2. 1.ICME can reduce the product development time by alleviating costly trial-and error physical design iterations (design cycles) and facilitate far more cost-effective virtual design optimization. 2.ICME can reduce product costs through innovations in material, product, and process designs. 3.ICME can reduce the number of costly large systems scale experiments. 4.ICME can increase product quality and performance by providing more accurate predictions of response to design loads. 5.ICME can help develop new materials. 6.ICME can help medical practice in making diagnostic and prognostic evaluations related to the human body.

3. 1.Downscaling and upscaling: Only use the minimum required degree(s) of freedom necessary for the type of problem considered 2.Downscaling and upscaling: energy consistency between the scales 3.Downscaling and upscaling: verify the numerical model’s implementation before starting calculations 4.Downscaling: start with downscaling before upscaling to help make clear the final goal, requirements, and constraints at the highest length scale.

4. 5.Downscaling: find the pertinent variable and associated equation(s) to be the repository of the structure- property relationship from subscale information. 6.Upscaling: find the pertinent “effect” for the next higher scale by applying ANOVA methods 7.Upscaling: validate the “effect” by an experiment before using it in the next higher length scale. 8.Upscaling: Quantify the uncertainty (error) bands (upper and lower values) of the particular “effect” before using it in the next higher length scale and then use those limits to help determine the “effects” at the next higher level scale.

6. Requires: 1. theory, 2. computations, and 3. experiments

7. 1. Requirements

8. 2. Downscaling Requirements

9. 1. Requirements 2. Downscaling Requirements 3. Upscaling Reultss

10. 1. Requirements 4. Process-Structure-Property Modeling 2. Downscaling Requirements 3. Upscaling Reultss

11. Length ScaleConstitutive Model Computational Code Vernacular Structures Macoscale Internal State Variable (ISV) ABAQUS, DynaContinuum Theory Phases Mesoscale Phase FieldCALPHADMesomechanics Atoms Nanoscale Modified Embedded Atom Method LAMMPS, DynamoMolecular Dynamics/Statics. Atomistics Electrons Electronic Scale Density Funcitonal Theory VASPFirst Principles, Ab-Initio, Electronics

12. Density Functional Theory (DFT) Modified Embedded Atom Method (MEAM) Phase Field Internal State Variable Theory (ISV) Cohesive Energy, Elastic Moduli Phase Coefficients Elastic moduli, electromagnetic properties Phase Stresses Phase Comp.

13. Solid Mechanics: Hierarchical Numerical Methods: Concurrent Materials Science: Hierarchical Physics: Hierarchical Mathematics: Hierarchical and Concurrent continuum electrons atoms dislocations grains Concurrent retain only the minimal amount of information Hierarchical

14. Macroscale ISV Continuum Bridge 1 = Interfacial Energy, Elasticity Atomistics (EAM,MEAM,MD,MS, Nm Bridge 2 = Mobility Bridge 3 = Hardening Rules Bridge 4 = Particle Interactions Bridge 5 = Particle- Void Interactions Bridge 12 = FEA ISV Bridge 13 = FEA Dislocation Dynamics (Micro-3D) 100’s Nm Electronics Principles (DFT) Å Å Crystal Plasticity (ISV + FEA) 10-100 µm Crystal Plasticity (ISV + FEA) µm Crystal Plasticity (ISV + FEA) 100-500µm Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8 = Dislocation Motion Bridge 9 = Void \ Crack Nucleation Bridge 10 = Void \ Crack Growth Macroscale ISV Continuum Bridge 11 = void-crack interactions

15. IVS Model Void Growth Void/Void Coalescence Void/Particle Coalescence Fem Analysis Idealized Geometry Realistic RVE Geometry Monotonic/Cyclic Loads Crystal Plasticity Experiment Fracture of Silicon Growth of Holes Experiment Uniaxial/torsion Notch Tensile Fatigue Crack Growth Cyclic Plasticity FEM Analysis Torsion/Comp Tension Monotonic/Cyclic Continuum Model Cyclic Plasticity Damage Structural Scale Experiments FEM Model Cohesive Energy Critical Stress Analysis Fracture Interface Debonding Nanoscale Experiment SEM Optical methods ISV Model Void Nucleation FEM Analysis Idealized Geometry Realistic Geometry Microscale Mesoscale Macroscale ISV Model Void Growth Void/Crack Nucleation Experiment TEM 1.Exploratory exps 2.Model correlation exps 3.Model validation exps

