Background

Multiscale modeling diagram for Paddlefish Rostrum.

The rostrum, or nose, of the paddlefish is a unique structure composed of a network of cartilage, tissue, and interlocking star-shaped bones called stellate bones. Capturing the behavior of the paddlefish rostrum, requires consideration of the structure-property relations of all the length scales. To accomplish this, the length scales must be linked.

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 rostrum stress response to applied force, effects of geometry.

Mesoscale

• Downscaling: Information required from microscale calculations.
  • Extracellular matrix composition.
• Upscaling: Information passed to higher levels
  • Macroscale:Composite interaction.
  • Continuum: Damage propogation.

Microscale

• Downscaling: Information required from atomistic scale calculations.
• Upscaling: Information passed to higher levels
  • Mesoscale: Bundle interaction, extracellular matrix composition.
  • Continuum: Hardening, Temperature effects.

Nanoscale

• Downscaling: Information required from electronic scale calculations.
  • Elastic modulus and heat of formation.
• Upscaling: Information passed to higher levels
  • Microscale: Fiber Interaction, collagen fiber bond strength.
  • Continuum: Bonding, Mobility.

Electronic Scale

• 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.