continuum simulation monday, 9/30/2002. class progress visualization: abstract concept (stress,2d,...
TRANSCRIPT
Continuum Simulation
Monday, 9/30/2002
Class ProgressVisualization: abstract concept (stress,2D, 3D), mechanical fieldStochastic simulations: random walk, Brownian movementMonte Carlo method (MC) EnsembleMolecular Dynamics (MD) Trajectory
Multiscale simulationAdaptive Mesh Refinement/Coarsening; Renormalization
Continuum simulationFinite Element Method (FEM); Material Point Method (MPM)
Continuum vs. Atomistic
Continuum Atomistic
Matter Indefinitely divisible
Atom aggregate
Interaction Stress; strain Interatomic force
Model Constitutive model
Potential model
Continuum Problems
€
σij, j +bi =ρai
Equilibrium equations:
Material constitutive equations (linear):
€
σij =Eijklεkl
Boundary conditions
Discretization inFinite Element Method (FEM)
The basic concept is that a body or structure may be divided into smaller elements.
Discretization in Material Point Method (MPM)
Solid line is an outline of the body analyzed.Black dots are the material points.Dashed lines show a regular, background grid for calculation.
Lagrangian & Eulerian Description
Lagrangian: quantities like position, velocity, stress, are given for a particular moving particle at varying times.
Eulerian:the velocities are given at fixed points in space as time varies. Imagine a case where both the measuring device and the frame of reference are fixed.
Approximation to Region
MPM FEM
FEM Simulation ofCrack Tip Process
MPM Simulation ofCrack Tip Process
Adaptive Mesh Refinement/Coarsening
MPM Simulation ofFragmentation