Composite materials often exhibit mechanical anisotropy owing to the material properties or geometrical configurations of the microstructure. This makes their inverse design a two-fold problem. First, we must learn the type and orientation of anisotropy and then find the optimal design parameters to achieve the desired mechanical response. In our work, we solve this challenge by first training a forward surrogate model based on the macroscopic stress-strain data obtained via computational homogenization for a given multiscale material. To this end, we use partially Input Convex Neural Networks (pICNNs) to obtain a polyconvex representation of the strain energy in terms of the invariants of the Cauchy-Green deformation tensor. The network architecture and the strain energy function are modified to incorporate, by construction, physics and mechanistic assumptions into the framework. While training the neural network, we find the type of anisotropy, if any, along with the preferred directions. Once the model is trained, we solve the inverse problem using an evolution strategy to obtain the design parameters that give a desired mechanical response. We test the framework against synthetic macroscale and also homogenized data. For cases where polyconvexity might be violated during the homogenization process, we present viable alternate formulations. The trained model is also integrated into a finite element framework to invert design parameters that result in a desired macroscopic response. We show that the invariant-based model is able to solve the inverse problem for a stress-strain dataset with a different preferred direction than the one it was trained on and is able to not only learn the polyconvex potentials of hyperelastic materials but also recover the correct parameters for the inverse design problem.

翻译：复合材料常因微结构的材料属性或几何构型而呈现力学各向异性，这使得其逆向设计成为双重问题：首先需识别各向异性的类型与取向，进而寻找实现目标力学响应的最优设计参数。本研究通过训练基于计算均匀化所得宏观应力-应变数据的正向代理模型来解决该挑战。为此，我们采用部分输入凸神经网络（pICNNs），以柯西-格林变形张量不变量为变量构建应变能的多凸表示。通过改进网络架构与应变能函数，将物理机理假设内嵌于框架之中。在神经网络训练过程中，我们同步识别各向异性类型（若存在）及其主取向。模型训练完成后，采用进化策略求解逆向问题以获得实现目标力学响应的设计参数。该框架在合成宏观数据与均匀化数据上均通过验证。针对均匀化过程中可能违反多凸性的情形，我们提出了可行的替代方案。训练完成的模型还可集成至有限元框架中，逆向求解实现目标宏观响应的设计参数。研究表明，基于不变量的模型能够处理与训练数据主取向不同的应力-应变数据集逆向问题，不仅能学习超弹性材料的多凸势函数，还能为逆向设计问题恢复正确的参数。