Variational Theory and Computations in Stochastic Plasticity

[1]  Dishi Liu,et al.  To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations - the "Plain Vanilla" Galerkin Case , 2013, SIAM J. Sci. Comput..

[2]  Michael Aichinger,et al.  Monte Carlo Simulation , 2013 .

[3]  A. Erdolen.  Uncertainty Definition in Structural Systems with Elasto-Plastic Materials Under the Bending Moment Effect by Using Interval Analysis , 2013 .

[4]  Lars Grasedyck,et al.  F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig a Projection Method to Solve Linear Systems in Tensor Format a Projection Method to Solve Linear Systems in Tensor Format , 2022 .

[5]  B. Rosic.  Variational Formulations and Functional Approximation Algorithms in Stochastic Plasticity of Materials , 2012 .

[6]  Hermann G. Matthies,et al.  Sampling-free linear Bayesian update of polynomial chaos representations , 2012, J. Comput. Phys..

[7]  Howard C. Elman,et al.  Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems , 2012, SIAM J. Sci. Comput..

[8]  Hermann G. Matthies,et al.  A deterministic filter for non-Gaussian Bayesian estimation— Applications to dynamical system estimation with noisy measurements , 2012 .

[9]  Roger Ghanem,et al.  A variational‐inequality approach to stochastic boundary value problems with inequality constraints and its application to contact and elastoplasticity , 2012 .

[10]  O. Ernst,et al.  ON THE CONVERGENCE OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS , 2011 .

[11]  Hermann G. Matthies,et al.  Parameter Identification in a Probabilistic Setting , 2012, ArXiv.

[12]  Christian Soize,et al.  Non‐Gaussian positive‐definite matrix‐valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries , 2011 .

[13]  Daniel Kressner,et al.  Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems , 2011, SIAM J. Matrix Anal. Appl..

[14]  Anna Kučerová,et al.  Acceleration of uncertainty updating in the description of transport processes in heterogeneous materials , 2011, J. Comput. Appl. Math..

[15]  Ying Xiong,et al.  Weighted stochastic response surface method considering sample weights , 2011 .

[16]  Boris N. Khoromskij,et al.  Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs , 2011, SIAM J. Sci. Comput..

[17]  Waad Subber,et al.  Primal and dual-primal iterative substructuring methods of stochastic PDEs , 2010 .

[18]  D. Xiu.  Numerical Methods for Stochastic Computations: A Spectral Method Approach , 2010 .

[19]  O. L. Maître,et al.  Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics , 2010 .

[20]  M. Kaminski.  A generalized stochastic perturbation technique for plasticity problems , 2010 .

[21]  Dishi Liu,et al.  Uncertainty quantification with shallow water equations , 2009 .

[22]  Charbel Farhat,et al.  A FETI‐preconditioned conjugate gradient method for large‐scale stochastic finite element problems , 2009 .

[23]  Gerhard Starke,et al.  Adaptive Least Squares Finite Element Methods in Elasto-Plasticity , 2009, LSSC.

[24]  Xiang Ma,et al.  An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations , 2009, J. Comput. Phys..

[25]  M. Mićunović.  Thermomechanics of Viscoplasticity: Fundamentals and Applications , 2009 .

[26]  G. Starke,et al.  Least‐squares mixed finite elements for small strain elasto‐viscoplasticity , 2009 .

[27]  C. Schwab,et al.  Sparse high order FEM for elliptic sPDEs , 2009 .

[28]  D. Xiu.  Fast numerical methods for stochastic computations: A review , 2009 .

[29]  Christian Soize,et al.  Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices , 2008 .

[30]  H. Matthies.  Stochastic finite elements: Computational approaches to stochastic partial differential equations , 2008 .

[31]  Fabio Nobile,et al.  A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..

[32]  E. Ullmann.  Solution strategies for stochastic finite element discretizations , 2008 .

[33]  Klaus Hackl,et al.  On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[34]  Hermann G. Matthies,et al.  Uncertainty Quantification with Stochastic Finite Elements , 2007 .

[35]  Ulisse Stefanelli,et al.  A Variational Principle for Hardening Elastoplasticity , 2007, SIAM J. Math. Anal..

