Emergence of surface roughness from plastic deformation of amorphous materials

Many man made and natural surfaces show intrinsic surface roughness which controls material properties such as adhesion or friction. Over several length scales and in different materials, ranging from rocks to gold crystals, roughness shows a self-affine scaling behaviour. We investigate the emergence of self-affine surface roughness in amorphous solids through plastic deformation. Our simulations are performed using a fast Fourier transform (FFT)-based continuum mechanics solver. The typical plastic deformation avalanche dynamics of an amorphous material is simulated by a fully tensorial stochastic plasticity model. The crucial role of avalanches for self-affine surface roughness is shown by comparing the stochastic plasticity model with a finite strain J₂-plasticity formulation with linear isotropic hardening. We present avalanche statistics and analyse the spatiotemporal distribution of the plastic events. The non-affine deformations in the bulk of the material is related to the self-affine surface roughness of the free surface.