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

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Microstructural Hierarchy <strong>and</strong> Behavioral Complexity
More on the Theory: Motion Assumptions Microstructural Kinematics l* * ( ( ), , Φ) ≡ ( ( ),0, Φ ) + ∫ ∂α ( ( ), , Φ) 0 x� p ξ l x� p ξ x� p ξ α dα Beginning from the fundamental theorem of calculus on the second argument… Meaning of the first term �x(p(ξ),0,Φ) Local (intrinsic) point behavior Meaning of the second term l* ∫ ∂ x� α ( p( ξ), α, Φ) dα 0 Corrected influence at p due to the inhomogeneous neighborhood x p
Page 1 and 2: Mathematical Science Methodologies
Page 3 and 4: Multiresolution Modeling Scope: Pro
Page 5 and 6: Mathematical Science Foundation, Co
Page 7 and 8: Multiresolution Concept: zoom into
Page 9 and 10: High Strength Alloy Analysis & Unce
Page 11: Equations of Archetype Multiresolut
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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