828 citations · 3.2k across the 31 of their papers we have counts for
31 papers
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…
Data-driven fracture mechanics
Pietro Carrara, Laura De Lorenzis, Laurent Stainier +1
We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemmin…
Model-free Data-Driven Computational Mechanics Enhanced by Tensor Voting
Robert Eggersmann, Laurent Stainier, Michael Ortiz +1
The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent s…
Ice penetration by a bluff-body melting probe
Kerstin Weinberg, Michael Ortiz
We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenabl…
Mollified finite element approximants of arbitrary order and smoothness
Eky Febrianto, Michael Ortiz, Fehmi Cirak
The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise suc…
Large scale ab-initio simulations of dislocations
Mauricio Ponga, Kaushik Bhattacharya, Michael Ortiz
We present a novel methodology to compute relaxed dislocations core configurations, and their energies in crystalline metallic materials using large-scale \emph{ab-intio} simulatio…
Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers
Laurent Stainier, Adrien Leygue, Michael Ortiz
This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displaceme…
Model-Free Data-Driven Inelasticity
Robert Eggersmann, Trenton Kirchdoerfer, Stefanie Reese +2
We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in…
A Line-free Method of Monopoles for 3D Dislocation Dynamics
A. Deffo, M. P. Ariza, M. Ortiz
We develop an approximation scheme for three-dimensional dislocation dynamics in which the dislocation line density is concentrated at points, or monopoles. Every monopole carries…
A variational approach to Navier-Stokes
Michael Ortiz, Bernd Schmidt, Ulisse Stefanelli
We present a variational resolution of the incompressible Navier-Stokes system by means of stabilized Weighted-Inertia-Dissipation-Energy (WIDE) functionals. The minimization of th…
Proliferation of Twinning in HCP Metals: Application to Magnesium
Dingyi Sun, Mauricio Ponga, Kaushik Bhattacharya +1
Plastic deformation of metallic alloys usually takes place through slip, but occasionally involves twinning. In particular, twinning is important in hexagonal close packed material…
Data Driven Computing with Noisy Material Data Sets
Trenton Kirchdoerfer, Michael Ortiz
We formulate a Data Driven Computing paradigm, termed max-ent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outlie…
Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations
Phani Motamarri, Vikram Gavini, Kaushik Bhattacharya +1
We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamil…
A multiscale model of distributed fracture and permeability in solids in all-round compression
Maria Laura De Bellis, Gabriele Della Vecchia, Michael Ortiz +1
We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. F…
Data-driven computational mechanics
Trenton Kirchdoerfer, Michael Ortiz
We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertin…
Coarse-graining Kohn-Sham Density Functional Theory
Phanish Suryanarayana, Kaushik Bhattacharya, Michael Ortiz
We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss o…
The Optimal Uncertainty Algorithm in the Mystic Framework
M. McKerns, H. Owhadi, C. Scovel +2
We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a…
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
T. J. Sullivan, M. McKerns, D. Meyer +3
We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework wi…
Mesoscopic approach to granular crystal dynamics
Marcial Gonzalez, Jinkyu Yang, Chiara Daraio +1
We present a mesoscopic approach to granular crystal dynamics, which comprises a three-dimensional finite-element model and a one-dimensional regularized contact model. The approac…
Convergence Analysis of Meshfree Approximation Schemes
Agustin Bompadre, Bernd Schmidt, Michael Ortiz
This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the Local Maximum-Entropy…