An anisotropic hyperelastic material model is used with viscoelasticity for the ACL simulation. Anisotropic hyperelasticity is a potential-based-function with parameters to define the volumetric part, the isochoric part, and the material directions.
The exponential strain energy potential is used for characterizing the isochoric part.
The strain energy potential for anisotropic hyperelasticity is given by:
where:
 = Determinant of the elastic deformation gradient |
 = Cauchy-Green tensor |
 = Constitutive material directions |
The volumetric strain energy is given by:
The exponential-function-based strain energy potential is given by:
The constants a1, c1, and c2 are taken from Peña et al.,[1] and the compressibility parameter d is considered to be small.
| Anisotropic Hyperelastic Material Properties | |
|---|---|
| a1 | 1.5 (MPa) |
| c1 | 4.39056 (MPa) |
| c2 | 12.1093 |
| d | 0.001(MPa-1) |
| Viscoelastic Material Properties | |
| α 1 G | 0.3 |
| τ1G | 0.3 (sec) |
| α 2 G | 0.4 |
| τ2G | 9.0 (sec) |
The following example input defines the material properties:
! Anisotropic Hyperelastic Material A1=1.5 A2=0 A3=0 B1=0 B2=0 B3=0 C1=4.39056 C2=12.1093 E1=0 E2=0 d=1E-03 TB,AHYPER,1,,10,EXP TBDATA,1, A1,A2,A3,B1,B2,B3 TBDATA,7, C1,C2,E1,E2 TB,AHYPER,1,,,AVEC ! aligned with uniaxial strain direction TBDATA,1, 0, 1, 0 TB,AHYPER,1,,,PVOL TBDATA,1, d ! Viscoelasticity alpha1=0.30 alpha2=0.4 tau1=0.3 tau2=9.0 TB,PRONY,1,,2,SHEAR TBDATA,1,alpha1,tau1 TBDATA,3,alpha2,tau2
The preferred orientation of the collagen fibers of the ACL induces the transversely isotropic symmetry of the ligament;[5] therefore, only the direction vector aligned with the loading (-y) axis is considered for performing the uniaxial extension simulation.