Strain Rate Dependent Microplane Constitutive Model for Comminution of Concrete under Projectile Impact

Abstract

The pulverization, fracturing and crushing of materials, briefly called comminution, creates numerous cracks which dissipate a large amount of kinetic energy during projectile impact. At high shear strain rates (10/s − 10/s), this causes an apparent large increase of strength, called ‘dynamic overstress’. This long debated phenomenon has recently been explained by the theory of release of local kinetic energy of shear strain rate in finite size particles that are about to form. The theory yields the particle size and the additional kinetic energy density that must be dissipated in finite element codes. In previous research, it was dissipated by additional viscosity, in a model partly analogous to turbulence theory. Here it is dissipated by scaling up the material strength. Microplane model M7 is used and its stress-strain boundaries are scaled up by theoretically derived factors proportional to the −4/3 power of the effective deviatoric strain rate and to its time derivative. The crack band model with a random tetrahedral mesh is used and all the artificial damping is eliminated from the finite element program. The scaled model M7 is seen to predict the crater shapes and exit velocities of projectiles penetrating concrete walls as closely as the previous models. The choice of the finite strain threshold for element deletion, which can have a big effect, is also studied. It is proposed to use the highest threshold above which a further increase has a negligible effect.