Capturing Strain Induced Orthotropy Through a Novel Free Energy Density Definition

The work is a specific implementation of Schapery’s Thermodynamics based approach to viscoelasticity and mechanics. The change in free energy density from mechanical deformation is presented as a function of logarithmic principal strains.  Principal strain calculation provides 3 of the 9 mathematical relationships needed to capture strain induced orthotropy.  The proposed strain energy density is then made up of 6 separate functions, each defining an independent sub-state in terms of a single strain.  Three sub-state functions are dependent on each of the principal strains.  These axial contributions reduce to the dilatational contribution to 3D stress for isotropic materials.  Three distortional sub-state functions are each defined in terms of the stretch ratios on each principal plane.  The derivative of the proposed free energy density function cleanly separates distortion from axial (dilatational) stress in the large strain stress-strain response.  Based in thermodynamics, the approach provides a mathematical framework for scaling MD simulations up to the continuum level.