Non-riemannian and finslerian approaches to the theory of yielding

Abstract

‘Plasticity’ is to assume an arbitrary torsion and a Riemann-Christoffel curvature tensor associated with the material manifold and so to ‘tear’ it. If it reduces the curvature to nil, the tearing is ‘perfect’. A perfect tearing is not always realized and can be only ‘virtual’. The criterion for yielding can be reached by statistical summary as a variation over a finite region from the equation of geodesic deviation which includes the curvature tensor. The details being immaterial, the views can be restricted to the variation of the metric tensor and an extension of the three-dimensional analogue of Einstein's field equation in general relativity theory is derived, the analogue of the material-energy tensor being given a thermodynamical interpretation. The Einsteinian assumption is shown to be a special case of general possibilities. The approach can be made in terms of Finsler's as well as of simpler non-Riemannian geometry.