calculation of the stress distribution in geometrically complex components, the finite element method, Irequently under the assumption of a linear elastic materials behavior, is widely used. If the results of these finite element calculations are used for a fatigue life analysis, the local strength has to be considered. For the assessment of finite element results, with regard to its fatigue strength, the application of the concept of local stresses offers a solution Local S/N-curves are calculated. 

The mathematical treatment of joint analysis is to set up a series of differential equations to describe the state of stress and strain in a joint. By using stress functions or other methods, closed-form algebraic solutions may be obtained. In the simplest elastic case it should be possible to devise a solution for given boundary conditions. As non-linearities arise, such as joint rotation and material plasticity, various assumptions need to be made to give solutions. However, once obtained, these solutions may be used to great advantage in a parametric study, provided the limits of the simplifications are borne in mind. The classical early work of Volkersen(15) and of... 

---