A regularized variational mechanics theory for modeling the evolution of brittle crack networks in composite materials with sharp interfaces

Abstract

In the design of structural materials, there is traditionally a tradeoff between achieving high strength and achieving high toughness. Nature offers creative solutions to this problem in the form of structural biomaterials (SBs), intelligent arrangements of mineral and organic phases which possess greater strength and toughness than the constituents. The micro-architecture of SBs like nacre and sea sponge spicules are characterized by weak organic interfaces between brittle mineral phases. To better understand the toughening mechanisms in SBs requires simulation techniques which can resolve arbitrary interface and bulk fracture patterns.

In this work, we present a modified regularization of Variational Fracture Theory (VFT) that allows for simulation of fracture in materials and structures with weak interfaces. The core of our approach is to widen the weak interfaces on a length scale proportional to that of the diffuse damage field, and assign a reduced fracture toughness therein. We show that in 2D the modified regularized functionals $\Gamma$-converge to that for sharp cracks. The resulting thin weak interfaces have fracture toughness which depends on the bulk material fracture toughness, the widened interface fracture toughness, and the ratio of the widened interface length scale to the crack regularization length scale. We next apply our modified regularization within a computer implementation of regularized VFT, which we term RVFTI. We assess the performance of RVFTI in 2D by reproducing the effective interface fracture toughness predicted by the $\Gamma$-convergence theory and simulating crack trapping at a bi-material interface. We then use RVFTI to study toughening in SB-inspired microarchitectures, namely layered materials and materials with wavy interfaces.