Edit Profile (opens in new tab) Ortiz, Michael Compute Distance To: Compute Author ID: ortiz.michael Published as: Ortiz, M.; Ortiz, Michael Homepage: https://www.ortiz.caltech.edu/ External Links: MGP · dblp Documents Indexed: 209 Publications since 1982 4 Contributions as Editor Biographic References: 2 Publications Co-Authors: 164 Co-Authors with 201 Joint Publications 3,497 Co-Co-Authors all top 5 Co-Authors 4 single-authored 18 Conti, Sergio 14 Marsden, Jerrold Eldon 14 Pandolfi, Anna 12 Stainier, Laurent 11 Bhattacharya, Kaushik 9 Repetto, Eduardo A. 7 Knap, Jaroslaw 7 Leyendecker, Sigrid 6 Ariza, Maria P. 6 Lew, Adrian J. 6 Mota, Alejandro 6 Radovitzky, Raúl A. 6 Schmidt, Bernd 6 Weinberg, Kerstin 5 Bower, Allan F. 5 Needleman, Alan 5 West, Matthew 4 Bompadre, Agustín 4 Carter, Emily A. 4 Cirak, Fehmi 4 Gioia, Gustavo 4 Müller, Stefan 4 Nour-Omid, Bahram 4 Sullivan, Tim 3 Arroyo, Marino 3 Aubry, Sylvie 3 Cuitiño, Alberto M. 3 Cyron, Christian Johannes 3 Eggersmann, Robert 3 Fago, Matt 3 Fraternali, Fernando 3 Garroni, Adriana 3 Hauret, Patrice 3 Heyden, S. 3 Kirchdoerfer, T. 3 Klug, William Scott 3 Li, Bo 3 Mosler, Jörn 3 Owhadi, Houman 3 Perotti, Luigi E. 3 Phillips, Rob 3 Ravichandran, Guruswami 3 Reese, Stefanie 3 Rosakis, Ares J. 3 Simo, Juan Carlos 3 Suryanarayana, Phanish 3 Theil, Florian 2 Blesgen, Thomas 2 Camacho, G. T. 2 Carrara, Pietro 2 de Lorenzis, Laura 2 Fokoua, Landry 2 Gavini, Vikram 2 Gavinia, Vikram 2 Hackl, Klaus 2 Hayes, Robin L. 2 Hurtado, Daniel E. 2 Johnson, Gwen 2 Krysl, Petr 2 Kulkarni, Yashashree 2 Leroy, Yves M. 2 Leygue, Adrien 2 Marusich, T. D. 2 McKerns, M. 2 Mielke, Alexander 2 Molinari, Jean-Francois 2 Ponga, Mauricio 2 Popov, E. P. 2 Ramasubramaniam, A. 2 Reina, Celia 2 Romero, Ignacio 2 Sotelino, Elisa D. 2 Tadmor, Ellad B. 2 Thoutireddy, P. 2 Yavari, Arash 1 Andrade, José E. 1 Arca, F. 1 Arias, Irene 1 Ariza, Pilar 1 Balzani, Daniel 1 Beltz, Glen 1 Belytschko, Ted Bohdan 1 Beyerlein, Irene J. 1 Bigoni, Davide 1 Bjerkén, Christina 1 Bloch, Anthony Michael 1 Borcea, Liliana 1 Braides, Andrea 1 Caspersen, K. 1 Cendra, Hernán 1 Chalivendra, Vijaya Bhaskar 1 Chorin, Alexandre Joel 1 Colonius, Tim 1 Courte, Luca 1 Dahlberg, Carl F. O. 1 de-Andrés, A. 1 Dellnitz, Michael 1 Desbrun, Mathieu 1 DeSimone, Antonio 1 Djodom, Landry Fokoua ...and 67 more Co-Authors all top 5 Serials 47 International Journal for Numerical Methods in Engineering 39 Journal of the Mechanics and Physics of Solids 33 Computer Methods in Applied Mechanics and Engineering 14 Archive for Rational Mechanics and Analysis 9 International Journal of Solids and Structures 7 Computational Mechanics 5 Multiscale Modeling & Simulation 3 Journal of Applied Mechanics 3 Journal of Computational Physics 3 European Journal of Mechanics. A. Solids 3 Oberwolfach Reports 2 International Journal of Engineering Science 2 Journal of Mathematical Physics 2 Journal of Nonlinear Science 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 International Journal of Fracture 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Inverse Problems 1 Nonlinearity 1 SIAM Journal on Numerical Analysis 1 Optimal Control Applications & Methods 1 Engineering with Computers 1 Journal of Elasticity 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 Notices of the American Mathematical Society 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Engineering Computations 1 AMRX. Applied Mathematics Research eXpress 1 SIAM Journal on Applied Dynamical Systems 1 Mathematical Medicine and Biology 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Discrete and Continuous Dynamical Systems. Series S all top 5 Fields 173 Mechanics of deformable solids (74-XX) 41 Numerical analysis (65-XX) 24 Statistical mechanics, structure of matter (82-XX) 16 Partial differential equations (35-XX) 13 Mechanics of particles and systems (70-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 10 Biology and other natural sciences (92-XX) 7 Fluid mechanics (76-XX) 7 Quantum theory (81-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 General and overarching topics; collections (00-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Computer science (68-XX) 3 Operations research, mathematical programming (90-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 186 Publications have been cited 4,774 times in 2,921 Documents Cited by ▼ Year ▼ Computational modelling of