A data-driven computational scheme for the nonlinear mechanical properties of cellular mechanical metamaterials under large deformation

Xue, Tianju; Beatson, Alex; Chiaramonte, Maurizio; Roeder, Geoffrey; Ash, Jordan T.; Mengüç, Yiğit; Adriaenssens, Sigrid; Adams, Ryan P.; Sheng, Mao

doi:10.1039/d0sm00488j

Cited by 38 publications

(23 citation statements)

References 62 publications

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“…We observe from the contour plots that the building blocks with five different shapes show similar responses when d > 0. This indicates that under tensile forces, the springs generally have similar mechanical behaviors, which is consistent with our previous work [Xue et al, 2020]. On the contrary, the energy contours show richer responses that are highly nonlinear when d < 0, i.e., under compression.…”

Section: Training Validation and Testsupporting

confidence: 91%

“…Previous studies have shown that the mechanical properties of CMMs are highly sensitive to the pore shapes [Bertoldi et al, 2010, Overvelde et al, 2012, Overvelde and Bertoldi, 2014, Xue et al, 2020. Under uniaxial compression, mechanical instabilities at the scale of unit-cell often lead to pattern transformations at the structural scale.…”

Section: Quasi-static Loadingmentioning

confidence: 99%

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Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

Xue¹,

Adriaenssens²,

Sheng³

2022

Preprint

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The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic responses of the continuum metamaterials. Yet it remains a challenge to accurately construct such systems based on the geometry of the building blocks of the metamaterial. In this work, we propose a machine learning approach to address this challenge. A metamaterial graph network (MGN) is used to represent the discrete system, where the nodal features contain the positions and orientations the rigid elements, and the edge update functions describe the mechanics of the nonlinear springs. We use Gaussian process regression as the surrogate model to characterize the elastic energy of the nonlinear springs as a function of the relative positions and orientations of the connected rigid elements. The optimal model can be obtained by "learning" from the data generated via finite element calculation over the corresponding building block of the continuum metamaterial. Then, we deploy the optimal model to the network so that the dynamics of the metamaterial at the structural scale can be studied. We verify the accuracy of our machine learning approach against several representative numerical examples. In these examples, the proposed approach can significantly reduce the computational cost when compared to direct numerical simulation while reaching comparable accuracy. Moreover, defects and spatial inhomogeneities can be easily incorporated into our approach, which can be useful for the rational design of soft mechanical metamaterials.

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Section: Training Validation and Testsupporting

confidence: 91%

Section: Quasi-static Loadingmentioning

confidence: 99%

Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

Xue¹,

Adriaenssens²,

Sheng³

2022

Preprint

Self Cite

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show abstract

“…These two properties have been shown to be sensitive to the geometric features of the pores. 3,40 Here, we use MSOM to optimize these features for the desired properties under given macroscopic loadings.…”

Section: Optimizing Static Macroscopic Properties Of Cmms Due To Inst...mentioning

confidence: 99%

Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation

Xue

Sheng

2022

Numerical Meth Engineering

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Soft cellular mechanical metamaterials (CMMs) have gained increasing attention due to their unique mechanical properties, especially when under large deformation. However, the strong nonlinearities and complex instabilities brought by the large deformation field is a critical challenge for the rational design of soft CMMs. In this work, we propose a mapped shape optimization method as a computational framework for inverse designs of soft CMMs.The core of this method is to introduce a fixed referential configuration. The geometric changes of the cellular structures are reflected by altering a differentiable shape map; and the deformation of the corresponding structures are determined by mapping the finite element computations to the referential configuration. Such formulation avoids the need to alter the background mesh and more importantly, provides an efficient way to compute the gradient of the objective functions with respect to the design variables via the adjoint method. The proposed method is of general purpose, and three distinct yet representative numerical examples are used to demonstrate the effectiveness of the method: optimizing unique overall mechanical properties, precise control of the onset of instability, and optimizing phononic band gaps. These examples cover a broad range of important engineering applications of soft CMMs.

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“…In recent years, many such datadriven constitutive modeling approaches have been presented for anisotropic, hyperelastic, and inelastic material behavior, e.g., using reduced basis models [34,35], clustering techniques such as self-consistent clustering analysis [36][37][38], polynomial or spline interpolation [39][40][41], or machine mearning (ML) with artificial neural networks (ANN) [42][43][44][45][46][47][48][49][50]. To the best of our knowledge, only in [51] ANN-based constitutive models have been applied to the multiscale simulation of highly geometrically nonlinear, buckling-prone microstructures. However, the work is restricted to 2D applications, material symmetry is not considered in the material model formulation, and the accuracy of the effective constitutive model itself is not assessed.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

2021

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A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models built upon artificial neural networks are trained on the homogenization data and investigated: one is hyperelastic and fulfills the material symmetry conditions by construction, while the other two are hyperelastic and elastic, respectively, and approximate the material symmetry through data augmentation based on strain energy densities and stresses. Finally, macroscopic nonlinear finite element simulations are conducted and compared to fully resolved simulations of a lattice structure. The good agreement between both approaches in tension and compression scenarios shows that the sequential multiscale approach based on anisotropic constitutive models can accurately reproduce the highly nonlinear behavior of buckling-driven 3D metamaterials at lesser computational effort.

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A data-driven computational scheme for the nonlinear mechanical properties of cellular mechanical metamaterials under large deformation

Abstract: Cellular mechanical metamaterials are a special class of materials, whose mechanical properties are primarily determined by their geometry. But capturing the nonlinear mechanical behavior of these materials, especially with complex...

Cited by 38 publications

References 62 publications

Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks

Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation

Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

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