Simulation of dynamic behavior of quasi-brittle materials with new rate dependent damage model

Stress-based nonlocal model, Damage, Rate dependency, Dynamic crack-branching Abstract. In concrete often complex fracture and fragmentation patterns develop when subjected to high straining loads. The proper simulation of the dynamic cracking process in concrete is crucial for good predictions of the residual bearing capacity of structures in the risk of being exposed to extraordinary events like explosions, high velocity impacts or earthquakes. As it is well known, concrete is a highly rate dependent material. Experimental and numerical studies indicate that the evolution of damage is governed by complex phenomena taking place simultaneously at different material scales, i.e. micro, meso and macro-scales. Therefore, the constitutive law, and its rate dependency, must be adjusted to the level of representation. For a proper phenomenological (macroscopic) representation of the reality, the constitutive law has to explicitly describe all phenomena taking place at the lower material scales. Macro-scale inertia effects are implicitly simulated by the equation of motion. In the current paper, dynamic crack propagation and branching is studied with a new rate-dependent stress-based nonlocal damage model. The definition of rate in the constitutive law is changed to account for the inherent meso-scale structural inertia effects. This is accomplished by a new concept of effective rate which governs the dynamic delayed response of the material to variations of the deformation (strain) rate, usually described as micro-inertia effects. The proposed model realistically simulates dynamic crack propagation and crack branching phenomena in concrete