impact damage in brittle materials. Zbl 0929.74101Camacho, G. T.; Ortiz, M. 262 1996 Finite-deformation irreversible cohesive elements for three-dimensional crack propagation analysis. Zbl 0932.74067Ortiz, M.; Pandolfi, A. 219 1999 Subdivision surfaces: A new paradigm for thin-shell finite element analysis. Zbl 0983.74063Cirak, Fehmi; Ortiz, Michael; Schröder, Peter 209 2000 Nonconvex energy minimization and dislocation structures in ductile single crystals. Zbl 0964.74012Ortiz, M.; Repetto, E. A. 166 1999 The variational formulation of viscoplastic constitutive updates. Zbl 0938.74016Ortiz, M.; Stainier, L. 155 1999 A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Zbl 0566.73035Simo, J. C.; Ortiz, M. 131 1985 An adaptive finite element approach to atomic-scale mechanics. – The quasicontinuum method. Zbl 0982.74071Shenoy, V. B.; Miller, R.; Tadmor, E. B.; Rodney, D.; Phillips, R.; Ortiz, M. 131 1999 Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Zbl 0585.73057Ortiz, M.; Popov, E. P. 129 1985 An analysis of a new class of intergration algorithms for elastoplastic constitutive relations. Zbl 0585.73058Ortiz, M.; Simo, J. C. 115 1986 Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems. Zbl 0969.70004Kane, C.; Marsden, J. E.; Ortiz, M.; West, M. 105 2000 Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Zbl 1146.74048Arroyo, M.; Ortiz, M. 102 2006 A finite element method for localized failure analysis. Zbl 0597.73105Ortiz, Michael; Leroy, Yves; Needleman, Alan 101 1987 Fully \(C^1\)-conforming subdivision elements for finite deformation thin-shell analysis. Zbl 1039.74045Cirak, Fehmi; Ortiz, Michael 100 2001 Data-driven computational mechanics. Zbl 1425.74503Kirchdoerfer, T.; Ortiz, M. 96 2016 An analysis of the quasicontinuum method. Zbl 1002.74008Knap, J.; Ortiz, M. 95 2001 Formulation of implicit finite element methods for multiplicative finite deformation plasticity. Zbl 0724.73221Moran, B.; Ortiz, M.; Shih, C. F. 82 1990 Variational time integrators. Zbl 1060.70500Lew, A.; Marsden, J. E.; Ortiz, M.; West, M. 82 2004 Asynchronous variational integrators. Zbl 1055.74041Lew, A.; Marsden, J. E.; Ortiz, M.; West, M. 77 2003 Symplectic-energy-momentum preserving variational integrators. Zbl 0983.70014Kane, C.; Marsden, J. E.; Ortiz, M. 67 1999 Adaptive Lagrangian modelling of ballistic penetration of metallic targets. Zbl 0892.73056Camacho, G. T.; Ortiz, M. 65 1997 A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals. Zbl 1094.74563Koslowski, M.; Cuitiño, A. M.; Ortiz, M. 59 2002 A theory of subgrain dislocation structures. Zbl 1001.74007Ortiz, M.; Repetto, E. A.; Stainier, L. 59 2000 Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Zbl 0957.74058Radovitzky, R.; Ortiz, M. 59 1999 Dislocation microstructures and the effective behavior of single crystals. Zbl 1064.74144Conti, Sergio; Ortiz, Michael 55 2005 A variational formulation of the coupled thermo-mechanical boundary value problem for general dissipative solids. Zbl 1120.74367Yang, Q.; Stainier, L.; Ortiz, M. 54 2006 Fracture analysis of cellular materials: a strain gradient model. Zbl 1056.74508Chen, J. Y.; Huang, Y.; Ortiz, M. 44 1998 Optimal BV estimates for a discontinuous Galerkin method for linear elasticity. Zbl 1115.74021Lew, Adrian; Neff, Patrizio; Sulsky, Deborah; Ortiz, Michael 44 2004 A continuum model of kinetic roughening and coarsening in thin films. Zbl 0962.76009Ortiz, M.; Repetto, E. A.; Si, H. 43 1999 Variational integrators for constrained dynamical systems. Zbl 1153.70004Leyendecker, Sigrid; Marsden, Jerrold E.; Ortiz, Michael 42 2008 On spatial and material covariant balance laws in elasticity. Zbl 1111.74004Yavari, Arash; Marsden, Jerrold E.; Ortiz, Michael 42 2006 Discrete crystal elasticity and discrete dislocations in crystals. Zbl 1115.74012Ariza, M. P.; Ortiz, M. 41 2005 The morphology and folding patterns of buckling-driven thin-film blisters. Zbl 0832.73051Ortiz, Michael; Gioia, Gustavo 41 1994 Finite element analysis of nonsmooth contact. Zbl 0963.74061Kane, C.; Repetto, E. A.; Ortiz, M.; Marsden, J. E. 40 1999 Model-free data-driven inelasticity. Zbl 1441.74048Eggersmann, R.; Kirchdoerfer, T.; Reese, S.; Stainier, L.; Ortiz, M. 40 2019 A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043Mielke, Alexander; Ortiz, Michael 39 2008 Nonsmooth Lagrangian mechanics and variational collision integrators. Zbl 