Opening of mode I fractures in geomaterials with rotating particles: Small-scale cosserat continuum approach and its verification

Abstract

Geomaterials often contain constituents (e.g., grains, blocks) capable of rotating. Modelling of such geomaterials requires the use of Cosserat continua. A Cosserat continuum possesses characteristic lengths, which distinguish it from the scale-independent classical continuum. For geomaterials with grains these characteristic lengths are of the order of grain size, which restricts the use of continuum modelling to scales (e.g., crack lengths) macroscopic with respect to the grain size and to the Cosserat characteristic lengths. This automatically brings us to the pseudo-Cosserat continuum with constrained microrotations leading to what we call a small-scale Cosserat continuum. We consider a 2D Mode I crack in such a continuum and determine its characteristics, in particular the opening. We then verify this approach using physical modelling and a direct numerical simulation based on discrete element modelling.