Supplemental Material for:“Driving rate dependence of avalanche statistics and shapes at the yielding transition”

摘要: An amorphous system is represented by a coarsegrained scalar field σ (r, t), denoting the instantaneous deviatoric shear stress of the system at spatial position r and time t upon the application of a simple shear. An over-damped dynamics is imposed for this scalar quantity following some basic rules:(i) The stress loads locally in an elastic manner while it is below a certain yield stress σY (r).(ii) When the local stress overcomes the local yield stress, a plastic event occurs. Dissipation occurs locally, expressed as a progressive drop of the local stress, together with a redistribution of the stresses in the rest of the system, provided by a long-range elastic perturbation. This process stops when a criterion for the accumulated local strain is met, the region recovers its elastic properties and a new local yield threshold is chosen from a given distribution. The shear stress perturbation caused on the system is computed within the framework of tensorial linear elasticity assuming an isotropic incompressible material [2]. A Green’s function G (r, r) relates the stress variation δσ at each point in space with the corresponding component of the plastic strain γpl (r; t) associated with a plastic event occurring at r. The perturbation given by the elastic propagator G (r, r) can be approximated by the far field expression [2, 3] of the continuum mechanics solution [4] δσ (r, t)= µ