[36]  Boris Jeremić,et al.  Probabilistic elasto-plasticity: formulation in 1D , 2007 .

[37]  Boris Jeremić,et al.  Probabilistic elasto-plasticity: solution and verification in 1D , 2007 .

[38]  Christian Wieners,et al.  Nonlinear solution methods for infinitesimal perfect plasticity , 2007 .

[39]  Randall J. LeVeque,et al.  Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems , 2007 .

[40]  Boris Jeremić,et al.  The role of nonlinear hardening/softening in probabilistic elasto‐plasticity , 2007 .

[41]  Nicholas Zabaras,et al.  A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes , 2007 .

[42]  Carsten Carstensen,et al.  A convergent adaptive finite element method for the primal problem of elastoplasticity , 2006 .

[43]  J. Gwinner,et al.  On a Class of Random Variational Inequalities on Random Sets , 2006 .

[44]  Kurt Marti,et al.  Reliability analysis for elastoplastic mechanical structures under stochastic uncertainty , 2006 .

[45]  Viktor Winschel,et al.  Estimation with Numerical Integration on Sparse Grids , 2006 .

[46]  N. Zabaras,et al.  Uncertainty propagation in finite deformations––A spectral stochastic Lagrangian approach , 2006 .

[47]  Stefan Müller,et al.  F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Lower Semi-continuity and Existence of Minimizers in Incremental Finite-strain Elastoplasticity , 2022 .

[48]  M. Ortiz,et al.  A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids , 2006 .

[49]  Lori Graham-Brady,et al.  Efficient numerical strategies for spectral stochastic finite element models , 2005 .

[50]  A. Bertram.  Elasticity and Plasticity of Large Deformations: An Introduction , 2005 .

[51]  Hermann G. Matthies,et al.  Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations , 2005 .

[52]  D. V. Griffiths,et al.  Three-Dimensional Probabilistic Foundation Settlement , 2005 .

[53]  Habib N. Najm,et al.  Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes , 2005, SIAM J. Sci. Comput..

[54]  Andreas Keese,et al.  Numerical Solution of Systems with Stochastic Uncertainties : A General Purpose Framework for Stochastic Finite Elements , 2004 .

[55]  M. K. Ghosh,et al.  A probabilistic approach to second order variational inequalities with bilateral constraints , 2003, math/0406076.

[56]  Hans-Joachim Bungartz,et al.  Multivariate Quadrature on Adaptive Sparse Grids , 2003, Computing.

[57]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[58]  Rudolf Schürer,et al.  A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems , 2003, Math. Comput. Simul..

[59]  M. Levent Kavvas,et al.  Nonlinear Hydrologic Processes: Conservation Equations for Determining Their Means and Probability Distributions , 2003 .

[60]  D. Xiu,et al.  Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos , 2002 .

[61]  Frank Lam,et al.  A stochastic plasticity approach to strength modeling of strand-based wood composites , 2002 .

[62]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[63]  Carsten Carstensen,et al.  Non–convex potentials and microstructures in finite–strain plasticity , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[64]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[65]  Liu Ning,et al.  Reliability of elasto-plastic structure using finite element method , 2002 .

[66]  Muneo Hori,et al.  Three‐dimensional stochastic finite element method for elasto‐plastic bodies , 2001 .

[67]  C Soize,et al.  Maximum entropy approach for modeling random uncertainties in transient elastodynamics. , 2001, The Journal of the Acoustical Society of America.

[68]  R. Ghanem,et al.  Iterative solution of systems of linear equations arising in the context of stochastic finite elements , 2000 .

[69]  Joachim Gwinner,et al.  A class of random variational inequalities and simple random unilateral boundary value problems - existence, discretization, finite element approximation , 2000 .

[70]  Muneo Hori,et al.  Stochastic finite element method for elasto‐plastic body , 1999 .

[71]  J. Moreau.  Numerical aspects of the sweeping process , 1999 .

[72]  R. Ghanem.  Hybrid Stochastic Finite Elements and Generalized Monte Carlo Simulation , 1998 .

[73]  Martin Ostoja-Starzewski,et al.  Random field models of heterogeneous materials , 1998 .

