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  1. Material
  2. Material3D
  3. Elastic

Yeoh

PreviousOrthotropicElastic3DNextHoffman

Last updated 9 months ago

Regularized Yeoh Material For Compressible Rubbers

The following strain energy density is used.

W=∑i=1nCi0(J1−3)i+∑i=1nCi1(J3−1)2i.W=\sum_{i=1}^nC_{i0}(J_1-3)^i+\sum_{i=1}^nC_{i1}(J_3-1)^{2i}.W=i=1∑n​Ci0​(J1​−3)i+i=1∑n​Ci1​(J3​−1)2i.

where Ci0C_{i0}Ci0​ and Ci1C_{i1}Ci1​ are material constants. J1J_1J1​ and J3J_3J3​ are reduced invariants of the right Cauchy-Green deformation tensor.

Syntax

material Yeoh (1) (2...)
# (1) int, unique material tag
# (2...) double, material constants with possible density

Remarks

  1. The above command takes input list of arbitrary length (≥2\ge2≥2, excluding tag).

  2. If the number of double inputs is odd, the last one is interpreted as density.

  3. If the number of double inputs is even, the density is assumed to be zero.

  4. The first half of double inputs is read as Ci0C_{i0}Ci0​ and the second half Ci1C_{i1}Ci1​.

Examples

The following command shall be used.

material Yeoh 1 20 4000
material Yeoh 1 20 4000 1E-4

The following command shall be used.

material Yeoh 1 20 30 40 2000 3000 4000

For i=1i=1i=1, let C10=20C_{10}=20C10​=20 and C11=4000C_{11}=4000C11​=4000, the strain energy density is

W=20(J1−3)+4000(J3−1)2.W=20(J_1-3)+4000(J_3-1)^2.W=20(J1​−3)+4000(J3​−1)2.

If density is nonzero, say for example ho=10−4ho=10^{-4}ho=10−4, then the following command shall be used.

For i=3i=3i=3, let C10=20C_{10}=20C10​=20, C20=30C_{20}=30C20​=30, C30=40C_{30}=40C30​=40, C11=2000C_{11}=2000C11​=2000,C21=3000C_{21}=3000C21​=3000 and C31=4000C_{31}=4000C31​=4000, the strain energy density is

W=20(J1−3)+30(J1−3)2+40(J1−3)3+2000(J3−1)2+3000(J3−1)4+4000(J3−1)6.W=20(J_1-3)+30(J_1-3)^2+40(J_1-3)^3+2000(J_3-1)^2+3000(J_3-1)^4+4000(J_3-1)^6.W=20(J1​−3)+30(J1​−3)2+40(J1​−3)3+2000(J3​−1)2+3000(J3​−1)4+4000(J3​−1)6.