Constitutive modeling of engineering materials is a prerequisite to making predictions about systems of which those materials are components. Often the analyst is faced with a new material or a traditional material in a state (strain, strain rate, temperature, etc.) for which there is no accepted constitutive model. In such cases the analyst must construct a constitutive model suitable to the purpose in an ad hoc manner, a task often dependent on individual experience or serendipity.Here, we firstly explore a naive genetic programming approach to constructing consti- tutive equations suitable for engineering analysis, but the results of its direct application are disappointing. Next, a number of approaches are employed to address the problem in its components resulting in significantly better equations with respect to criteria regu- larly applied to assessing the utility of constitutive models. We refer to this collection of approaches as "guided evolution". For instance, one of those approached is to generate the basis functions of subsets of model parameters, making it easier to formulate the nonlinear behavior for engineering materials. This consideration of the separate effects of each variable or set of variables facilitates selection of experiments to identify subsets of parameters and to ascribe physical meaning to the corresponding terms. Further, by using such basis functions, we can generate hierarchical models with varying conformity to experimental data, complexity, and condition number. This and other forms of guided evolution constitute the bulk of this dissertation and are a major portion of the research reported in this dissertation. It is conventional to try to find a vector of parameters in the process of model calibration that yields an adequate fit with the calibration data and to use that for model predictions. A measure of merit for constitutive models is that though there be a unique parameter vector that best fits the data. If this condition is not satisfied there may be substantial variance for the models that can be fit equally well by a multitude of parameter vectors and uncertainty quantification becomes impossible. The contribution of non-uniqueness of calibrated parameter vectors to meaningful prediction is illustrated on two different problems. Addressing this issue is another significant portion of the research reported in this dissertation. A mathematical formulation involving condition number of a Hessian matrix is pro- posed so as to incorporate this parameterization issue in the production of candidate constitutive models. Multi-objective optimization is employed to generate constitutive models with good fitness, complexity, and condition number. The evaluation of one of these, the condition number, is computationally prohibitive when incorporated into the problem in a conventional manner. We developed an approach to alleviate this issue and generate models at great efficiency. This appears to be a new, and efficient approach to multi-objective optimization through genetic programming.
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