Abstract

We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures forming during spinodal decomposition) admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field. The macroscale boundary value problem is discretized by finite elements, which in addition to the displacement field continuously interpolate the microscale design parameters. By assuming a separation of scales, the local constitutive behavior on the macroscale is identified as the homogenized elastic response of the microstructure based on the local design parameters. As a departure from classical FE2-type approaches, we replace the costly microscale homogenization by a data-driven surrogate model, using deep neural networks, which accurately and efficiently maps design parameters onto the effective elasticity tensor. The model is trained on homogenized stiffness data obtained from numerical homogenization by finite elements. As an added benefit, the machine learning setup admits automatic differentiation, so that sensitivities (required for the optimization problem) can be computed exactly and without the need for numerical derivatives – a strategy that holds promise far beyond the elastic stiffness. Therefore, this framework presents a new opportunity for multiscale topology optimization based on data-driven surrogate models.

Highlights

  • Supported by developments in advanced manufacturing, mechanical metamaterials with tunable microstructure and controllable properties have made significant strides towards realizing materials by design [1,2,3,4,5,6]

  • The chosen spinodoid topology for the cellular network on the microscale admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field

  • We present a multiscale topology optimization framework for cellular structures based on spinodoid topologies, with simultaneous optimization of the macroscale material distribution and the microstructural design and orientation, where the effective microscale response and associated sensitivities are provided by a data-driven surrogate model that replaces nested FE calculations on the microscale

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Summary

Introduction

Supported by developments in advanced manufacturing, mechanical metamaterials with tunable microstructure and controllable properties have made significant strides towards realizing materials by design [1,2,3,4,5,6]. Key challenges have persisted, which can be exemplified by truss-, plate-, and shell-based cellular materials, which have dominated the design of metamaterials over the past decade. Most truss-based architectures exhibit poor scaling of stiffness and strength with relative density due to bending deformation of struts [7].

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