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Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids
Kaushik Bhattacharya, Vikram Gavini, Michael Ortiz +2
This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects…
Multiscale modeling of materials: Computing, data science,uncertainty and goal-oriented optimization
Nikola Kovachki, Burigede Liu, Xingsheng Sun +4
The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular…
Data-Driven Rate-Dependent Fracture Mechanics
Pietro Carrara, Michael Ortiz, Laura De Lorenzis
We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng.…
Hierarchical multiscale quantification of material uncertainty
Burigede Liu, Xingsheng Sun, Kaushik Bhattacharya +1
The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material beh…
A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture
Anna Pandolfi, Kerstin Weinberg, Michael Ortiz
We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phase-field (PF) methods. For purposes of comparison, we specifically consider the standar…