Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.

Evolution of Phase Transitions : A Continuum Theory

Abstract: Part I. Introduction: 1. What this monograph is about 2. Some experiments 3. Continuum mechanics 4. Quasilinear systems 5. Outline of monograph Part II. Two-Well Potentials, Governing Equations and Energetics: 1. Introduction 2. Two-phase nonlinearly elastic materials 3. Field equations and jump conditions 4. Energetics of motion, driving force and dissipation inequality Part III. Equilibrium Phase Mixtures and Quasistatic Processes: 1. Introduction 2. Equilibrium states 3. Variational theory of equilibrium mixtures of phases 4. Quasistatic processes 5. Nucleation and kinetics 6. Constant elongation rate processes 7. Hysteresis Part IV. Impact-Induced Transitions in Two-Phase Elastic Materials: 1. Introduction 2. The impact problem for trilinear two-phase materials 3. Scale-invariant solutions of the impact problem 4. Nucleation and kinetics 5. Comparison with experiment 6. Other types of kinetic relations 7. Related work Part V. Multiple-Well Free Energy Potentials: 1. Introduction 2. Helmholtz free energy potential 3. Potential energy function and the effect of stress 4. Example 1: the van der Waals fluid 5. Example 2: two-phase martensitic material with cubic and tetragonal phases Part VI. The Continuum Theory of Driving Force: 1. Introduction 2. Balance laws, field equations and jump conditions 3. The second law of thermodynamics and the driving force Part VII. Thermoelastic Materials: 1. Introduction 2. The thermoelastic constitutive law 3. Stability of a thermoelastic material 4. A one-dimensional special case: uniaxial strain Part VIII. Kinetics and Nucleation: 1. Introduction 2. Nonequilibrium processes, thermodynamic fluxes and forces, kinetic relation 3. Phenomenological examples of kinetic relations 4. Micromechanically-based examples of kinetic relations 5. Nucleation Part IX. Models for Two-Phase Thermoelastic Materials in One Dimension: 1. Preliminaries 2. Materials of Mie-Gruneisen type 3. Two-phase Mie-Gruneisen materials Part X. Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile Bars: 1. Preliminaries 2. Thermomechanical equilibrium states for a two-phase material 3. Quasistatic processes 4. Trilinear thermoelastic material 5. Stress cycles at constant temperature 6. Temperature cycles at constant stress 7. The shape-memory cycle 8. The experiments of Shaw and Kyriakides 9. Slow thermomechanical processes Part XI. Dynamics of Phase Transitions in Uniaxially Strained Thermoelastic Solids: 1. Introduction 2. Uniaxial strain in adiabatic thermoelasticity 3. The impact problem Part XII. Statics: Geometric Compatibility: 1. Preliminaries 2. Examples Part XIII. Dynamics: Impact-Induced Transition in a CuA1Nl Single Crystal: 1. Introduction 2. Preliminaries 3. Impact without phase transformation 4. Impact with phase transformation 5. Application to austenite-B1 martensite transformation in CuA1Nl Part XIV. Quasistatics: Kinetics of Martensitic Twinning: 1. Introduction 2. The material and loading device 3. Observations 4. The model 5. The energy of the system 6. The effect of the transition layers: further observations 7. The effect of the transition layers: further modeling 8. Kinetics.

Peridynamics as an Upscaling of Molecular Dynamics

Abstract: Peridynamics is a formulation of continuum mechanics based on integral equations. It is a nonlocal model, accounting for the effects of long-range forces. Correspondingly, classical molecular dynamics is also a nonlocal model. Peridynamics and molecular dynamics have similar discrete computational structures, as peridynamics computes the force on a particle by summing the forces from surrounding particles, similarly to molecular dynamics. We demonstrate that the peridynamics model can be cast as an upscaling of molecular dynamics. Specifically, we address the extent to which the solutions of molecular dynamics simulations can be recovered by peridynamics. An analytical comparison of equations of motion and dispersion relations for molecular dynamics and peridynamics is presented along with supporting computational results.