Kinematics and Mechanics of Large Deformations

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After noting that his approach to the development of the nonlinear stress-strain-history relationship in large deformations of living tissues “is theoretical, although in search for simplicity we shall be guided by experimental data,” Y. C. Fung (1967) writes “One may ask what is the merit of the theoretical approach? The answer is threefold: (1) To facilitate data collection and data analysis. If an experimental curve can be characterized mathematically by a few parameters, then these parameters can be tabulated and used to correlate the mechanical property of the tissues with other physical and physiological parameters, such as age, sex, injury, temperature, chemical environment, etc. (2) To derive three-dimensional stress-strain-history law under finite deformation. Such a law is needed for the analysis of any practical boundary-value problems, but is not yet available. Since it is very difficult to experiment with biological materials in three-dimensional stress fields, it is natural to turn to theoretical formulation and then derive solutions to appropriate problems that can be tested experimentally. In other words, a theoretical study may be used to formulate critical experiments to validate the basic hypotheses. (3) To unify different types of experiments, such as the static (very slow) elasticity, dynamic elasticity (finite strain rate), stress relaxation under fixed strain, creep deformation under fixed stress, strain-cycle hysteresis, and cyclic stress fatigue. A correct theoretical formulation should bring out the unity among these experiments. Only the formulation that is consistent with all the experimental results can be accepted.”