Inverse multi-objective design of three-dimensional plate-based heterogeneous mechanical metamaterials

• A clustering-aware, data-efficient inverse design approach was developed for 3D plate metamaterials. • The approach integrates a deep neural network with a genetic algorithm, guided by finite element simulations. • The framework outputs are lightweight structures with tunable stiffness and high energy absorption. • A case study is presented on optimized implants with biocompatible stiffness and improved impact energy dissipation. Energy-absorbing architected metamaterials, featuring dissimilar sub-elements arranged in deliberate patterns, can achieve a notably wider array of mechanical properties compared to their uniform counterparts. The traditional design of these heterogeneous structures typically depends on expert knowledge and requires considerable trial-and-error effort. Here, we introduce a data-efficient approach for the inverse multi-objective design of high-energy absorbing, three-dimensional, heterogeneous mechanical metamaterials comprised of the combination of two distinct plate-based unit cell topologies. This approach proposes a framework that pairs a Deep Neural Network (DNN) with a Genetic Algorithm (GA), supported by finite element (FE) simulations, to inverse design heterogeneous metamaterials with tailored Young’s modulus ( E ), while maximizing energy absorption capacity and minimizing relative density(ρ). We applied this method to orthopaedic implants, as a case study, to design structures with a desirable biocompatible elastic modulus, enhanced energy absorption efficiency and minimized ρ. To the best of our knowledge, this is the first inverse design framework that integrates clustering-aware deep neural networks with evolutionary optimization, enabling accurate and efficient design of heterogeneous plate-based lattices with tailored mechanical performance.

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Publication Details

Journal
International Journal of Mechanical Sciences
Published
2026-01-14
DOI
https://doi.org/10.1016/j.ijmecsci.2026.111253
Primary Topic
Topology Optimization in Engineering
Type
article
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article

Inverse multi-objective design of three-dimensional plate-based heterogeneous mechanical metamaterials

Sara Bagherifard, F. Berto, Mario Guagliano, Nima Razavi et al.
International Journal of Mechanical Sciences
Topology Optimization in Engineering
article

Inverse multi-objective design of three-dimensional plate-based heterogeneous mechanical metamaterials

Sara Bagherifard, F. Berto, Mario Guagliano, Nima Razavi, Ramin Yousefi-Nooraie
article en

Abstract

• A clustering-aware, data-efficient inverse design approach was developed for 3D plate metamaterials. • The approach integrates a deep neural network with a genetic algorithm, guided by finite element simulations. • The framework outputs are lightweight structures with tunable stiffness and high energy absorption. • A case study is presented on optimized implants with biocompatible stiffness and improved impact energy dissipation. Energy-absorbing architected metamaterials, featuring dissimilar sub-elements arranged in deliberate patterns, can achieve a notably wider array of mechanical properties compared to their uniform counterparts. The traditional design of these heterogeneous structures typically depends on expert knowledge and requires considerable trial-and-error effort. Here, we introduce a data-efficient approach for the inverse multi-objective design of high-energy absorbing, three-dimensional, heterogeneous mechanical metamaterials comprised of the combination of two distinct plate-based unit cell topologies. This approach proposes a framework that pairs a Deep Neural Network (DNN) with a Genetic Algorithm (GA), supported by finite element (FE) simulations, to inverse design heterogeneous metamaterials with tailored Young’s modulus ( E ), while maximizing energy absorption capacity and minimizing relative density(ρ). We applied this method to orthopaedic implants, as a case study, to design structures with a desirable biocompatible elastic modulus, enhanced energy absorption efficiency and minimized ρ. To the best of our knowledge, this is the first inverse design framework that integrates clustering-aware deep neural networks with evolutionary optimization, enabling accurate and efficient design of heterogeneous plate-based lattices with tailored mechanical performance.

International Journal of Mechanical SciencesVol. 312
Norwegian University of Science and Technology (NO), Sapienza University of Rome (IT), Politecnico di Milano (IT)
Affordable and clean energy
Openalex Percentile: Top 88%
Topology Optimization in Engineering
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