A new effective rate dependent damage model for dynamic tensile failure of concrete

From a macroscopic point of view, the dynamic tensile response of concrete is mainly due to the viscous behavior of the bulk material and inertia effects at multi-scale levels. It has been suggested that almost all of these mechanisms have to be considered as intrinsic material properties and explicitly included in the constitutive relations of the continuum model. It is discussed and demonstrated that the use of semi-empirical dynamic strength increase factor (DIF) functions to numerically describe rate effects do not characterize true constitutive relations of the material. A strain-rate dependent formulation is used to describe the strength and fracture energy increase of concrete under dynamic tensile loading conditions. However, instead of the commonly used e (instantaneous strain-rate) to update the constitutive law, an effective rate (R) is considered. With this new concept a time scale is introduced in the constitutive law which restrains the ‘evolution of rate’, to represent the inherent dynamic properties of concrete. This has a weak regularization effect and acts as a localization limiter. Mesh objectivity is recovered with the addition of a material length scale to the constitutive relations, here accomplished by an explicit stress-based nonlocal regularization scheme. Two sets of modified split Hopkinson bar tests are simulated for validation, using respectively notched and un-notched specimens. The results are objective and in good agreement with the experiments.