ICME Overview for Alligator Gar Fish Scale

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Contents

ICME hierarchy for Alligator Gar Fish Scale

Multiscale modeling diagram for Alligator Gar Fish Scale.

Background Information

The Alligator Gar received it's named from the elongated snout and dual rows of teeth that give it an alligator like appearance. The largest of all the Gar species, the Alligator Gar can grow up to three meters long and weigh over ninety kilograms. Its scaly outer layer can be brown or olive in color and the scales themselves are diamond shaped and interlocked with the other scales around it. Each scale is attached to the musculature of the fish and can be used as defense against potential predators.

The scales range from 10-40 mm in diameter and consist of two layers. The thinner, external layer (600 {\mu}m) is a highly mineralized material called "ganoine" and is analogous to the enamel in a human tooth. The inner layer ( 3.5 mm) is made up of bone.

Capturing the behavior of the composite that makes up the Gar's scales, requires consideration of the structure-property relations of all the length scales (see Fig. 1). To accomplish this, the length scales must be linked. [1]

Continuum Scale

  • Downscaling: Information required from macroscale calculations.
    • Interactions between layers, stress response of composite material
  • Upscaling: Formulation of Damage and thermodynamics ISV equations.


Macroscale

  • Downscaling: Information required from mesoscale calculations.
    • Interactions between particles, pores, and matrix material.
  • Upscaling: Information passed to the continuum level.
    • Interactions between material layers, entire fish scale stress response to penetrating force.

Mesoscale

  • Downscaling: Information required from microscale calculations.
    • Pore/void nucleation and growth parameters.
  • Upscaling: Information passed to higher levels
    • Macroscale:Particle-pore interactions.
    • Continuum: Crack growth rate.

Microscale

  • Downscaling: Information required from atomistic scale calculations.
    • Dislocation mobility.
  • Upscaling: Information passed to higher levels
    • Mesoscale: Driving forces for crack propagation.
    • Continuum: Pore/crack nucleation, void volume fraction.

Atomistic

  • Downscaling: Information required from electronic scale calculations.
    • Lattice constant, heat of formation, and elastic modulus.
  • Upscaling: Information passed to higher levels
    • Microscale: Ductile fracture properties, collagen fiber bond strength.
    • Continuum: High rate effects, penetration properties.

Electronic

  • Downscaling: Information required to start density functional theory.
    • Exchange correlation energy for corresponding homogeneous gas as a function of density.
  • Upscaling: Information passed to higher levels
    • Atomistic Level: Elasticity, Interfacial energy.
    • Continuum: Elastic Modulus.

References

  1. W. Yang, I. Chen, J. Mckittrick, M. Meyers. Flexible Dermal Armor in Nature. TMS, 64(4):475-485, 2012.
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