Abstract Homogenizing the constitutive response of materials with nonlinear and history-dependent behavior at the microscale is particularly challenging. In this case, the only option is generally to homogenize numerically via concurrent multiscale models (CMMs). Unfortunately, these methods are not practical as their computational cost becomes prohibitive for engineering-scale applications. In this work, we develop an alternative formulation to CMMs that leverage state-of-the-art micromechanical modeling and advanced machine learning techniques to develop what we call smart constitutive laws (SCLs). We propose a training scheme for our SCLs that makes them suitable for arbitrary loading histories, making them equivalent to traditional constitutive models. We also show how to implement a SCL into a traditional finite element solver and investigate the response of an engineering-scale component. We compare our results to those obtained via a high fidelity simulation. Our findings indicate that SCLs can dramatically boost the computational efficiency and scalability of computational homogenization for nonlinear and history-dependent materials with arbitrary microstructures, enabling in this way the automatic and systematic generation of microstructurally-informed constitutive laws that can be adopted for the solution of macro-scale complex structures.

中文翻译：

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智能本构法则：通过机器学习实现非弹性同质化

摘要 在微观尺度上均匀化具有非线性和历史相关行为的材料的本构响应尤其具有挑战性。在这种情况下，唯一的选择通常是通过并发多尺度模型 (CMM) 进行数值同质化。不幸的是，这些方法并不实用，因为它们的计算成本对于工程规模的应用来说变得过高。在这项工作中，我们开发了 CMM 的替代公式，它利用最先进的微机械建模和先进的机器学习技术来开发我们所说的智能本构定律 (SCL)。我们为我们的 SCL 提出了一个训练方案，使它们适用于任意加载历史，使它们等同于传统的本构模型。我们还展示了如何将 SCL 实施到传统的有限元求解器中，并研究工程规模组件的响应。我们将我们的结果与通过高保真模拟获得的结果进行比较。我们的研究结果表明，SCL 可以显着提高具有任意微观结构的非线性和历史相关材料的计算均质化的计算效率和可扩展性，从而能够以这种方式自动和系统地生成可用于解决宏观尺度的复杂结构。