Materials
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Hyper Elastic Materials Overview
For hyper elastic materials, different constitutive material models are supported, such as: Neo-Hookean (both compressible and incompressible), Mooney-Rivlin, and Yeoh models that are used to model a hyper elastic NLFE Body.
Hyper elastic materials can undergo large deformations with a non-linear stress strain relationship.
The constitutive models for hyper elastic materials are characterized using the strain energy density function.
Type | Equation | Description |
---|---|---|
Neo-Hookean Compressible | U=μ2(I1−3)−μlnJ+λ2(lnJ)2 | U - Strain Energy density function μ - Shear modulus I1−rTxrx+rTyry+rTzrz - rx, ry, and rz are the gradients of NLFE grids λ=2μv1−2v, is called the 2nd Lame's constant, v is the Poisson's ratio J=det(J)=rTx(ry×rz) |
Neo-Hookean Incompressible | U=μ2(ˉI1−3)+k2(J−1)2 | ˉI1=J−23I1 k=2μ(1+v)3(1−2v), bulk modulus |
Mooney-Rivlin | U=μ10(ˉI−13)+μ01(ˉI2−3)+k2(J−1)2 | μ01 and μ10 are material constants ˉI2=J−43I2 ˉI2=12((tr(C))2−(tr(C2))), where C is the Cauchy-Green deformation tensor C=JTJ J=[rxryrz] rxryrz are the gradient vectors |
Yeoh | U=C10(ˉI1−3)+C20(ˉI1−3)2+C30(ˉI1−3)3+k2(J−1)2 | C10, C20, and C30 are material constants |
The material constants for these models have to be derived through testing, such as: uniaxial, bending, and shear tests.