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On rate-independent hysteresis models
This paper deals with a general approach to the modeling of rate–independent processes which may display hysteretic behavior. Such processes play an important role in many applications like
A Proof of Crystallization in Two Dimensions
This work shows rigorously that under suitable assumptions on the potential V which are compatible with the growth behavior of the Lennard-Jones potential the ground state energy per particle converges to an explicit constant E*: where E* ∈ ℝ is the minimum of a simple function on [0,∞).
Validity and Failure of the Cauchy-Born Hypothesis in a Two-Dimensional Mass-Spring Lattice
The main tool in the proof is a novel notion of lattice polyconvexity which allows us to overcome the difficulty that the elastic energy as a function of atomic positions can never be convex, due to frame-indifference.
A mathematical model for rate–independent phase transformations with hysteresis∗
The modeling of phase transformations (PT) in single and poly crystals is important to make the shape memory effect applicable in practical engineering where complex geometries and loading behavior
A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle
Abstract We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase transformations in shape-memory alloys. The model uses the deformation and phase-indicator function as
Single-Slip Elastoplastic Microstructures
Abstract.We consider rate-independent crystal plasticity with constrained elasticity, and state the variational formulation of the incremental problem. For generic boundary data, even the first time
Justification of the Cauchy–Born Approximation of Elastodynamics
We present sharp convergence results for the Cauchy—Born approximation of general classical atomistic interactions, for static problems with small data and for dynamic problems on a macroscopic time
Surface energies in a two-dimensional mass-spring model for crystals
We study an atomistic pair potential-energy E((n))(y) that describes the elastic behavior of two-dimensional crystals with n atoms where y is an element of R(2xn) characterizes the particle
A Gentle Stochastic Thermostat for Molecular Dynamics
We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys.
Derivation of an effective thermal electrochemical model for porous electrode batteries using asymptotic homogenisation
Thermal electrochemical models for porous electrode batteries (such as lithium ion batteries) are widely used. Due to the multiple scales involved, solving the model accounting for the porous