1088.37045Fetecau, R. C.; Marsden, J. E.; Ortiz, M.; West, M. 38 2003 Non-periodic finite-element formulation of Kohn-Sham density functional theory. Zbl 1193.81006Suryanarayana, Phanish; Gavini, Vikram; Blesgen, Thomas; Bhattacharya, Kaushik; Ortiz, Michael 37 2010 Lagrangian finite element analysis of Newtonian fluid flows. Zbl 0945.76047Radovitzky, R.; Ortiz, M. 37 1998 Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael 35 2009 The computation of the exponential and logarithmic mappings and their first and second linearizations. Zbl 0995.65053Ortiz, M.; Radovitzky, R. A.; Repetto, E. A. 35 2001 Optimal transportation meshfree approximation schemes for fluid and plastic flows. Zbl 1202.74200Li, B.; Habbal, F.; Ortiz, M. 34 2010 Modelling and simulation of high-speed machining. Zbl 0835.73077Marusich, T. D.; Ortiz, M. 34 1995 Discrete mechanics and optimal control for constrained systems. Zbl 1211.49039Leyendecker, S.; Ober-Blöbaum, S.; Marsden, J. E.; Ortiz, M. 33 2010 Effective cohesive behavior of layers of interatomic planes. Zbl 1093.74013Braides, Andrea; Lew, Adrian J.; Ortiz, Michael 33 2006 A variational \(r\)-adaption and shape-optimization method for finite-deformation elasticity. Zbl 1079.74597Thoutireddy, P.; Ortiz, M. 32 2004 Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts. Zbl 0704.73030Ortiz, Michael; Martin, John B. 31 1989 An eigenerosion approach to brittle fracture. Zbl 1352.74299Pandolfi, A.; Ortiz, M. 31 2012 Smooth, second order, non-negative meshfree approximants selected by maximum entropy. Zbl 1176.74208Cyron, C. J.; Arroyo, M.; Ortiz, M. 29 2009 Data driven computing with noisy material data sets. Zbl 1464.62282Kirchdoerfer, T.; Ortiz, M. 29 2017 Delamination of compressed thin films. Zbl 0930.74024Gioia, Gustavo; Ortiz, Michael 28 1997 Data-driven problems in elasticity. Zbl 1402.35276Conti, S.; Müller, S.; Ortiz, M. 27 2018 A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials. Zbl 1054.74697Aubry, Sylvie; Fago, Matt; Ortiz, Michael 25 2003 A cohesive approach to thin-shell fracture and fragmentation. Zbl 1082.74052Cirak, Fehmi; Ortiz, Michael; Pandolfi, Anna 24 2005 A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops. Zbl 0796.73067Xu, G.; Ortiz, M. 24 1993 An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids. Zbl 1427.74028Hill, D. J.; Pullin, D.; Ortiz, M.; Meiron, D. 23 2010 Time-discretized variational formulation of non-smooth frictional contact. Zbl 1035.74043Pandolfi, A.; Kane, C.; Marsden, J. E.; Ortiz, M. 23 2002 The line-tension approximation as the dilute limit of linear-elastic dislocations. Zbl 1457.35079Conti, Sergio; Garroni, Adriana; Ortiz, Michael 23 2015 Optimal uncertainty quantification. Zbl 1278.60040Owhadi, H.; Scovel, C.; Sullivan, T. J.; Mckerns, M.; Ortiz, M. 22 2013 The mechanics of deformation-induced subgrain-dislocation structures in metallic crystals at large strains. Zbl 1041.74506Aubry, S.; Ortiz, M. 22 2003 Minimum principles for the trajectories of systems governed by rate problems. Zbl 1162.74369Conti, S.; Ortiz, M. 21 2008 On the numerical implementation of variational arbitrary Lagrangian-Eulerian (VALE) formulations. Zbl 1113.74073Mosler, J.; Ortiz, M. 20 2006 Study and validation of a variational theory of thermo-mechanical coupling in finite visco-plasticity. Zbl 1183.74037Stainier, L.; Ortiz, M. 19 2010 On the \(\Gamma\)-convergence of discrete dynamics and variational integrators. Zbl 1136.37350Müller, S.; Ortiz, M. 19 2004 A variational constitutive model for porous metal plasticity. Zbl 1102.74007Weinberg, K.; Mota, A.; Ortiz, M. 19 2006 A discrete mechanics approach to the Cosserat rod theory. I: Static equilibria. Zbl 1217.74069Jung, Pascal; Leyendecker, Sigrid; Linn, Joachim; Ortiz, Michael 18 2011 A variational approach to coarse graining of equilibrium and non-equilibrium atomistic description at finite temperature. Zbl 1171.74310Kulkarni, Yashashree; Knap, Jaroslaw; Ortiz, Michael 18 2008 Model-free data-driven methods in mechanics: material data identification and solvers. Zbl 1470.74077Stainier, Laurent; Leygue, Adrien; Ortiz, Michael 18 2019 Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity. Zbl 1194.74406Hauret, P.; Kuhl, E.; Ortiz, M. 17 2007 Variational \(h\)-adaption in finite deformation elasticity and plasticity. Zbl 1194.74451Mosler, J.; Ortiz, M. 17 2007 Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation. Zbl 