A Dynamical System Theory of Large Deformations and Patterns in Non-Cohesive Solids

Abstract

We propose a dynamical system theory of triaxial-test deformationS and localization bifurcation in brittle media. We apply it to predict that localization may occur in a packing looser than "critical" and that the general localization shape is a spiral staircase in axisymmetric 3-D cells. These two facts have recently been confirmed experimentally. This theory provides a framework for understanding the development of complex deformation patterns from the mechanics of localization and rupture.

Magnitude of Earthquakes Controls the Size Distribution of Their Triggered Events

“…When a cylinder of such material is subjected to an axisymmetric state of stress, a bifurcation occurs when one of the conjugate slip surfaces finally localizes all the deformation after the load has reached a critical value, to finally lead to the failure of the sample along that single plane. Right at the bifurcation, surprisingly symmetric patterns of failure surfaces may emerge: Some developing as revolution cones around the main stress axis (Desrues et al, ), or as spiral staircases gyrating around that same axis (Desrues et al, ; Evesque & Sornette, ). Both kinds of structures attempt to preserve, at least partly, the initial cylindrical symmetry although it will be ultimately destroyed when loading further the sample, beyond the critical point.…”