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Relaxation and the Computation of Effective Energies and Microstructures in Solid Mechanics

https://doi.org/10.1007/3-540-35657-6_8
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Optimal design and relaxation of variational problems, I
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Surface energy and microstructure in coherent phase transitions
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Analysis of microstructure development in shearbands by energy relaxation of incremental stress potentials: Large‐strain theory for standard dissipative solids
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Direct Methods in the Calculus of Variations
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Bayesian Inference in Wavelet-Based Models
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Parametrized Measures and Variational Principles
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Direct Methods in the Calculus of Variations
inferredcites →https://doi.org/10.1007/978-3-642-56468-0openalex-snapshot
Fundamentals of Convex Analysis
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Theory and numerics of differential equations : Durham 2000
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Numerical Analysis of Microstructure
inferredcites →https://doi.org/10.1007/978-94-015-8124-0openalex-snapshot
Fundamentals of Convex Analysis: Duality, Separation, Representation, and Resolution
inferredcites →https://doi.org/10.1007/978-94-017-0297-3openalex-snapshot
IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains
inferredcites →https://doi.org/10.1007/978-94-017-0297-3_7openalex-snapshot
On the Calculation of Microstructures for Inelastic Materials using Relaxed Energies
inferredcites →https://doi.org/10.1007/b10191openalex-snapshot
Variational Methods for Crystalline Microstructure - Analysis and Computation
inferredcites →https://doi.org/10.1007/b98874openalex-snapshot
Numerical Optimization
inferredcites →https://doi.org/10.1007/bf00279992openalex-snapshot
Convexity conditions and existence theorems in nonlinear elasticity
inferredcites →https://doi.org/10.1007/bf00281246openalex-snapshot
Fine phase mixtures as minimizers of energy
inferredcites →https://doi.org/10.1007/bf00375279openalex-snapshot
Characterizations of young measures generated by gradients
inferredcites →https://doi.org/10.1007/bf01135336openalex-snapshot
The relaxation of a double-well energy
inferredcites →https://doi.org/10.1007/bfb0092667openalex-snapshot
Calculus of Variations and Geometric Evolution Problems
inferredcites →https://doi.org/10.1007/bfb0092670openalex-snapshot
Variational models for microstructure and phase transitions
inferredcites →https://doi.org/10.1007/pl00005395openalex-snapshot
Estimates for numerical approximations of rank one convex envelopes
inferredcites →https://doi.org/10.1007/s00161-003-0120-xopenalex-snapshot
Energetic formulation of multiplicative elasto-plasticity using dissipation distances
inferredcites →https://doi.org/10.1007/s00205-004-0353-2openalex-snapshot
Dislocation Microstructures and the Effective Behavior of Single Crystals
inferredcites →https://doi.org/10.1007/s00205-005-0371-8openalex-snapshot
Single-Slip Elastoplastic Microstructures
inferredcites →https://doi.org/10.1007/s002050100174openalex-snapshot
Macroscopic Response of¶Nematic Elastomers via Relaxation of¶a Class of SO(3)-Invariant Energies
inferredcites →https://doi.org/10.1007/s00211-003-0483-8openalex-snapshot
Multiscale resolution in the computation of crystalline microstructure
inferredcites →https://doi.org/10.1007/s002110050003openalex-snapshot
Numerical approximation of young measuresin non-convex variational problems
inferredcites →https://doi.org/10.1007/s00607-003-0027-1openalex-snapshot
Adaptive Finite Element Methods for Microstructures? Numerical Experiments for a 2-Well Benchmark
inferredcites →https://doi.org/10.1007/s11012-005-2106-1openalex-snapshot
Modelling of Microstructure and its Evolution in Shape-Memory-Alloy Single-Crystals, in Particular in CuAlNi
inferredcites →https://doi.org/10.1016/j.cma.2003.12.065openalex-snapshot
Effective relaxation for microstructure simulations: algorithms and applications
inferredcites →https://doi.org/10.1016/j.cma.2004.07.003openalex-snapshot
Deriving new evolution equations for microstructures via relaxation of variational incremental problems
inferredcites →https://doi.org/10.1016/j.jmps.2004.05.011openalex-snapshot
Analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods: evolving deformation microstructures in finite plasticity
inferredcites →https://doi.org/10.1016/s0022-5096(01)00120-xopenalex-snapshot
Soft elastic response of stretched sheets of nematic elastomers: a numerical study
inferredcites →https://doi.org/10.1016/s0022-5096(97)00096-3openalex-snapshot
