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            <title xml:lang="en">Hyperelastic anisotropic effective strain gradient models based on large strains homogenization and applications to architected materials</title>
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                <forename type="first">Ahmed</forename>
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            <funder>This work was supported by the Agence Nationale de la Recherche (ANR) through the AMOC project.</funder>
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                <term xml:lang="en">Hyperelasticity, Homogenization, Strain gradient continua, Anisotropy, Material symmetry groups, Structural tensors, Thin-walled lattice materials</term>
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              <p>Higher gradient nonlinear models capturing size effects are elaborated for soft composites and architected media. A two-scale homogenization method is established to identify the nonlinear response of the underlying periodic microstructure, in the framework of strain gradient mechanics. The response of the base material is supposed to obey isotropic nonlinear elasticity. The anisotropy of the microstructure is captured by structural tensors reflecting its material symmetry group. A set of kinematic invariants of the macroscopic energy density is derived as the components of the Cauchy–Green first and second gradient tensors in the basis of the principal directions of anisotropy, proving to be invariant under the action of the material symmetry group, and accounting for rotations, reflections and permutations of the principal directions of anisotropy. The developed hyperelastic formulation is validated thanks to both full-field FE simulations and comparison with measurements done over pantographic structures exhibiting pronounced strain gradient effects. We exemplify the proposed homogenization method with different 2D microstructures and demonstrate the predictive capacity of the identified anisotropic hyperelastic model.</p>
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