Homogenisation methods in mechanics of fragmented solids and hybrid materials

Fragmented solids - solids consisting of elements or fragments not directly connected to each other such that the structural integrity is maintained by a combination of kinematic constraints and compressive stresses at the boundary - play an important role in some natural and engineering systems. They are characterised by reduced shear stresses on the interfaces and the rotation and 'elbowing' of fragments. Fragmented solids are hybrid materials whose internal architecture (geometry) is a design parameter. First, we propose a finite element model of such a hybrid material with a small number of fragments followed by a continuum model for a large number of fragments. We find that the thermal stresses caused by non-uniform heating are substantially reduced in the hybrid as compared to the thermal stresses generated in the solid of the same geometry. The initial stage of block rotations involves delamination of inter-block contacts. A 1D continuum model of delamination (the fragmented beam) shows that delamination reduces the bending stiffness and increases the beam deflections. The reduction in bending stiffness is caused by the bending moment. The bending stiffness is affected by the cross-section geometry, however its influence is minor.