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Hypoelastic soft tissues. II: In-plane biaxial experiments. (English) Zbl 1320.74020
Summary: In Part I, a novel hypoelastic framework for soft tissues was presented. One of the hallmarks of this new theory is that the well-known exponential behavior of soft tissues arises consistently and spontaneously from the integration of a rate based formulation. In Part II, we examine the application of this framework to the problems of biaxial kinematics, which are common in experimental soft-tissue characterization. We confine our attention to an isotropic formulation in order to highlight the distinction between nonlinearity and anisotropy. In order to provide a sound foundation for the membrane extension of our earlier hypoelastic framework, the kinematics and kinetics of in-plane biaxial extension are revisited, and some enhancements are provided. Specifically, the conventional stress-to-traction mapping for this boundary value problem is shown to violate the conservation of angular momentum. In response, we provide a corrected mapping. In addition, a novel means for applying loads to in-plane biaxial experiments is proposed. An isotropic, isochoric, hypoelastic, constitutive model is applied to an in-plane biaxial experiment done on glutaraldehyde-treated bovine pericardium. The experiment is comprised of eight protocols that radially probe the biaxial plane. Considering its simplicity (two adjustable parameters), the model does a reasonably good job of describing the nonlinear normal responses observed in these experimental data, which are more prevalent than are the anisotropic responses exhibited by this tissue.

MSC:
74B20 Nonlinear elasticity
70B15 Kinematics of mechanisms and robots
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