1162.74314Gavinia, Vikram; Bhattacharya, Kaushik; Ortiz, Michael 17 2007 Fracture paths from front kinetics: relaxation and rate independence. Zbl 1170.74007Larsen, C. J.; Ortiz, M.; Richardson, C. L. 16 2009 Tetrahedral composite finite elements. Zbl 1112.74544Thoutireddy, P.; Molinari, J. F.; Repetto, E. A.; Ortiz, M. 16 2002 Effect of strain hardening and rate sensitivity on the dynamic growth of a void in a plastic material. Zbl 0761.73089Ortiz, M.; Molinari, A. 15 1992 Triangular composite finite elements. Zbl 0985.74068Guo, Yong; Ortiz, Michael; Belytschko, Ted; Repetto, Eduardo A. 15 2000 Data-driven fracture mechanics. Zbl 07337885Carrara, P.; De Lorenzis, L.; Stainier, L.; Ortiz, M. 15 2020 Effect on interfacial compliance on bifurcation of a layer bonded to a substrate. Zbl 0942.74564Bigoni, D.; Ortiz, M.; Needleman, A. 15 1997 Solid modeling aspects of three-dimensional fragmentation. Zbl 0933.68141Pandolfi, A.; Ortiz, M. 15 1998 Three-dimensional finite element simulation of the dynamic Brazilian tests on concrete cylinders. Zbl 1029.74048Ruiz, Gonzalo; Ortiz, Michael; Pandolfi, Anna 14 2000 Computational micromechanics. Zbl 0890.73054Ortiz, M. 13 1996 A variational Cam-clay theory of plasticity. Zbl 1067.74510Ortiz, M.; Pandolfi, A. 13 2004 Non-periodic finite-element formulation of orbital-free density functional theory. Zbl 1162.74461Gavinia, Vikram; Knap, Jaroslaw; Bhattacharya, Kaushik; Ortiz, Michael 12 2007 Concurrent multiscale computing of deformation microstructure by relaxation and local enrichment with application to single-crystal plasticity. Zbl 1135.74005Conti, Sergio; Hauret, Patrice; Ortiz, Michael 12 2007 A class of variational strain-localization finite elements. Zbl 1081.74045Yang, Q.; Mota, A.; Ortiz, M. 12 2005 Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Zbl 0941.74060de-Andrés, A.; Pérez, J. L.; Ortiz, M. 12 1999 Convergent meshfree approximation schemes of arbitrary order and smoothness. Zbl 1253.65191Bompadre, Agustín; Perotti, L. E.; Cyron, Christian J.; Ortiz, Michael 11 2012 Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior. Zbl 1004.74009Nguyen, O.; Ortiz, M. 11 2002 Folding energetics in thin-film diaphragms. Zbl 1065.74046Gioia, G.; DeSimone, A.; Ortiz, M.; Cuitiño, A. M. 11 2002 Variational \(r\)-adaption in elastodynamics. Zbl 1158.74507Zielonka, M. G.; Ortiz, M.; Marsden, J. E. 10 2008 Convergence analysis of meshfree approximation schemes. Zbl 1416.65469Bompadre, A.; Schmidt, B.; Ortiz, M. 10 2012 Model-free data-driven computational mechanics enhanced by tensor voting. Zbl 07337781Eggersmann, Robert; Stainier, Laurent; Ortiz, Michael; Reese, Stefanie 10 2021 Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation. Zbl 0980.74080Radovitzky, R.; Ortiz, M. 10 2000 An analysis of non-planar crack growth under mixed mode loading. Zbl 0946.74570Xu, G.; Bower, A. F.; Ortiz, M. 10 1994 Hierarchical modeling in the mechanics of materials. Zbl 1075.74024Tadmor, E. B.; Phillips, R.; Ortiz, M. 10 2000 Stability of solids with interfaces. Zbl 0760.73030Suo, Z.; Ortiz, M.; Needleman, A. 9 1992 A finite element method for analyzing localization in rate dependent solids at finite strains. Zbl 0688.73042Nacar, A.; Needleman, A.; Ortiz, M. 9 1989 Data-driven finite elasticity. Zbl 1437.35654Conti, S.; Müller, S.; Ortiz, M. 9 2020 Biomechanics of traumatic brain injury. Zbl 1194.74199El Sayed, Tamer; Mota, Alejandro; Fraternali, Fernando; Ortiz, Michael 8 2008 A discrete mechanics approach to dislocation dynamics in BCC crystals. Zbl 1173.74007Ramasubramaniam, A.; Ariza, M. P.; Ortiz, M. 8 2007 Effect of boundaries and interfaces on shear-band localization. Zbl 0749.73024Needleman, A.; Ortiz, M. 8 1991 Finite element simulation of dynamic fracture and fragmentation of glass rods. Zbl 0992.74073Repetto, E. A.; Radovitzky, R.; Ortiz, M. 8 2000 A spatially adaptive phase-field model of fracture. Zbl 07532553Phansalkar, Dhananjay; Weinberg, Kerstin; Ortiz, Michael; Leyendecker, Sigrid 1 2022 Model-free data-driven computational mechanics enhanced by tensor voting. Zbl 07337781Eggersmann, Robert; Stainier, Laurent; Ortiz, Michael; Reese, Stefanie 10 2021 A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture. Zbl 07427319Pandolfi, A.; Weinberg, K.; Ortiz, M. 6 2021 Finite element solver for data-driven finite strain elasticity. Zbl 