RATE-DEPENDENT DAMAGE MODEL FOR CONCRETE IN DYNAMICS

This paper presents a rate dependent damage model and its implementati on in transient dynamics. The rate dependent model is derived from a r ate independent damage model simply by changing the expression of the damage evolution equation. The principle of the model follows the form at of Perzyna viscoplasticity whereby the definition of the plastic mu ltiplier is modified compared to a standard rate independent plasticit y model. The rate dependent model can reproduce very well the major ef fects of the rate of loading on the response of concrete; that is, an increase of the material strength and a decrease of the softening tang ent modulus with increasing strain rate. The wave propagation problem is assessed. We show that the resulting equations of motion are uncond itionally hyperbolic. Well-posedness and mesh objectivity are verified numerically on a simple one-dimensional (1D) problem. As an example o f implementation in a finite element calculation, the computation of t he response of a reinforced concrete beam subjected to an impact is pr esented.