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Continuum Simulation Monday, 9/30/2002

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Class Progress Visualization: abstract concept (stress,2D, 3D), mechanical field Stochastic simulations: random walk, Brownian movement Monte Carlo method (MC) Ensemble Molecular Dynamics (MD) Trajectory Multiscale simulation Adaptive Mesh Refinement/Coarsening; Renormalization Continuum simulation Finite Element Method (FEM); Material Point Method (MPM)

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Continuum vs. Atomistic ContinuumAtomistic MatterIndefinitely divisible Atom aggregate InteractionStress; strainInteratomic force ModelConstitutive model Potential model

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Continuum Problems Equilibrium equations: Material constitutive equations (linear): Boundary conditions

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Discretization in Finite Element Method (FEM) The basic concept is that a body or structure may be divided into smaller elements.

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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.

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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.

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Approximation to Region MPMFEM

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FEM Simulation of Crack Tip Process

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MPM Simulation of Crack Tip Process

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Adaptive Mesh Refinement/Coarsening

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MPM Simulation of Fragmentation

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