Predictive computations of failure mechanisms and ultimate load-carrying capacity of structures are among the most burdensome exercises in civil and mechanical engineering. This is a direct consequence emanating from the intrinsic non-smooth character of damage and fracture phenomena, which render the tasks of modeling and simulation of crack initiation and growth in solid materials extremely demanding. A typical example is the analysis of brittle fracture in concrete, but the same concepts also apply to ductile failure and delamination.

In this talk we shall deal with the graded damage approach to quasi-brittle fracture [1], in which progressive damage takes place in layers of finite thickness where the transition between the sound material and the completely damaged one occurs. The graded damage model is a weakly non-local theory that fits in the so-called non-local standard approach, whereby the framework of Generalized Standard Materials is extended to include gradients of internal variables and information about material microstructure is synthetically represented through a characteristic length parameter.

Key to the effective implementation of the model are the choice of a pair of constitutive functions and the implicit tracking of regions in a state of progressive damage via Lagrange multipliers acting on internal convex constraints. The ideas are developed for a standard (Cauchy) continuum and representative numerical simulations are included that show the model capabilities.

References
[1] Valoroso, N, Stolz, C. “Graded damage in quasi-brittle solids”, International Journal for Numerical Methods in Engineering, 123( 11) : 2467– 2498, 2022. https://doi.org/10.1002/nme.6947