TITLE:
Anisotropic Continuum Stored Energy Functional Solved by Lie Group and Differential Geometry
AUTHORS:
Fuzhang Zhao
KEYWORDS:
Anisotropic Continuum Stored Energy, Constitutive Modeling, Finite Deformations, Invariant Component Groups, Soft Biological Tissues
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.7,
July
19,
2018
ABSTRACT: An anisotropic continuum stored energy (CSE), which
is essentially composed of invariant component groups (ICGs), is postulated to
be balanced with its stress work done, constructing a partial differential
equation (PDE). The anisotropic CSE PDE is generally solved by the Lie group
and the ICGs through curvatures of elasticity tensor are particularly grouped
by differential geometry, representing three general deformations: preferred
translational deformations, preferred rotational deformations, and preferred
powers of ellipsoidal deformations. The anisotropic CSE constitutive models
have been curve-fitted for uniaxial tension tests of rabbit abdominal skins and
porcine liver tissues, and biaxial tension and triaxial shear tests of human ventricular myocardial tissues. With
the newly defined second invariant component, the anisotropic CSE constitutive
models capture the transverse effects in uniaxial tension deformations and the
shear coupling effects in triaxial shear deformations.