Wing Kam Liu* and Wei Chen, Northwestern University ... - SAMSI

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Multiresolution Concept t0 t f Macroscale Demonstration Ice “Reinforced” Ice Dropped Dropped Newspaper Fine resolution material morphology Structure dictates the bulk properties Properties dictate the bulk performance
Multiresolution Concept: zoom into a microstructure in the same way that modern satellite technology allows us to zoom into an image of the earth a. Small Number of pixels per km 2 – suitable for a global image TiC ~5 um 0 u Small Number of degrees of freedom – suitable for average behavior b. Increasing Image Resolution More resolution – cities can be observed 1 u Discrete behavior of TiN primary inclusions begins to be observed Increasing Constitutive Resolution c. d. Increasing resolution – buildings can be observed ~1 um ~0.1 um 10 nm u Discrete behavior of TiC secondary particles is observed 2 <strong>Northwestern</strong> <strong>University</strong> - a fine institution Macro Micro TiN Sub-Micro TiC Nano 3 u Very fine resolution – material interface is observed
Page 1 and 2: Mathematical Science Methodologies
Page 3 and 4: Multiresolution Modeling Scope: Pro
Page 5: Mathematical Science Foundation, Co
Page 9 and 10: High Strength Alloy Analysis & Unce
Page 11 and 12: Equations of Archetype Multiresolut
Page 13 and 14: More on the Theory: Motion Assumpti
Page 15 and 16: More on the Theory: Variational Sta
Page 17 and 18: Three Invariants (Strain rates, Inh
Page 19 and 20: Illustrative Example: Two-Scale Ela
Page 21 and 22: Two-Scale Concurrent Multiresolutio
Page 23 and 24: Summary: comparison with experiment
Page 25 and 26: Animation of the Fracture Process I
Page 27 and 28: Northwestern University Materials D
Page 29 and 30: Uncertainty Sources and Quantificat
Page 31 and 32: Stochastic Mathematical Formulation
Page 33 and 34: Stochastic Constitutive Theory Denu
Page 35 and 36: Desired Features Multiresolution Mi

Wing Kam Liu* and Wei Chen, Northwestern University ... - SAMSI

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