Kinetic relations and the propagation of phase boundaries in solids
From MaRDI portal
Publication:1814189
DOI10.1007/BF00375400zbMath0745.73001OpenAlexW2017935165MaRDI QIDQ1814189
James K. Knowles, Rohan C. Abeyaratne
Publication date: 25 June 1992
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00375400
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Thermodynamics in solid mechanics (74A15) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)
Related Items
Analyticity of the nonlinear term forces convergence of solutions to two equations of continuum mechanics ⋮ Thermo-elastic aspects of dynamic nucleation ⋮ The propagation of impact-induced tensile waves in a kind of phase-transforming materials ⋮ Comparison of macro- and microscopic solutions of the Riemann problem. II: Two-phase shock tube ⋮ On the thermodynamic conditions at moving phase-transition fronts in thermoelastic solids ⋮ Non-existence of one-dimensional stress problems in solid-solid phase transitions and uniqueness conditions for incompressible phase-transforming materials ⋮ Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics ⋮ Dynamics of propagating phase boundaries: Thermoelastic solids with heat conduction ⋮ Closed-form solutions for inhomogeneous states of a slender 3-D SMA cylinder undergoing stress-induced phase transitions ⋮ On the driving traction acting on a surface of discontinuity within a continuum in the presence of electromagnetic fields ⋮ Mesoscale kinetics produces martensitic microstructure ⋮ Dynamics of propagating phase boundaries: Adiabatic theory for thermoelastic solids ⋮ The Riemann problem for thermoelastic materials with phase change ⋮ Martensitic phase transitions with surface effects ⋮ On modeling of phase transformations in ferroelectric materials ⋮ Towards shock absorbing hyperelastic metamaterial design. I: Macroscopic scale: computational shock-capturing ⋮ Moving interfaces that separate loose and compact phases of elastic aggregates: a mechanism for drastic reduction or increase in macroscopic deformation ⋮ The nature of configurational forces ⋮ Wave front tracking in systems of conservation laws. ⋮ Generalized Stefan models accounting for a discontinuous temperature field ⋮ Capturing nonclassical shocks in nonlinear elastodynamic with a conservative finite volume scheme ⋮ A dissipation-rate reserving DG method for wave catching-up phenomena in a nonlinearly elastic composite bar ⋮ Dynamic behavior of the interface between two solid phases in an elastic bar ⋮ Effect of bulk deformation and surface tension on the growth of a coherent inclusion ⋮ Coexistent phases in nonlinear thermoelasticity: Radially symmetric equilibrium states of aeolotropic bodies ⋮ Traffic flow models with phase transitions ⋮ Compaction waves as phase transitions ⋮ On configurational inertial forces at a phase interface ⋮ A material momentum balance law for rods ⋮ On dissipation induced by phase transformations ⋮ On configurational balance in slender bodies ⋮ Phase boundary motion in an elastic bar of finite length ⋮ \(L^1\) well posedness of Euler equations with dynamic phase boundaries ⋮ Diminishing functionals for nonclassical entropy solutions selected by kinetic relations ⋮ Global structure stability of impact-induced tensile waves in phase-transforming materials ⋮ Traveling waves in a relaxation system ⋮ Analytical study on phase transition of shape memory alloy wire under uniaxial tension ⋮ On stretching of a bar capable of undergoing phase transitions ⋮ Shocks versus kinks in a discrete model of displacive phase transitions ⋮ Beyond kinetic relations ⋮ Kinetic relations for a lattice model of phase transitions ⋮ Partial constraint singularities in elastic rods ⋮ Why many theories of shock waves are necessary: Kinetic functions, equivalent equations, and fourth-order models ⋮ Viscous-capillary traveling waves associated with classical and nonclassical shocks in van der Waals fluids ⋮ Rate-independent dissipation in phase-field modelling of displacive transformations ⋮ Dynamics of phase transitions in a piecewise linear diatomic chain ⋮ Properties of Rankine-Hugoniot curves for van der Waals fluids. ⋮ A local discontinuous Galerkin method for the propagation of phase transition in solids and fluids ⋮ A low-order approximation for viscous-capillary phase transition dynamics ⋮ Thermal trapping and kinetics of martensitic phase boundaries ⋮ The influence of surface tension and configurational forces on the stability of liquid-vapor interfaces ⋮ Two-phase solutions for one-dimensional non-convex elastodynamics ⋮ Multiscale modeling of the dynamics of solids at finite temperature ⋮ Pulse attenuation by kinetically active phase boundary scattering during displacive phase transformations. ⋮ Transformation-induced plasticity in ferrous alloys ⋮ Kinetics of phase transformations in the peridynamic formulation of continuum mechanics ⋮ Dynamics of propagating phase boundaries in NiTi ⋮ Deformation of adaptive materials. I: Constrained deformation of polydomain crystals ⋮ The Riemann problem for van der Waals fluids with nonclassical phase transitions ⋮ Singular and selfsimilar solutions for Euler equations with phase transitions ⋮ Normal modes and nonlinear stability behaviour of dynamic phase boundaries in elastic materials ⋮ Nonequilibrium thermodynamics of pseudoelasticity ⋮ Propagating phase boundaries: Formulation of the problem and existence via the Glimm method ⋮ Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid ⋮ Local discontinuous Galerkin method for the impact-induced wave in a slender cylinder composed of a non-convex elastic material ⋮ A continuum model of a thermoelastic solid capable of undergoing phase transitions ⋮ Stress-induced phase-transition front propagation in thermoelastic solids ⋮ Free-energy density functions for nematic elastomers ⋮ Modelling evaporation fronts with reactive Riemann solvers ⋮ A sharp interface model for the propagation of martensitic phase boundaries ⋮ Numerical simulation of equilibrium shocks in maximally dissipative elastic systems. I: The one-dimensional case ⋮ Energy release, friction, and supplemental relations at phase interfaces ⋮ Energy minimization and the formation of microstructure in dynamic anti- plane shear ⋮ Dynamics of strings made of phase-transforming materials ⋮ A micromechanical continuum model for the tensile behavior of shape memory metal nanowires ⋮ The Riemann problem and the existence of weak solutions to a system of mixed-type in dynamic phase transition ⋮ Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity ⋮ Multidimensional stability of martensite twins under regular kinetics ⋮ Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity ⋮ The positive entropy production property for augmented nonlinear hyperbolic models ⋮ Impact-induced phase transformation in shape memory alloys ⋮ A level-set approach to the computation of twinning and phase-transition dynamics ⋮ Nonlinear stability for dissipative nonlinear evolution equations with ellipticity ⋮ A kinetic decomposition for singular limits of non-local conservation laws ⋮ On the derivation of an admissibility condition for phase boundary propagation in an SMA bar based on a 3-D formulation ⋮ Nonlinear hyperbolic problems: modeling, analysis, and numerics. Abstracts from the workshop held May 19--25, 2019 ⋮ Temperature-induced phase transformation in a shape memory alloy: Phase diagram based kinetics approach ⋮ Unstable kinetic relations and the dynamics of solid-solid phase transitions ⋮ The dynamics of solid-solid phase transitions. I: Coherent interfaces ⋮ Stability of a two-phase process in an elastic solid ⋮ Riemann solvers for phase transition in a compressible sharp-interface method ⋮ A new method to discretize a model for isothermal flow with a multi-component equation of state ⋮ On the dissipation due to wave ringing in nonelliptic elastic materials ⋮ Exact Riemann solvers for conservation laws with phase change ⋮ A sharp interface framework based on the inviscid Godunov-Peshkov-Romenski equations: simulation of evaporating fluids ⋮ Visco-elastic relaxation with a van der Waals type stress ⋮ Diffusive-dispersive traveling waves and kinetic relations. I: Nonconvex hyperbolic conservation laws ⋮ Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion ⋮ Transition to detonation in dynamic phase changes ⋮ On energy balance and the structure of radiated waves in kinetics of crystalline defects ⋮ On convergence of solutions to the equation of viscoelasticity with capillarity ⋮ On spatial and material covariant balance laws in elasticity ⋮ Dynamically Induced Phase Transitions and the Modeling of Comminution in Brittle Solids ⋮ Adiabatic Phase Boundary Propagation in a Theromoelastic Solid ⋮ Wave propagation in a non-linearly elastic bar with phase transformations ⋮ A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics, , ⋮ The mathematical theory of splitting-merging patterns in phase transition dynamics ⋮ A molecular-continuum multiscale model for inviscid liquid-vapor flow with sharp interfaces ⋮ Why condensation by compression in pure water vapor cannot occur in