Breakdown of disordered media by surface loads

TL;DR

This paper presents a simple elastic spring model to analyze how shear forces cause damage and eventual breakdown in disordered materials, revealing phase transition-like behavior near failure points.

Contribution

It introduces a minimal model connecting damage accumulation with shear load, providing analytical and numerical insights into the breakdown process of disordered media.

Findings

Damage behaves like a first-order phase transition.

Shear modulus scales with damage parameter near critical points.

Material failure occurs when damage reaches a critical threshold.

Abstract

We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus, G, as a function of the order parameter, \phi, describing the state of damage, and also the ``spalled'' material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behaviour in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behaviour of G with \phi is explored analytically and numerically, close to \phi=0 and \phi=1 and in the vicinity of \phi_c, when the shear load is close but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.