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.
Highlights
Soft biological tissues (SBTs) are recognized as anisotropic hyperelastic materials since they are naturally made of fiber reinforcements and a fluid-like matrix for supporting reversible finite deformations
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 grouped by differential geometry, representing three general deformations: preferred translational deformations, preferred rotational deformations, and preferred powers of ellipsoidal deformations
Summary
Soft biological tissues (SBTs) are recognized as anisotropic hyperelastic materials since they are naturally made of fiber reinforcements and a fluid-like matrix for supporting reversible finite deformations. Many influential discoveries in constitutive modeling of SBTs, including the structural tensors by Spencer (1971) [9], the exponential strain energy function by Fung (1973) [14], the anisotropic constitutive model by Holzapfel, Gasser, and Ogden (2000) [15], the extension of polyconvexity to invariant components by Schröder and Neff (2003) [12], and the selection of invariant components by Itskov, Ehret, and Mavrilas (2006) [13], have been achieved. Where the four coefficients for a preferred fiber direction i, c1,i , c2,i , c3,i , and c4,i , are unknown constitutive constants to be determined by experimental tests of anisotropic hyperelastic materials
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