Direction Dependent Mullins Model for Transversely Isotropic Soft Tissues
MHBM Shariff (Khalifa University)
Soft Materials and Structures
Wed 9:00 - 10:30
Barus-Holley 158
It is known that the Mullins effect is not, in general, isotropic; after a virgin isotropic Mullins material is deformed, the non-virgin reference (stress-free) state is no longer isotropic [1]. In the case of transversely isotropic virgin Mullins materials, previous stress softening models assumed that the reference states for both the virgin and non-virgin materials are transversely isotropic. This assumption is, as in the case of isotropic virgin materials, not true; we cannot expect a transversely isotropic virgin Mullins material to remain transversely isotropic after it is being deformed. In this work, we propose a direction dependent constitutive equation for transversely isotropic virgin materials, where the non-virgin reference state is anisotropic but not, in general, transversely isotropic; the anisotropy depends on the deformation history. The proposed model is based on the anisotropic principal axis formulations developed by Shariff [1-3]. The proposed model contains invariants that have immediate physical interpretation. Mechanical responses of a constitutive equation, where all of its invariants have immediate physical interpretation are generally easier to analyse than those of constitutive equations with invariants that have some or no immediate physical intepretations. A specific constitutive model is proposed for soft tissues, and the model fits reasonably well with existing experimental data; it is also able to predict experimental data. Constitutive inequality is discussed. References: [1] Shariff, MHBM (2006) An anisotropic model of the Mullins effect. J Eng Math 56: 415-435. [2] Shariff, MHBM (2008) Nonlinear transversely isotropic elastic solids: an alternative representation, Quart J Mech Appl Math 61(2):129-149. [3] Shariff, MHBM (2011) Physical invariants for nonlinear orthotropic solids, Int. J Solids Struct 48:1906-1914.