An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity Academic Article uri icon

abstract

  • A novel constitutive formulation is developed for finitely deforming hyperelastic materials that exhibit isotropic behavior with respect to a reference configuration. The strain energy per unit reference volume, W, is defined in terms of three natural strain invariants, K1-3, which respectively specify the amount-of-dilatation, the magnitude-of-distortion, and the mode-of-distortion. Distortion is that part of the deformation that does not dilate. Moreover, pure dilatation (K2 = 0), pure shear (K3 = 0), uniaxial extension (K3 = 1), and uniaxial contraction (K3 = -1) are tests which hold a strain invariant constant. Through an analysis of previously published data, it is shown for rubber that this new approach allows W to be easily determined with improved accuracy. Albeit useful for large and small strains, distinct advantage is shown for moderate strains (e.g. 2-25%). Central to this work is the orthogonal nature of the invariant basis. If represents natural strain, then {K1,K2,K3} are such that the tensorial contraction of (Ki/) with (Kj/) vanishes when ij. This result, in turn, allows the Cauchy stress t to be expressed as the sum of three response terms that are mutually orthogonal. In particular (summation implied) t = AiW/Ki, where the W/Ki are scalar response functions and the Ai are kinematic tensors that are mutually orthogonal.

published proceedings

  • JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

author list (cited authors)

  • Criscione, J. C., Humphrey, J. D., Douglas, A. S., & Hunter, W. C.

citation count

  • 155

publication date

  • December 2000