6 th European Solid Mechanics Conference ESMC 2006 28 August – 1 September, 2006 Budapest, Hungary SIMULATION OF SHOCK WAVE LOADED CONCRETE WITH DISCRETE CRACKS Martin Larcher 1 and Lothar Stempniewski 2 1 Institut f ¨ ur Massivbau und Baustofftechnologie Universit¨ at Karlsruhe (TH) 76128 Karlsruhe, Germany E-mail: larcher@ifmb.uka.de 2 Institut f ¨ ur Massivbau und Baustofftechnologie Universit¨ at Karlsruhe (TH) 76128 Karlsruhe, Germany E-mail: stempniewski@ifmb.uka.de Keywords: shock wave, element-free Galerkin method, discrete cracks, strain rate effect, Hugoniot, blasting Summary. The aim of the presented research is to simulate the blasting of concrete. The element-free Galerkin method is used to describe discrete cracks in the concrete. The cracks are developed by using a simple Rankine criterion. The nonlinear behavior of concrete is described by a cohesive crack model. In consideration of the strain rate effect and the Hugoniot-curve shock waves in concrete and the damage and fragmentation are calculated. 1 INTRODUCTION Simulation of high dynamic loading of concrete needs special material models. The development of shock waves has to be considered and with them the discontinuity in front of the shock wave. Another problem is how to calculate the fragmentation of the concrete. The idea of this work is to use discrete cracks with a cohesive crack model instead of a damage material model. The results of these calculations will be compared with experimental results of blasting of concrete. 2 ELEMENT-FREE GALERKIN METHOD Belytschko [1] proposed the element-free Galerkin method (EFG) which approximates a field by using a moving least-squares interpolation. Cracks can be implemented in EFG by cutting off the shape functions at the location of the crack. There are two possible ways to integrate over the domain. The integration with a background mesh is easy to implement but with this integration method the computing time is high. The nodal integration needs less computing time and is used therefore in the presented work. Another question is the size of the radius of influence. A smaller radius gives a singular matrix; a bigger radius gives a high computing time and a bad convergence. The influence of the size of support is shown in the work. 3 MATERIAL MODEL You can distinguishtwo general material models for concrete: smeared and discrete crack models. Smeared crack models often have a problem to identify when a crack is going through the material and fragmentation is beginning. A discrete crack model helps to consider the fragmentation of the concrete for example after the high dynamic loading. In the presented work discrete cracks are implemented with EFG. The use of discrete cracks with a cohesive zone makes it possible to use a material model without damage formulation. For the high dynamic loading there are also two effects to consider for the calculation: the building of shock waves and the strain rate effect. 3.1 Nonlinear stress-strain relation Concrete responds very nonlinear to loading. A linear fracture mechanic is not usable. In this work cohesive cracks are implemented to describe the effects in the meso and micro scale cracking. In a zone – called fracture process