Multiscale modeling aims to evaluate material properties or behavior on one level using information or models from different levels and properties of elementary processes. Usually, the following levels, addressing a phenomenon over a specific window of length and time, are recognized: • Structural scale:
Finite element,
finite volume and
finite difference partial differential equation are solvers used to simulate structural responses such as
solid mechanics and
transport phenomena at large (meters) scales. • process modeling/simulations: extrusion, rolling, sheet forming, stamping, casting, welding, etc. • product modeling/simulations: performance, impact, fatigue, corrosion, etc. • Macroscale: constitutive (rheology) equations are used at the continuum level in
solid mechanics and
transport phenomena at millimeter scales. • Mesoscale: continuum level formulations are used with discrete quantities at multiple micrometer scales. "Meso" is an ambiguous term that means "intermediate" so it has been used as representing different intermediate scales. In this context, it can represent modeling from crystal plasticity for metals, Eshelby solutions for any materials, homogenization methods, and unit cell methods. • Microscale: modeling techniques that represent the micrometer scale such as dislocation dynamics codes for metals and phase field models for multiphase materials.
Phase field models of
phase transitions and
microstructure formation and evolution on nanometer to millimeter scales. • Nanoscale: semi-empirical atomistic methods are used such as Lennard-Jones, Brenner potentials, embedded atom method (EAM) potentials, and modified embedded atom potentials (MEAM) in
molecular dynamics (MD), molecular statics (MS),
Monte Carlo (MC), and
kinetic Monte Carlo (KMC) formulations. • Electronic scale: Schroedinger equations are used in a computational framework as
density functional theory (DFT) models of electron orbitals and bonding on angstrom to nanometer scales. There are some software codes that operate on different length scales such as: •
CALPHAD computational
thermodynamics for prediction of equilibrium
phase diagrams and even non-equilibrium phases. •
Phase field codes for simulation of microstructure evolution •
Databases of processing parameters,
microstructure features, and
properties from which one can draw correlations at various length scales • GeoDict - The Digital Material Laboratory by Math2Market • VPS-MICRO is a multiscale probabilistic fracture mechanics software. • SwiftComp is a multiscale constitutive modeling software based on mechanics of structure genome. • Digimat is a multiscale material modeling platform A comprehensive compilation of software tools with relevance for ICME is documented in the Handbook of Software Solutions for ICME == Examples of Model integration ==