A multi-variant martensitic phase transformation model: Formulation and numerical implementation

DOI10.1016/S0045-7825(01)00271-7zbMath1007.74061MaRDI QIDQ5956794

Christian Miehe, Sanjay Govindjee

Publication date: 27 March 2003

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

evolution equationshabit plane-like variantslattice correspondence variantsmulti-variant martensitic phase transformationnonlinear programming problemthermodynamic forcestrial elastic state method

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Stefan problems, phase changes, etc. (80A22) Crystals in solids (74N05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Thermomechanical modeling of polycrystalline smas under cyclic loading. I: Theoretical derivations
• The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis
• Consistent tangent operators for rate-independent elastoplasticity
• A model for memory alloys in plane strain
• Fine phase mixtures as minimizers of energy
• The relaxation of a double-well energy
• Evolution problem associated with a moving convex set in Hilbert space
• Cyclic effects in shape-memory alloys: A one-dimensional continuum model
• A one-dimensional continuum model for shape-memory alloys
• Constitutive equations for polycrystalline thermoelastic shape memory alloys. I: Intragranular interactions and behavior of the grain
• Finite element analysis of the behavior of shape memory alloys and their applications
• A thermodynamical constitutive model for shape memory materials. I: The monolithic shape memory alloy
• A thermodynamical constitutive model for shape memory materials. II: The SMA composite material
• Generalized plasticity and shape-memory alloys
• A multivariant micromechanical model for SMAs. I: Crystallographic issues for single crystal model. II: Polycrystal model
• Application of a partially relaxed shape memory free energy function to estimate the phase diagram and predict global microstructure evolution
• Computational aspects of one-dimensional shape memory alloy modeling with phase diagrams
• Elastoplastic materials with martensitic phase transition and twinning at finite strains: Numerical solution with the finite element method
• A multivariant model for single crystal shape memory alloy behavior
• A computational model for shape memory alloys
• An approach to nonlinear programming
• Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms
• H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• Non-linear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity
• On the relation of a three-well energy
• Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms

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