Multiscale topology optimization (TO) of hyperelastic materials remains computationally prohibitive due to the repeated solution of microscale boundary value problems. In this work, we present a concurrent multiscale topology optimization framework that overcomes this limitation by leveraging physics-augmented neural networks (PANNs) as surrogate constitutive models. The proposed approach enables the simultaneous optimization of macroscale material distribution and microscale descriptors, within a unified nonlinear finite strain setting. The surrogate models are constructed using input-specific neural networks (ISNNs) that enforce key physical principles directly within the architecture, including convexity and material symmetry through invariant-based representations and structural tensors. This ensures thermodynamic consistency and numerical stability while accurately representing homogenized anisotropic hyperelastic responses. The trained PANNs replace the microscale boundary value problem and provide efficient evaluations of stresses and consistent tangent moduli using analytical first and second derivatives of the neural network, enabling tractable large-scale multiscale optimization. The framework is demonstrated on representative microstructures exhibiting transversely isotropic, cubic anisotropic, and nearly incompressible isotropic behavior. The results show that the proposed method captures complex multiscale interactions and enables physically meaningful spatial tailoring of material properties, while significantly reducing computational cost compared to classical FE$^2$ approaches. These findings establish PANNs as a powerful tool for high-fidelity multiscale topology optimization of nonlinear anisotropic materials.

翻译：超弹性材料的多尺度拓扑优化因需要反复求解微观尺度边值问题而计算代价高昂。本文提出一种并发式多尺度拓扑优化框架，通过采用物理增强神经网络作为本构替代模型来克服此局限性。所提方法在统一的非线性有限应变框架内，能够同时优化宏观材料分布与微观描述符。替代模型采用输入特异性神经网络构建，其架构直接融入了关键物理原理：通过基于不变量的表示和结构张量确保凸性和材料对称性。这既保证了热力学一致性与数值稳定性，又能精确表征均质化的各向异性超弹性响应。训练后的物理增强神经网络替代了微观边值问题，并利用神经网络的一阶和二阶解析导数高效计算应力及一致切线模量，从而实现了可计算的大规模多尺度优化。该框架在展示横观各向同性、立方各向异性及近似不可压缩各向同性行为的代表性微结构上得到验证。结果表明，所提方法能捕捉复杂的多尺度相互作用，实现材料特性的物理意义空间定制，同时相比经典有限元平方方法显著降低计算成本。这些发现确立了物理增强神经网络作为非线性各向异性材料高保真多尺度拓扑优化强大工具的地位。