Data-driven nonlocal damage mechanics and fracture of shells

Abstract

This paper proposes a data-driven modeling approach to address the problem of fracture in plates and shells, based on damage mechanics. The fracture problem today faces difficulties in simulating the non-local effects associated with microstructural features of comparable scale to plate thickness, setting corresponding criteria for crack initiation and propagation, and describing the subsequent evolution of damage. The inter-dependence of these three factors can result in very complicated modeling needs. To overcome these difficulties, a data-driven generalized yield function is herein proposed, which can account for the stress state, hardening parameters, and a local second-order gradient of plastic strain and damage. Specifically, prior material knowledge is harnessed to identify key features from its mechanical data to define a generalized yield surface. Next, by training neural networks, a quantitative description of the yielding surface is generated so that complex material behaviors can be described. The yield function learned through this data-driven approach is subsequently implemented into a finite element framework. The implementation is finally utilized to analyze size-dependent fracture of plates and shells. The reliability of the proposed method is validated through the several representative cases, demonstrating its potential to describe complex fracture patterns in plates and shells. Limitations of the proposed approach are also discussed.