07340362Platzer, Auriane; Leygue, Adrien; Stainier, Laurent; Ortiz, Michael 6 2021 Efficient data structures for model-free data-driven computational mechanics. Zbl 07415021Eggersmann, Robert; Stainier, Laurent; Ortiz, Michael; Reese, Stefanie 4 2021 Mollified finite element approximants of arbitrary order and smoothness. Zbl 07337794Febrianto, Eky; Ortiz, Michael; Cirak, Fehmi 2 2021 Data-driven nonlocal mechanics: discovering the internal length scales of materials. Zbl 07427309Karapiperis, K.; Ortiz, M.; Andrade, J. E. 1 2021 Data-driven fracture mechanics. Zbl 07337885Carrara, P.; De Lorenzis, L.; Stainier, L.; Ortiz, M. 15 2020 Data-driven finite elasticity. Zbl 1437.35654Conti, S.; Müller, S.; Ortiz, M. 9 2020 Symmetric div-quasiconvexity and the relaxation of static problems. Zbl 1434.74010Conti, S.; Müller, S.; Ortiz, M. 3 2020 Model-free data-driven inelasticity. Zbl 1441.74048Eggersmann, R.; Kirchdoerfer, T.; Reese, S.; Stainier, L.; Ortiz, M. 40 2019 Model-free data-driven methods in mechanics: material data identification and solvers. Zbl 1470.74077Stainier, Laurent; Leygue, Adrien; Ortiz, Michael 18 2019 Functional optimality of the sulcus pattern of the human brain. Zbl 1418.92007Heyden, S.; Ortiz, M. 2 2019 Fractional strain-gradient plasticity. Zbl 1472.74035Dahlberg, C. F. O.; Ortiz, M. 1 2019 Data-driven problems in elasticity. Zbl 1402.35276Conti, S.; Müller, S.; Ortiz, M. 27 2018 A variational approach to Navier-Stokes. Zbl 1406.35237Ortiz, Michael; Schmidt, Bernd; Stefanelli, Ulisse 4 2018 Kinematics of elasto-plasticity: validity and limits of applicability of \(\mathbf{F}=\mathbf{F}^{\mathrm{e}}\mathbf{F}^{\mathrm{p}}\) for general three-dimensional deformations. Zbl 1479.74016Reina, Celia; Fokoua Djodom, Landry; Ortiz, Michael; Conti, Sergio 2 2018 Variational modeling of dislocations in crystals in the line-tension limit. Zbl 1402.82018Ariza, Pilar; Conti, Sergio; Garroni, Adriana; Ortiz, Michael 1 2018 Data driven computing with noisy material data sets. Zbl 1464.62282Kirchdoerfer, T.; Ortiz, M. 29 2017 Data-driven computational mechanics. Zbl 1425.74503Kirchdoerfer, T.; Ortiz, M. 96 2016 Optimal scaling in solids undergoing ductile fracture by crazing. Zbl 1343.35226Conti, Sergio; Ortiz, Michael 3 2016 A variational framework for spectral approximations of Kohn-Sham density functional theory. Zbl 1338.35381Wang, Xin-Cindy; Blesgen, Thomas; Bhattacharya, Kaushik; Ortiz, Michael 2 2016 A sublinear-scaling approach to density-functional-theory analysis of crystal defects. Zbl 1482.74052Ponga, M.; Bhattacharya, K.; Ortiz, M. 1 2016 The line-tension approximation as the dilute limit of linear-elastic dislocations. Zbl 1457.35079Conti, Sergio; Garroni, Adriana; Ortiz, Michael 23 2015 A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity. Zbl 1349.74034Heyden, S.; Li, B.; Weinberg, K.; Conti, S.; Ortiz, M. 4 2015 Acceleration of material-dominated calculations via phase-space simplicial subdivision and interpolation. Zbl 1352.65035Klusemann, B.; Ortiz, M. 2 2015 Optimal scaling in solids undergoing ductile fracture by void sheet formation. Zbl 1294.35161Fokoua, Landry; Conti, Sergio; Ortiz, Michael 6 2014 Optimal scaling laws for ductile fracture derived from strain-gradient microplasticity. Zbl 1323.74074Fokoua, Landry; Conti, Sergio; Ortiz, Michael 6 2014 Discontinuous variational time integrators for complex multibody collisions. Zbl 1352.70040Johnson, G.; Leyendecker, S.; Ortiz, M. 3 2014 A massively parallel implementation of the optimal transportation meshfree method for explicit solid dynamics. Zbl 1325.74166Li, B.; Stalzer, M.; Ortiz, M. 2 2014 The special-linear update: an application of differential manifold theory to the update of isochoric plasticity flow rules. Zbl 1352.74065Hurtado, D. E.; Stainier, L.; Ortiz, M. 2 2014 Atomistic long-term simulation of heat and mass transport. Zbl 1349.82063Venturini, G.; Wang, K.; Romero, I.; Ariza, M. P.; Ortiz, M. 1 2014 Optimal uncertainty quantification. Zbl 1278.60040Owhadi, H.; Scovel, C.; Sullivan, T. J.; Mckerns, M.; Ortiz, M. 22 2013 Coarse-graining Kohn-Sham density functional theory. Zbl 1258.81090Suryanarayana, Phanish; Bhattacharya, Kaushik; Ortiz, Michael 8 2013 A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories. Zbl 1352.74302Reina, Celia; Li, Bo; Weinberg, Kerstin; Ortiz, Michael 6 2013 Finite element analysis of geometrically necessary dislocations in