（unfinished）

Prerequisite: Knowledge about mechanics of materials(helpful link)

Elastic materials are important because:

• Cool visual effects
• Not too hard to implement
• Base of other materials

Deformation: A mapping function from rest material position to deformed material position.

Deformation gradient F:

Deform/rest volume ratio $J=det(\textbf{F})$

Hyperelastic materials: materials whose stress-strain relationship is defined by a strain energy density function.

• Stress: Internal elastic forces to let material resotre original shape.
• Strain: Just replace it with deformation gradients F for now.

The Finite Element Method(有限元)

Linear tetrahedral(triangle) FEM

affine transform

F is constant within an element

Advanced Reading

• The classical FEM method and discretization methodology(link)
• The Material Point Method for Simulating Continuum Materials(link)