[74]  I. Rozanov,et al.  Random Fields and Stochastic Partial Differential Equations , 1998 .

[75]  Alex H. Barbat,et al.  Monte Carlo techniques in computational stochastic mechanics , 1998 .

[76]  R. Caflisch.  Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.

[77]  S. Janson.  Gaussian Hilbert Spaces , 1997 .

[78]  Klaus Hackl,et al.  Generalized standard media and variational principles in classical and finite strain elastoplasticity , 1997 .

[79]  Bernt Øksendal,et al.  Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach , 1996 .

[80]  Roger Ghanem,et al.  Numerical solution of spectral stochastic finite element systems , 1996 .

[81]  Tuan D. Pham,et al.  Elasto‐plastic finite element analysis with fuzzy parameters , 1995 .

[82]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[83]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[84]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[85]  J. Haslinger,et al.  Solution of Variational Inequalities in Mechanics , 1988 .

[86]  C. Bucher.  Adaptive sampling — an iterative fast Monte Carlo procedure , 1988 .

[87]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[88]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[89]  Roger Temam,et al.  Mathematical Problems in Plasticity , 1985 .

[90]  Jacob Lubliner,et al.  A maximum-dissipation principle in generalized plasticity , 1984 .

[91]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[92]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[93]  N. Wiener.  The Homogeneous Chaos , 1938 .

[94]  Hermann G. Matthies,et al.  Sparse Representations in Stochastic Mechanics , 2011 .

[95]  J. Moreau.  On Unilateral Constraints, Friction and Plasticity , 2011 .

[96]  Ralf Kornhuber,et al.  A polynomial chaos approach to stochastic variational inequalities , 2010, J. Num. Math..

[97]  Elisabeth Ullmann,et al.  Stochastic Galerkin Matrices , 2010, SIAM J. Matrix Anal. Appl..

[98]  Omar M. Knio,et al.  Spectral Methods for Uncertainty Quantification , 2010 .

[99]  A. Ibrahimbegovic.  Nonlinear Solid Mechanics , 2009 .

[100]  Fabio Raciti,et al.  ON MONOTONE VARIATIONAL INEQUALITIES WITH RANDOM DATA , 2009 .

[101]  M. Mićunović.  Thermomechanics of Viscoplasticity , 2009 .

[102]  D. Owen,et al.  Computational methods for plasticity : theory and applications , 2008 .

[103]  H. Lang.  The difference of the solutions of the elastic and elastoplastic boundary value problem and an approach to multiaxial stress-strain correction , 2007 .

[104]  Hermann G. Matthies,et al.  QUANTIFYING UNCERTAINTY: MODERN COMPUTATIONAL REPRESENTATION OF PROBABILITY AND APPLICATIONS , 2007 .

[105]  Christian Soize.  Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators , 2006 .

[106]  Thomas Gerstner,et al.  Numerical integration using sparse grids , 2004, Numerical Algorithms.

[107]  J. Weiner,et al.  Fundamentals and applications , 2003 .

[108]  Hermann G. Matthies,et al.  Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations , 2003 .

[109]  Erich Novak,et al.  High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..

[110]  Roger Ghanem,et al.  Stochastic Finite Elements with Multiple Random Non-Gaussian Properties , 1999 .

[111]  W. Han,et al.  Plasticity: Mathematical Theory and Numerical Analysis , 1999 .

[112]  P. Chow.  Stochastic partial differential equations , 1996 .

[113]  Michał Kleiber,et al.  The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation , 1993 .

[114]  Y. Dafalias.  Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinematics , 1987 .

[115]  W. Hager.  Review: R. Glowinski, J. L. Lions and R. Trémolières, Numerical analysis of variational inequalities , 1983 .

[116]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[117]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[118]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[119]  H. Weinert.  Ekeland, I. / Temam, R., Convex Analysis and Variational Problems. Amsterdam‐Oxford. North‐Holland Publ. Company. 1976. IX, 402 S., Dfl. 85.00. US $ 29.50 (SMAA 1) , 1979 .

[120]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[121]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[122]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[123]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[124]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[125]  J. Doob.  Stochastic processes , 1953 .