In many applications, such as those which drive new material discovery, constitutive models are sought that have three characteristics: (1) the ability to be derived in automatic fashion with (2) high accuracy and (3) an interpretable nature. Traditionally developed models are usually interpretable but sacrifice development time and accuracy. Purely data-driven approaches are usually fast and accurate but lack interpretability. In the current work, a framework for the rapid development of interpretable, data-driven constitutive models is pursued. The approach is characterized by the use of symbolic regression on data generated with micromechanical finite element models. Symbolic regression is the search for equations of arbitrary functional form which match a given dataset. Specifically, an implicit symbolic regression technique is developed to identify a plastic yield potential from homogenized finite element response data. Through three controlled test cases of varying complexity, the approach is shown to successfully produce interpretable plasticity models. The controlled test cases are used to investigate the robustness and scalability of the method and provide reasonable recommendations for more complex applications. Finally, the recommendations are used in the application of the method to produce a porous plasticity model from data corresponding to a representative volume element of voids within a metal matrix.

在许多应用中，例如那些驱动新材料发现的应用，都寻求具有三个特征的本构模型：（1）具有以（2）高精度和（3）可解释的性质以自动方式导出的能力。传统开发的模型通常是可以解释的，但会牺牲开发时间和准确性。纯粹由数据驱动的方法通常快速准确，但缺乏可解释性。在当前的工作中，正在寻求一个用于快速发展可解释的，数据驱动的本构模型的框架。该方法的特征是对通过微机械有限元模型生成的数据使用符号回归。符号回归是对与给定数据集匹配的任意函数形式的方程式的搜索。具体来说，开发了一种隐式符号回归技术，以从均化的有限元响应数据中识别出塑性屈服潜力。通过三个复杂度不同的受控测试用例，该方法已成功显示出可解释的可塑性模型。受控测试用例用于研究该方法的鲁棒性和可扩展性，并为更复杂的应用提供合理的建议。最后，在该方法的应用中使用建议，以根据与金属基体内空隙的代表性体积元素相对应的数据生成多孔可塑性模型。受控测试用例用于研究该方法的鲁棒性和可扩展性，并为更复杂的应用提供合理的建议。最后，在该方法的应用中使用建议，以根据与金属基体内空隙的代表性体积元素相对应的数据生成多孔可塑性模型。受控测试用例用于研究该方法的鲁棒性和可扩展性，并为更复杂的应用提供合理的建议。最后，在该方法的应用中使用建议，以根据与金属基体内空隙的代表性体积元素相对应的数据生成多孔可塑性模型。