16. Optimal Product Process Optimal Product Process Environment (loads, boundary conditions) Environment (loads, boundary conditions) Product (material, shape, topology) Product (material, shape, topology) Process (method, settings, tooling) Design Options Cost Analysis Modeling FEM Analysis Experiment Multiscales Analysis Product & Process Performance (strength, reliability, weight, cost, manufactur- ability ) Product & Process Performance (strength, reliability, weight, cost, manufactur- ability ) Design Objective & Constraints Preference & Risk Attitude Optimization under Uncertainty

17. Engineering tools (CAD, CAE, etc.) Conceptual design process (user-friendly interfaces) IT technologies (hidden from the engineer)

18. Issues: Various sources of uncertainty across length and time scales: How should the bridge be designed? Key research issue for metals and polymers (nanocomposites, humans, and animals) Multiscale Material Models Length Material/Structure Response Remote Sensor System Safety/Huma n System Response Human Response In-situ Accident Bio-Inspired Protection System (BIPS) ISVs Design performance Robustness & Reliability Uncertain loads & boundary conditions Time Product Performance Material Processing Accident ISVs Pre-Accident Design

19. Produc Metals Structures Continuum element Grain Particles/Defects PPTs Dislocations Atoms Electrons Metals Structures Continuum element Grain Particles/Defects PPTs Dislocations Atoms Electrons Synthetic Polymers Structures Continuum element Fibers Hard Phases Entanglements Crosslinks Chains Molecules Atoms Electrons Synthetic Polymers Structures Continuum element Fibers Hard Phases Entanglements Crosslinks Chains Molecules Atoms Electrons Biological Polymers Human body Tendon Fascicles Fibrils MicroFibrils Collagen Molecules Atoms Electrons Biological Polymers Human body Tendon Fascicles Fibrils MicroFibrils Collagen Molecules Atoms Electrons Research to Development to Application Philosophy

20. III III Regime I: Elastic mechanisms such as bond stretching and chain rotation Regime II: Strain softening induced by slippage of blocks of polymeric chains (polymeric chains having enough energy too overcome their energy barrier) Regime III: Chain alignment and chain stretching/rotation between entanglements Chains slippage Chain alignment in the loading direction (Anisotropy) Defects: entanglement points Bouvard et al., Acta Mechanica, accepted

21. Bond stretching Bond torsion Van der Waals Nanoscopic specimen of idealized Linear amorphous polyethylene under uniaxial tension (T=100K, nc=200, n_monomers=1000) Typical terms in Inter-atomic potential Bond angle Van der Waals interaction Chains alignment (bond torsion)

23. Observable State Variables (strain, strain rate, temperature) Internal State Variables (dislocations, damage)

24. length scale 1: nanoscale length scale 2: submicron scale length scale 3: microscale length scale 4: macroscale stress strain Schematic showing the stress-strain responses at four different size scales.

25. Horstemeyer, M.F., Baskes, M.I., and Plimpton, S.J., “Computational Nanoscale Plasticity Simulations Using Embedded Atom Potentials,” Prospects in Mesomechanics, ed. George Sih, Theoretical and Applied Fracture Mechanics, Vol. 37, No. 1-3, pp. 49-98, 2001.

26. Macroscale ISV Continuum Bridge 1 = Energy, Elasticity Atomistics (EAM,MEAM,MD,MS, Nm Bridge 2 = Dislocation Mobilities Bridge 3 = Hardening Rules Bridge 12 = FEA Dislocation Dynamics (Micro-3D) 100’s Nm Electronics Principles (DFT) Å Crystal Plasticity (ISV + FEA) µm Bridge 9 = polycrystal stress- strain behavior Macroscale ISV Continuum Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8 = dislocation density and yield Can I create a formed compone nt without an experime nt? with multiscal e modeling ?

27. Quantify Performance Parameters First!!!