Nonconvex energy minimization and dislocation structures in ductile single crystals
inferredcites →https://doi.org/10.1016/s0022-5096(99)00104-0openalex-snapshot
A theory of subgrain dislocation structures
inferredcites →https://doi.org/10.1016/s0045-7825(03)00260-3openalex-snapshot
A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials
inferredcites →https://doi.org/10.1016/s0294-1449(99)80006-7openalex-snapshot
On the non-locality of quasiconvexity
inferredcites →https://doi.org/10.1016/s1874-5717(06)80009-5openalex-snapshot
Evolution of Rate-Independent Systems
inferredcites →https://doi.org/10.1017/9781108993456.011openalex-snapshot
Numerical optimization
inferredcites →https://doi.org/10.1017/s0308210500028730openalex-snapshot
A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems
inferredcites →https://doi.org/10.1017/s0962492900002658openalex-snapshot
On the computation of crystalline microstructure
inferredcites →https://doi.org/10.1051/m2an:2004040openalex-snapshot
Linear convergence in the approximation of rank-one convex envelopes
inferredcites →https://doi.org/10.1080/01630569508816659openalex-snapshot
Numerical approximation of parametrized measures
inferredcites →https://doi.org/10.1090/s0025-5718-97-00849-1openalex-snapshot
Numerical solution of the scalar double-well problem allowing microstructure
inferredcites →https://doi.org/10.1093/oso/9780198509349.001.0001openalex-snapshot
Microstructure of Martensite
inferredcites →https://doi.org/10.1098/rspa.2001.0864openalex-snapshot
Non–convex potentials and microstructures in finite–strain plasticity
inferredcites →https://doi.org/10.1098/rsta.1992.0013openalex-snapshot
Proposed experimental tests of a theory of fine microstructure and the two-well problem
inferredcites →https://doi.org/10.1137/0733054openalex-snapshot
A Convergent Adaptive Algorithm for Poisson’s Equation
inferredcites →https://doi.org/10.1137/s0036141003429906openalex-snapshot
Existence of Minimizers in Incremental Elasto-Plasticity with Finite Strains
inferredcites →https://doi.org/10.1137/s0036142902404091openalex-snapshot
Adaptive Approximation of Young Measure Solutions in Scalar Nonconvex Variational Problems
inferredcites →https://doi.org/10.1137/s0036142903428840openalex-snapshot
Reliable and Efficient Approximation of Polyconvex Envelopes
inferredcites →https://doi.org/10.1137/s0036142997325581openalex-snapshot
Numerical Computation of Rank-One Convex Envelopes
inferredcites →https://doi.org/10.1137/s0036142998337697openalex-snapshot
Numerical Analysis of Compatible Phase Transitions in Elastic Solids
inferredcites →https://doi.org/10.1177/1045389x9300400403openalex-snapshot
Computation of Microstructure Utilizing Young Measure Representations
inferredcites →https://doi.org/10.1515/9783110811919openalex-snapshot
Relaxation in Optimization Theory and Variational Calculus
inferredcites →https://doi.org/10.2140/pjm.1952.2.25openalex-snapshot
Quasi-convexity and the lower semicontinuity of multiple integrals
inferredcites →https://doi.org/10.2307/1913279openalex-snapshot
Lectures on the Calculus of Variations and Optimal Control Theory
inferredcites →https://doi.org/10.4171/ifb/99openalex-snapshot
Convergence for stabilisation of degenerately convex minimisation problems
inferredcites →https://doi.org/10.68381/jca03022openalex-snapshot
Numerical Approximation of Relaxed Variational Problems

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4634869openalex-extracted
On the Limit Behavior of Lattice-Type Metamaterials With Bi-Stable Mechanisms
inferred← citeshttps://doi.org/10.1002/nme.6280openalex-snapshot
An assessment of numerical techniques to find energy‐minimizing microstructures associated with nonconvex potentials
inferred← citeshttps://doi.org/10.1007/978-3-319-18242-1_3openalex-snapshot
Rate-Independent versus Viscous Evolution of Laminate Microstructures in Finite Crystal Plasticity
inferred← citeshttps://doi.org/10.1007/s00161-008-0082-0openalex-snapshot
Mixed analytical–numerical relaxation in finite single-slip crystal plasticity
inferred← citeshttps://doi.org/10.1016/j.cma.2018.03.003openalex-snapshot
Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium
inferred← citeshttps://doi.org/10.1016/j.ijplas.2008.02.002openalex-snapshot
Novel variational formulations for nonlocal plasticity
inferred← citeshttps://doi.org/10.1016/j.jmps.2018.02.001openalex-snapshot
An adaptive relaxation algorithm for multiscale problems and application to nematic elastomers
inferred← citeshttps://doi.org/10.1017/s0308210508000127openalex-snapshot
Infinite-order laminates in a model in crystal plasticity
inferred← citeshttps://doi.org/10.1063/1.5086848openalex-snapshot
Analytical results for the equilibrium configurations of a three-phase elastic material
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On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials
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