By Leuschner A. O.
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Extra info for Comparison of Theory with Observation for the Minor Planets 10 Hygiea and 175 Andromache with Respect to Perturbations by Jupiter
Shacklock. Biaxial Testing of Cardiac Tissue. Master's thesis, University of Auckland, New Zealand, 1987. D. Streeter. Gross morphology and fiber geometry of the heart. , editor, Handbook of Physiology, American Physiological Society, Bethesda, MD, 1979. Section 2. J. H. Rijnsburger, R. J. Nagelsmit. Tension development and sarcomere length in rat cardiac trabeculae: Evidence of length-dependent activation. Cire. , 46:703-714, 1980.  P. C. Fung. The stress-strain relationship for skin. J. , 9:649-657, 1976.
2). These basic assumptions will be subsequently supplemented by additional structural and mechanical arguments. 2. 1) where the components of the second Piola-Kirchoff stress tensor Sij and the Green's strain tensor 'Yij are referred to some general material coordinates, and where g and G are the determinants of the metric tensors before and after the deformation, respectively. In the case ofthe myocardium, the total strain energy in a unit of volume is assumed to be the sum of the strain energies of the myofibers and of the collagen struts.
1. + 'Y33 sm sm '1'. 21) The final forms of the stress expressions are obtained after substituting the appropriate distribution functions and uniaxial stress-strain relations. 22) 2. 23) (no summation over i), where J is the determinant of the transformation of 0' and fjJ' to 0 and fjJ. 24) (no summation over i and over j) in order to be compared to the stresses measured in the mechanical tests (which were also referred to the initial configuration) . The Results and their Significance The fitting of the stress expressions to the stress-strain curves measured in the biaxial tests of Yin and colleagues  requires carrying out a nonlinear least-squares procedure in order to estimate the values of the parameters that appear in those expressions.