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We present a novel framework to model the effective material behavior of irregular cellular materials such as stochastic strut-based lattices. The essential modeling tool is a parametric physics-augmented neural network establishing a flexible relation between lattice design variables and the effective constitutive stiffness tensor. We derive and implement hard constraints, ensuring that relevant physical principles such as material symmetry and positive definiteness of the stiffness tensor are satisfied. Additionally, we address the generation of training data from computational homogenization and model suitable parametric representative volume elements. Finally, we incorporate our model into a multiscale topology optimization problem to compute functionally graded lattice structures with improved stiffness properties.

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Modeling and Optimization of Irregular Cellular Materials Using Parametric Physics-Augmented Neural Networks

  • 会议论文

  • 发表日期：

    2026年

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  • Jonathan Stollberg,
  • Tarun Gangwar,
  • Oliver Weeger,
  • Dominik Schillinger

摘要

We present a novel framework to model the effective material behavior of irregular cellular materials such as stochastic strut-based lattices. The essential modeling tool is a parametric physics-augmented neural network establishing a flexible relation between lattice design variables and the effective constitutive stiffness tensor. We derive and implement hard constraints, ensuring that relevant physical principles such as material symmetry and positive definiteness of the stiffness tensor are satisfied. Additionally, we address the generation of training data from computational homogenization and model suitable parametric representative volume elements. Finally, we incorporate our model into a multiscale topology optimization problem to compute functionally graded lattice structures with improved stiffness properties.