Fracture and damage are intrinsically multi-scale phenomena, controlled by mechanisms happening at the atomic scale but being affected by, and affecting the macro scales. For many decades, because of the inability of continuum-level models to predict the observed behavior in some of the most difficult problems, e.g. dynamic fracture, brittle fragmentation, corrosion damage, etc., the belief was that these problems required full atomistic descriptions. Multiscale approaches have been trying to connect these scales with limited success. This is because, on the one hand, computationally intensive atomistic models produce massive amounts of data, over too-small of time spans and minute spatial dimensions, not all of which have relevance at the macro/engineering scales. On the other hand, transferring back-and-forth information across scales leads to its own approximations and losses.
We discuss some new approaches to simulating dynamic fracture, corrosion damage, and brittle fragmentation, which, when paired with extreme scale computations, allow us, for the first time, to accurately predict the observed behavior in these challenging problems. Two advances have made this possible: (1) a type of nonlocal modeling called peridynamics, and (2) a fast convolution-based method used to compute, with efficiency, solutions to the integro-differential equations resulting from peridynamic models. Nonlocality allows us to “embed” information on mechanisms and behavior at the microscale into continuum-level models. The natural convolutional structure of peridynamic kernels leads to the possibility of using efficient FFT algorithms in problems with fracture/damage. We focus on dynamic fracture and damage in brittle (glass, glassy polymers, ceramics), quasi-brittle (concrete, porous rock, composites), and ductile materials, as well as corrosion and corrosion-induced damage (pitting, intergranular, crevice, galvanic, stress corrosion cracking). For heterogeneous materials we show how stochastic homogenization in peridynamic models can be used to reduce complexity of computations without losing accuracy in predicting failure behavior. These new models can now solve, accurately, dynamic crack branching problems, in 3D macro-scale samples, or pitting corrosion with hundreds of pits in steel bars at engineering-relevant temporal and spatial scales, on a single processor or GPU system in a matter of minutes (see PeriFast on GitHub). When combined with massively parallel computational frameworks, larger and larger scales with multi-physical behavior of higher complexity appear within reach, for the first time.
Copyright. All Rights Reserved.