Constitutive modeling and numerical solution of field problems

Abstract In formulating phenomenological models and developing solution algorithms for problems in continuum and structural mechanics, experience with the behavior of actual systems has always played an important guidance role for the engineer concerned with predicting performance of feasible alternatives. By exercising control over various system parameters the engineer attempts to minimize the difference between a desired objective and a predicted approximation thereof. Constitutive modeling of mechanical behavior of materials is an example typical of this activity. In this paper constitutive modeling of an isolated material element is discussed as an identification problem. The mathematical structure of the problem is discussed and limitations arising from experimental sources, measurement errors, and material nonlinearity are noted. As a consequence of the structure of the problem it is shown that an inverse initial-boundary value problem must be considered, in which material identification and numerical analysis of this problem must proceed simultaneously. This paper discusses a discretized form of the inverse problem and illustrates the methodology by citing a number of examples in the literature which appear as special cases of the present treatment.

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