an approach based on Euler equations ⋮ Fine phase mixtures in one-dimensional non-convex elastodynamics ⋮ Numerical investigation of a thermoelastic model for a propagating phase boundary ⋮ Phase transitions in a slender cylinder composed of an incompressible elastic material. I. Asymptotic model equation ⋮ Damage as a material phase transition ⋮ On the motion of a shape memory cantilever subject to harmonic end displacement and proposal for a microdamper ⋮ Length scales and pinning of interfaces ⋮ The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity ⋮ A general existence result for isothermal two-phase flows with phase transition ⋮ Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws ⋮ On stress-affected propagation and stability of chemical reaction fronts in solids ⋮ Stability of chemical reaction fronts in solids: analytical and numerical approaches ⋮ On configurational forces in the mechanics of phase and chemical transformations ⋮ The incompleteness of the Born-Infeld model for non-linear multi-d Maxwell’s equations ⋮ Continuum mechanics of line defects in liquid crystals and liquid crystal elastomers ⋮ NON-MONOTONIC TRAVELING WAVES IN VAN DER WAALS FLUIDS ⋮ Quasi-steady growth of twins under stress. ⋮ High-order entropy-conservative schemes and kinetic relations for van der Waals fluids ⋮ Wave propagation in shape memory alloy rods under impulsive loads ⋮ The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques ⋮ Degenerate nonlinear hyperbolic conservation laws: Non classical geometrical theory ⋮ Numerical methods with controlled dissipation for small-scale dependent shocks ⋮ Characterization of Riemann Solvers for the Two Phasep-System ⋮ Computation of dynamical phase transitions in solids ⋮ A strain-softening bar with rehardening revisited ⋮ A Study of a Hamiltonian Model for Martensitic Phase fransformations Including Microkinetic Energy ⋮ The structure of shock and interphase layers for a heat conducting Maxwellian rate-type approach to solid-solid phase transitions ⋮ On Kinetic Nature of Hysteresis Phenomena in Stress-Induced Phase Transformations ⋮ Hyperbolic free boundary problems and applications to wave-structure interactions ⋮ Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition ⋮ EXISTENCE OF SOLUTIONS WITH MOVING PHASE BOUNDARIES IN THERMOELASTICITY ⋮ Kinetics and nucleation for driven thin film flow ⋮ Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension ⋮ Guided transition waves in multistable mechanical metamaterials ⋮ Schemes with Well-Controlled Dissipation ⋮ On the velocity of a moving phase boundary in solids
Cites Work
- Unnamed Item
- Unnamed Item
- Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: An example
- Two-phase deformations of elastic solids
- On the driving traction acting on a surface of strain discontinuity in a continuum
- Finite deformation by mechanical twinning
- An admissibility condition for equilibrium shocks in finite elasticity
- A limiting ``viscosity approach to the Riemann problem for materials exhibiting change of phase
- Admissible wave fans in nonlinear hyperbolic systems
- On the emergence and propagation of a phase boundary in an elastic bar with a suddenly applied end load
- Displacive phase transformations in solids
- Non-elliptic elastic materials and the modelling of elastic-plastic behavior for finite deformation
- Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid
- The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion: Nonisothermal case
- On the dissipative response due to discontinuous strains in bars of unstable elastic material
- The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion-isothermal case
- Co-existent phases in the one-dimensional static theory of elastic bars
- The propagation of phase boundaries in elastic bars
- Equilibrium of bars
- On the dissipation associated with equilibrium shocks in finite elasticity
- Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type
- Dynamics of non-equilibrium phase boundaries in a heat conducting nonlinearly elastic medium
- Phase changes induced by deformation in isothermal elastic crystals
- Admissibility criteria for propagating phase boundaries in a van der Waals fluid
- Discontinuous deformation gradients in the finite twisting of an incompressible elastic tube
- Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity
- The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
- Dynamic phase transitions in a van der Waals gas
This page was built for publication: Kinetic relations and the propagation of phase boundaries in solids