  We develop a novel constitutive modeling approach for the analysis of
fracture propagation in quasi-brittle materials using the Material Point
Method. The kinematics of constitutive models is enriched with an additional
mode of localized deformation to take into account the strain discontinuity
once cracking has occurred. The crack details therefore can be stored at
material point level and there is no need to enrich the kinematics of finite
elements to capture the localization caused by fracturing processes. This
enhancement also removes the drawback of classical smeared crack approach in
producing unphysical snapping back constitutive responses when the spatial
resolution is not fine enough. All these facilitate the implementation of the
new approach in the Material Point Method for analysis of large scale problems.
Numerical examples of fracture propagation are used to demonstrate the
effectiveness and potentials of the new approach.
