A Constrained Cauchy-Born Elasticity Accelerated Multigrid Method for Nanoindentation

We introduce a new multigrid method to study the lattice statics model arising from nanoindentation. A constrained Cauchy-Born elasticity model is used as the coarse-grid operator. This method accelerates the relaxation process and considerably reduces the computational cost. In particular, it saves quite a bit when dislocations nucleate and move, as demonstrated by the simulation results.

Microstructure simulations within the Lattice Statics formalism: elasticity and morphologies at the atomic scale

ABSTRACTIn this paper, the Lattice Statics formalism is used to perform Monte Carlo simulations of alloy microstructures when elastic effects are present. It provides sets of long-range effective pair interactions (EPIs), defined in a rigid average reference state, that allow us to compute microstructural evolutions on diffusion time scale. A wide composition range is investigated in order to characterize the different precipitation processes with elasticity (nucleation and growth, spinodal decomposition). An advantage of the approach is to include the concentration dependence of both the effective chemical interactions and the elastic properties of the reference state. The importance of this point is illustrated by comparing the precipitation sequences in two alloys with symmetric average concentrations.

A Review of some Theoretical Models for Point Defect Calculations

A Brief Sketch of Different Models for the Calculation of Defect Parameters in Metals and Alloys, Comparison of Data and Limitations Has Been Reviewed here; Especially Relaxations due to a Vacancy Type of Point Defect, its Formation, Migration, Activation Energies and Related other Parameters Based upon the Present Experimental Status. the Models Reviewed Are the Bond Model, Continuum Model, Semi-Discrete Model, Jellium Model, Thermodynamic Model, Lattice Statics Model, Atomistic Continuum Model and Pseudopotential Model. the Main Thrust Concerns the Last Model. the Taylor, Vashishta and Singwi, Harrison, Kleinmann and King and Kutler Form of Exchange and Correlation Function Are Almost Similar, Give Moderate Results and May Be Trusted for Better Results.

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

Large deformation kinematics and internal forces arising from defects in crystalline solids are addressed by a nonlinear kinematic description and multiscale averaging concepts. An element of crystalline material with spatially uniform properties and containing defects such as dislocation lines and loops is considered. The average deformation gradient for this element is decomposed multiplicatively into terms accounting for effects of dislocation flux, recoverable elastic stretch and rotation, and residual elastic deformation associated with self-equilibrating internal forces induced by defects. Two methods are considered for quantifying average residual elastic deformation: continuum elasticity and discrete lattice statics. Average residual elastic strains and corresponding average residual elastic volume changes are negligible in the context of linear elasticity or harmonic force potentials but are not necessarily inconsequential in the more general case of nonlinear elasticity or anharmonic interactions.