Failures and future directions of constitutive theories for experimental determination of mechanical behaviors
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Failure in experimentally determining the mechanical constitutive behavior of high strain, elastic materials and tissues is due to inadequate theory as opposed to inadequate experimental techniques or material tests. To demonstrate this, let us pose the existence of an ideal testing apparatus that can measure the stress completely and prescribe any permissible value of strain. With the best possible experimental situation, material response functions cannot be determined because the condition number of the system of equations is infinite when using conventional constitutive theories. With a change in constitutive theory, however, it becomes possible to determine material response functions with ideal and real world material tests.
