Limit State and Bifurcation Point in Hypoelastic Materials for Some Objective Stress Rates

Abstract

The limit state in hypoelastic materials, analogous to the failure or yield in classical theory of plasticity, along with the bifurcation point, corresponding to a localized instability, have been studied. Analytical equations for the limit state subject to various choices of the objective stress rates have been developed for a rather general form of the hypoelastic constitutive equation. In a rational procedure, it was shown that a general form of the limit state, which can be reduced to any conventional form of the failure criteria in the theory of plasticity, can be achieved. We mean by rationality, the nondependence of the equations on any physical assumption or a particular form of the constitutive equation. Results were examined against available experimental data. In many situations in geotechnical engineering, the stability and strength of materials are of particular interests. For example, consider a faulting mechanism in the lithosphere (a layer consisting of the crust and upper part of the Earth’s mantle) where a thick tectonic plate is sheared and abruptly breaks down causing seismic waves to propagate. Another example is a landslide where an earth slope suddenly loses its strength and a huge mass of soil starts to slide over lower layers. In such cases, engineers deal with failure, which may be a consequence of instability or the limiting strength of materials. For porous and granular materials, a theoretical study is often required in order to predict such failures. Instability analysis often predicts whether such a sudden loss of failure may take place, while a limit analysis defines the limiting strength of materials beyond which no further force or stress can be tolerated. This paper is expected to serve as a theoretical basis to deal with such problems in the context of rational mechanics.