Decoupling Hydrostatic and Deviatoric Strain Energy Density in Biomaterials with Poisson's Ratio Larger Than 0.5

Strain energy density is a scalar measure of deformation in nonbiological and biological materials. It represents the energy stored in the material during deformation and can be decomposed into two components: hydrostatic energy, responsible for volume change, and deviatoric energy, responsible for shape change (distortion). Decoupling strain energy density is a common engineering practice as each component guides different responses in the material. For example, hydrostatic energy is predictive of cortical bone remodeling, while deviatoric energy theory is an excellent predictor of failure in ductile materials. Deviatoric energy may also be a key predictor of damage, growth, and remodeling in soft fibrous tissues (e.g. ligament), but large Poisso n’s ratios in soft tissue ha ve made this analysis difficult.

 

Th e Poisson’s ratio is a fundamental metric that defines a material’s resistance to distortion or volume change. Several biological materials exhibit a large Poisson’s ratio under uniaxial tension (3.0 for tendon, 1.7 for collagen constructs), indicating volume loss. Previous studies have investigated the structural origins for these large Poisson’s ratio s, but little interest has been given to their strain energy. Finite element (FE) solvers can output strain energy values for deformed materials; yet several solvers, including ABAQUS, lack the energy decoupling feature. FEBio is one of the rare FE solvers that can decouple strain energy, but only for uncoupled materials with Poisson’s ratios less than 0.5. A need thus exists to develop a technique to decouple strain energy in materials with a large Poisson’s ratio .

 

The objective of this work is to present a numerical approach to decoupling strain energy density in materials with a large Poisson’s ratio. The method will be validated using a FE solver for a material with small Poisson’s ratio and will be used to decouple strain energy in type -I collagen constructs , known to have large Poisson’s ratios, under simple and complex loading.