crystal plasticity. Zbl 1352.74079Hurtado, Daniel E.; Ortiz, Michael 3 2013 A \(\Gamma\)-convergence analysis of the quasicontinuum method. Zbl 1355.70007Espanõl, Malena I.; Kochmann, Dennis M.; Conti, Sergio; Ortiz, Michael 2 2013 Automatically inf-sup compliant diamond-mixed finite elements for Kirchhoff plates. Zbl 1352.74166Perotti, L. E.; Bompadre, A.; Ortiz, M. 1 2013 An eigenerosion approach to brittle fracture. Zbl 1352.74299Pandolfi, A.; Ortiz, M. 31 2012 Convergent meshfree approximation schemes of arbitrary order and smoothness. Zbl 1253.65191Bompadre, Agustín; Perotti, L. E.; Cyron, Christian J.; Ortiz, Michael 11 2012 Convergence analysis of meshfree approximation schemes. Zbl 1416.65469Bompadre, A.; Schmidt, B.; Ortiz, M. 10 2012 Relaxed incremental variational formulation for damage at large strains with application to fiber-reinforced materials and materials with truss-like microstructures. Zbl 1352.74067Balzani, Daniel; Ortiz, Michael 6 2012 A linear programming-based algorithm for the signed separation of (non-smooth) convex bodies. Zbl 1253.90165Johnson, Gwen; Ortiz, Michael; Leyendecker, Sigrid 3 2012 A discrete mechanics approach to the Cosserat rod theory. I: Static equilibria. Zbl 1217.74069Jung, Pascal; Leyendecker, Sigrid; Linn, Joachim; Ortiz, Michael 18 2011 A mesh-free convex approximation scheme for Kohn-sham density functional theory. Zbl 1219.65058Suryanarayana, Phanish; Bhattacharya, Kaushik; Ortiz, Michael 6 2011 A duality-based method for generating geometric representations of polycrystals. Zbl 1235.74369Rimoli, J. J.; Ortiz, M. 2 2011 Replica time integrators. Zbl 1242.74195Venturini, G.; Yang, J. Z.; Ortiz, M.; Marsden, J. E. 2 2011 Non-periodic finite-element formulation of Kohn-Sham density functional theory. Zbl 1193.81006Suryanarayana, Phanish; Gavini, Vikram; Blesgen, Thomas; Bhattacharya, Kaushik; Ortiz, Michael 37 2010 Optimal transportation meshfree approximation schemes for fluid and plastic flows. Zbl 1202.74200Li, B.; Habbal, F.; Ortiz, M. 34 2010 Discrete mechanics and optimal control for constrained systems. Zbl 1211.49039Leyendecker, S.; Ober-Blöbaum, S.; Marsden, J. E.; Ortiz, M. 33 2010 An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids. Zbl 1427.74028Hill, D. J.; Pullin, D.; Ortiz, M.; Meiron, D. 23 2010 Study and validation of a variational theory of thermo-mechanical coupling in finite visco-plasticity. Zbl 1183.74037Stainier, L.; Ortiz, M. 19 2010 Energy-stepping integrators in Lagrangian mechanics. Zbl 1188.70002Gonzalez, M.; Schmidt, B.; Ortiz, M. 7 2010 Force-stepping integrators in Lagrangian mechanics. Zbl 1202.70006Gonzalez, M.; Schmidt, B.; Ortiz, M. 3 2010 Evolution of anodic stress corrosion cracking in a coated material. Zbl 1426.74258Bjerkén, C.; Ortiz, M. 1 2010 Corrigendum to “Non-periodic finite-element formulation of orbital-free density functional theory” [Journal of the Mechanics and Physics of Solids 55, 669-696 (2007; Zbl 1162.74461)]. Zbl 1225.74088Gavini, Vikram; Knap, Jaroslaw; Bhattacharya, Kaushik; Ortiz, Michael 1 2010 Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael 35 2009 Smooth, second order, non-negative meshfree approximants selected by maximum entropy. Zbl 1176.74208Cyron, C. J.; Arroyo, M.; Ortiz, M. 29 2009 Fracture paths from front kinetics: relaxation and rate independence. Zbl 1170.74007Larsen, C. J.; Ortiz, M.; Richardson, C. L. 16 2009 An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains. Zbl 1155.74412Mosler, J.; Ortiz, M. 7 2009 \(\Gamma \)-convergence of variational integrators for constrained systems. Zbl 1179.37112Schmidt, Bernd; Leyendecker, Sigrid; Ortiz, Michael 6 2009 On the behavior of dissipative systems in contact with a heat bath: application to Andrade creep. Zbl 1173.82348Sullivan, T.; Koslowski, M.; Theil, F.; Ortiz, M. 3 2009 Variational integrators for constrained dynamical systems. Zbl 1153.70004Leyendecker, Sigrid; Marsden, Jerrold E.; Ortiz, Michael 42 2008 A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. Zbl 1357.49043Mielke, Alexander; Ortiz, Michael 39 2008 Minimum principles for the trajectories of systems governed by rate problems. Zbl 1162.74369Conti, S.; Ortiz, M. 21 2008 A variational approach to coarse graining of equilibrium and non-equilibrium atomistic description at finite temperature. Zbl 1171.74310Kulkarni, Yashashree; Knap, Jaroslaw; Ortiz, Michael 18 2008 Variational \(r\)-adaption in elastodynamics. Zbl 1158.74507Zielonka, M. G.; Ortiz, M.; Marsden, J. E. 10 2008 Biomechanics of traumatic brain injury. Zbl 1194.74199El Sayed, Tamer; Mota, Alejandro; Fraternali, Fernando; Ortiz, Michael 8 2008 Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities. Zbl 1194.74550Lucas, L. J.; Owhadi, H.; Ortiz, M. 7 2008 Fracture and fragmentation of simplicial finite element meshes using graphs. Zbl 1163.74045Mota, Alejandro; Knap, Jaroslaw; Ortiz, Michael 7 2008 Erratum: Prediction of dislocation nucleation during nanoindentation by the orbital-free density functional theory local quasi-continuum method. Zbl 1171.74322Hayes, Robin L.; Fago, Matthew; Ortiz, Michael; Carter, Emily A. 5 2008 Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity. Zbl 1194.74406Hauret, P.; Kuhl, E.; Ortiz, M. 17 2007 Variational \(h\)-adaption in finite deformation elasticity and plasticity. Zbl 1194.74451Mosler, J.; Ortiz, M. 17 2007 Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation. Zbl 1162.74314Gavinia, Vikram; Bhattacharya, Kaushik; Ortiz, Michael 17 2007 Non-periodic finite-element formulation of orbital-free density functional theory. Zbl 1162.74461Gavinia, Vikram; Knap, Jaroslaw; Bhattacharya, Kaushik; Ortiz, Michael 12 2007 Concurrent multiscale computing of deformation microstructure by relaxation and local enrichment with application to single-crystal plasticity. Zbl 1135.74005Conti, Sergio; Hauret, Patrice; Ortiz, Michael 12 2007 A discrete mechanics approach to dislocation dynamics in BCC crystals. Zbl 1173.74007Ramasubramaniam, A.; Ariza, M. P.; Ortiz, M. 8 2007 Numerical modelling and experimental validation of dynamic fracture events along weak planes. Zbl 1173.74394Arias, Irene; Knap, Jaroslaw; Chalivendra, Vijaya B.; Hong, Soonsung; Ortiz, Michael; Rosakis, Ares J. 7 2007 A theory of anharmonic lattice statics for analysis of defective crystals. Zbl 1104.74018Yavari, Arash; Ortiz, Michael; Bhattacharya, Kaushik 6 2007 Local maximum-entropy approximation schemes. Zbl 1114.65136Arroyo, Marino; Ortiz, Michael 5 2007 A 3D cohesive investigation on branching for brittle materials. Zbl 1209.74065Yu, Rena C.; Pandolfi, Anna; Ortiz, Michael 1 2007 Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Zbl 1146.74048Arroyo, M.; Ortiz, M. 102 2006 A variational formulation of the coupled thermo-mechanical boundary value problem for general dissipative solids. Zbl 1120.74367Yang, Q.; Stainier, L.; Ortiz, M. 54 2006 On spatial and material covariant balance laws in elasticity. Zbl 1111.74004Yavari, Arash; Marsden, Jerrold E.; Ortiz, Michael 42 2006 Effective cohesive behavior of layers of interatomic planes. Zbl 1093.74013Braides, Andrea; Lew, Adrian J.; Ortiz, Michael 33 2006 On the numerical implementation of variational arbitrary Lagrangian-Eulerian (VALE) formulations. Zbl 1113.74073Mosler, J.; Ortiz, M. 20 2006 A variational constitutive model for porous metal plasticity. Zbl 1102.74007Weinberg, K.; Mota, A.; Ortiz, M. 19 2006 A recursive-faulting model of distributed damage in confined brittle materials. Zbl 1120.74735Pandolfi, A.; Conti, S.; Ortiz, M. 7 2006 BV estimates for mortar methods in linear elasticity. Zbl 1118.74048Hauret, Patrice; Ortiz, Michael 4 2006 A finite-deformation constitutive model of bulk metallic glass plasticity. Zbl 1138.74314Yang, Q.; Mota, A.; Ortiz, M. 4 2006 Quantum mechanics based multiscale modeling of stress-induced phase transformations in iron. Zbl 1120.74687Lew, A.; Caspersen, K.; Carter, E. A.; Ortiz, M. 1 2006 Dislocation microstructures and the effective behavior of single crystals. Zbl 1064.74144Conti, Sergio; Ortiz, Michael 55 2005 Discrete crystal elasticity and discrete dislocations in crystals. Zbl 1115.74012Ariza, M. P.; Ortiz, M. 41 2005 A cohesive approach to thin-shell fracture and fragmentation. Zbl 1082.74052Cirak, Fehmi; Ortiz, Michael; Pandolfi, Anna 24 2005 A class of variational strain-localization finite elements. Zbl 1081.74045Yang, Q.; Mota, A.; Ortiz, M. 12 2005 Prediction of dislocation nucleation during nanoindentation by the orbital-free density functional theory local quasi-continuum method. Zbl 1108.74319Hayes, Robin L.; Fago, Matt; Ortiz, Michael; Carter, Emily A. 3 2005 Three-dimensional director-field predictions of viral DNA packing arrangements. Zbl 1095.92032Klug, W. S.; Feldmann, M. T.; Ortiz, M. 1 2005 Variational time