TY - JOUR
T1 - Anisotropic finite strain viscoelasticity
T2 - Constitutive modeling and finite element implementation
AU - Liu, Hongliang
AU - Holzapfel, Gerhard A.
AU - Skallerud, Bjørn H.
AU - Prot, Victorien
PY - 2019/3/1
Y1 - 2019/3/1
N2 - A new anisotropic finite strain viscoelastic model is presented, which is based on the Holzapfel type anisotropic hyperelastic strain-energy function. The anisotropic viscous part is set to be independent from the isotropic viscous part. A corresponding multiplicative decomposition of the deformation gradient is presented, and a specific definition of the anisotropic viscous fiber term. A new method to develop the evolution equations of the viscous internal variables is also provided. The time derivatives of the internal variables for the isotropic and anisotropic viscous parts are obtained from the evolution equation of the second Piola–Kirchhoff stress for the viscous part. The corresponding analytical validation of non-negative dissipation using the second law of thermodynamics is provided. The incompressible plane stress case is used to achieve an analytical solution for the proposed constitutive model. A good agreement between the finite element results and the analytical solution is obtained. Finally, some numerical simulations are presented, including the viscous hysteresis response, experimental data fitting and a relaxation test.
AB - A new anisotropic finite strain viscoelastic model is presented, which is based on the Holzapfel type anisotropic hyperelastic strain-energy function. The anisotropic viscous part is set to be independent from the isotropic viscous part. A corresponding multiplicative decomposition of the deformation gradient is presented, and a specific definition of the anisotropic viscous fiber term. A new method to develop the evolution equations of the viscous internal variables is also provided. The time derivatives of the internal variables for the isotropic and anisotropic viscous parts are obtained from the evolution equation of the second Piola–Kirchhoff stress for the viscous part. The corresponding analytical validation of non-negative dissipation using the second law of thermodynamics is provided. The incompressible plane stress case is used to achieve an analytical solution for the proposed constitutive model. A good agreement between the finite element results and the analytical solution is obtained. Finally, some numerical simulations are presented, including the viscous hysteresis response, experimental data fitting and a relaxation test.
KW - Anisotropic viscoelasticity
KW - Finite strain
KW - Internal variable
KW - Numerical simulation
KW - Relaxation test
UR - http://www.scopus.com/inward/record.url?scp=85055057597&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2018.09.014
DO - 10.1016/j.jmps.2018.09.014
M3 - Article
AN - SCOPUS:85055057597
SN - 0022-5096
VL - 124
SP - 172
EP - 188
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
ER -