The general properties of the equations of the non-linear theory of elasticity for piecewise-linear potentials

✍ Scribed by G.I. Bykovtsev

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 569 KB
• Volume: 60
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(96)00063-9

✦ Synopsis

A theory of elasticity for piecewise-linear potentials is constructed assuming that the elastic potential consists of two terms, one of which depends on the hydrostatic pressure and other on the equivalent stress Z, which is a homogeneous function of the first power of the stress deviator. These assumptions limit the class of possible models compared with the previous assumptions [1], but they are more practi(.al since, when choosing a certain expression for X to determining the model, two experiments on uniaxial and volume extension-contraction are sufficient. The use of piecewise-linear expressions for ]g in some cases introduces certain simplifications, and some new properties of the models arise which do not occur for smooth convex functions of Z. Thus, under certain conditions it becomes possible for stress and strain surfaces of discontinuity to exist, characteristic surfaces occur, and problems arise regarding the uniqueness of the solution. The solution of these problems is considered in this paper.