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Sacks MS (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng 125:280–287 21. Spencer AJM (1971) Theory of invariants. In: Eringen A (ed) Continuum physics, vol I. Academic Press, New York, pp 239–353 22. Sverdlik A, Lanir Y (2002) Time-dependent mechanical behavior of sheep digitial tendons, including the effects of preconditioning. J Biomech Eng 124:78–84 Hysteretic Behavior of Ligaments and Tendons: Microstructural Analysis of Damage, Softening and Non-Recoverable Strain P.
D. A. , thin cell sheets). Herein, we present a technique to estimate the stress distribution and local material properties in an epithelial membrane. Circular holes are perforated through the tissue to determine the principal stretch ratios; experimentally measured changes in hole geometry are used in combination with finite element modeling to evaluate the stresses and constitutive response. The method is demonstratively applied to the embryonic chick blastoderm, since mechanical stresses have been identified as potential regulators of early development.
16, the equilibrium second Piola–Kirchhoff stress can be evaluated using the standard hyperelastic definition as, N X 1 @W @W @WM @WM F . I1 1 C/ C Seq D 2 M 1 C I3 C 1 C M˛ ; @I1 @I2 @I3 @ ˛ „ ƒ‚ … ˛D1 „ ƒ‚ ˛… eq eq eq eq eq (17) eq sf ˛ SM We then assume that the time-dependent stress response is given by the sum of the equilibrium stress and a time-dependent overstress as, eq S D SM . C/ C QM . C; t / C N X ˛D1 eq sf˛ . ˛; t / C qf˛ . Á ˛; t / : (18) Comparison of Models for Fibrous Tissues 25 The isotropic overstress QM for the matrix and the overstress qf˛ for the fiber families are modelled using a hereditary integral formulation, Z h i GM .