Continuous-discontinuous modelling of dynamic failure of concrete using a viscoelastic viscoplastic damage model

Concrete is a highly rate-dependent material at loading rates exceeding 15 GPa/s. This means that the apparent macroscopic mechanical properties of concrete depend on the applied loading rate. This has been determined, experimentally, for material strength and, to a smaller extent, for stiffness and fracture energy. The physical mechanisms responsible for the rate-dependency in high-rate dynamics are mainly inertia effects; moisture in nano- and micro pores contributes to an increase of the material parameters for moderate loading rates. Dynamic fracture of concrete is time dependent due to (i) viscoelastic material behaviour in the bulk material, and (ii) rate processes including inertia effects in the fracture process zone. In order to take the rate-dependency of concrete in dynamics into account we present a material model with viscous contribution to the bulk material in the elastic response and a viscous contribution to the cracked material. We elaborate the viscoelastic plastic model described in [

2

], [

3

] by coupling it to a viscoplastic damage model [

4

]. This model accounts for the strengthening effect associated with the viscous phenomenon due to moisture and includes retardation of micro-crack growth with an increase of strain rate. In the combined continuous-discontinuous approach, a crack opening is inserted after some degradation of the continuum material stiffness. Displacement discontinuities are incorporated via the partition of unity concept. The viscosity in the elastic bulk material is related to porosity and saturation level, while in the viscoplastic model the viscosity is linked to the width of the micro cracked zone. With this computational tool we examine the influence of the loading rate on the shape and size of the process zone as well as the crack velocity, and the increase in fracture energy for higher loading rates due to micro branching instabilities for crack velocities exceeding a critical velocity [

1

].