integrators. Zbl 1060.70500Lew, A.; Marsden, J. E.; Ortiz, M.; West, M. 82 2004 Optimal BV estimates for a discontinuous Galerkin method for linear elasticity. Zbl 1115.74021Lew, Adrian; Neff, Patrizio; Sulsky, Deborah; Ortiz, Michael 44 2004 A variational \(r\)-adaption and shape-optimization method for finite-deformation elasticity. Zbl 1079.74597Thoutireddy, P.; Ortiz, M. 32 2004 ...and 86 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,079 Authors 109 Ortiz, Michael 42 Conti, Sergio 33 Rabczuk, Timon 28 Miehe, Christian 28 Mosler, Jörn 25 Stainier, Laurent 25 Steinmann, Paul 25 Wriggers, Peter 23 Bazilevs, Yuri 23 Sun, WaiChing 20 Garroni, Adriana 20 Lew, Adrian J. 19 Leyendecker, Sigrid 19 Marsden, Jerrold Eldon 19 Stefanelli, Ulisse 19 Yavari, Arash 18 Belytschko, Ted Bohdan 18 Mielke, Alexander 18 Oñate Ibáñez de Navarra, Eugenio 18 Ortner, Christoph 17 Bordas, Stéphane Pierre Alain 17 Hackl, Klaus 17 Liu, Wing Kam 16 Arroyo, Marino 16 Hughes, Thomas J. R. 16 Ibrahimbegović, Adnan 16 Molinari, Jean-Francois 16 Müller, Stefan 15 Areias, Pedro M. A. 15 Geers, Marc G. D. 15 Weinberg, Kerstin 14 Braides, Andrea 14 Cirak, Fehmi 14 de Borst, René 14 Kiendl, Josef 14 Leok, Melvin 14 Sukumar, Natarajan 13 Bigoni, Davide 13 de Lorenzis, Laura 13 Kochmann, Dennis M. 13 Paulino, Glaucio H. 13 Romero, Ignacio 12 Ghosh, Somnath 12 Hsu, Ming-Chen 12 Le Khanh Chau 12 Li, Shaofan 12 Neff, Patrizio 12 Radovitzky, Raúl A. 11 Acharya, Amit 11 Borja, Ronaldo I. 11 Dondl, Patrick Werner 11 Gao, Huajian 11 Mota, Alejandro 11 Ober-Blöbaum, Sina 11 Simo, Juan Carlos 10 Armero, Francisco 10 Geubelle, Philippe H. 10 Luskin, Mitchell 10 Masud, Arif 10 Owen, David Roger Jones 10 Pandolfi, Anna 9 Balzani, Daniel 9 Benson, David J. 9 Fish, Jacob 9 Huerta, Antonio 9 Matouš, Karel 9 Noels, Ludovic 9 Perić, Djordje 9 Ponsiglione, Marcello 9 Ramesh, K. T. 9 Schmidt, Bernd 9 Scott, Michael A. 8 Alicandro, Roberto 8 Bhattacharya, Kaushik 8 Bletzinger, Kai-Uwe 8 Chen, Huajie 8 Chen, Jiun-Shyan 8 Cyron, Christian Johannes 8 De Luca, Lucia 8 DeSimone, Antonio 8 Friedrich, Manuel 8 Gravouil, Anthony 8 Holzapfel, Gerhard Alfred 8 Hu, Guanghui 8 Huang, Yonggang Young 8 Khoei, Amir R. 8 Larsson, Ragnar 8 Linder, Christian 8 Meschke, Günther 8 Millán, Daniel 8 Needleman, Alan 8 Paggi, Marco 8 Pan, Qing 8 Peerlings, Ron H. J. 8 Reese, Stefanie 8 Reina, Celia 8 Runesson, Kenneth 8 Rungamornrat, Jaroon 8 Sevilla, Ruben 8 Verhoosel, Clemens V. ...and 3,979 more Authors all top 5 Cited in 243 Serials 730 Computer Methods in Applied Mechanics and Engineering 272 International Journal for Numerical Methods in Engineering 226 Journal of the Mechanics and Physics of Solids 219 Computational Mechanics 108 Journal of Computational Physics 69 European Journal of Mechanics. A. 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(English Edition) ...and 143 more Serials all top 5 Cited in 45 Fields 2,280 Mechanics of deformable solids (74-XX) 727 Numerical analysis (65-XX) 245 Partial differential equations (35-XX) 229 Fluid mechanics (76-XX) 162 Calculus of variations and optimal control; optimization (49-XX) 149 Statistical mechanics, structure of matter (82-XX) 132 Mechanics of particles and systems (70-XX) 84 Dynamical systems and ergodic theory (37-XX) 82 Biology and other natural sciences (92-XX) 53 Computer science (68-XX) 48 Differential geometry (53-XX) 39 Quantum theory (81-XX) 34 Classical thermodynamics, heat transfer (80-XX) 29 Probability theory and stochastic processes (60-XX) 23 Operations research, mathematical programming (90-XX) 22 Ordinary differential equations (34-XX) 22 Optics, electromagnetic theory (78-XX) 20 Systems theory; control (93-XX) 18 Statistics (62-XX) 15 Global analysis, analysis on manifolds (58-XX) 13 Approximations and expansions (41-XX) 12 Operator theory (47-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 9 Real functions (26-XX) 9 Difference and functional equations (39-XX) 9 Integral equations (45-XX) 9 Relativity and gravitational theory (83-XX) 8 Geophysics (86-XX) 7 Functional analysis (46-XX) 7 Information and communication theory, circuits (94-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 4 Measure and integration (28-XX) 4 Convex and discrete geometry (52-XX) 3 Topological groups, Lie groups (22-XX) 2 Combinatorics (05-XX) 2 Algebraic topology (55-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year