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Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities. (English) Zbl 1398.74024

Summary: The asymptotic homogenization technique is presently developed in the framework of geometrical nonlinearities to derive the large strains effective elastic response of network materials viewed as repetitive beam networks. This works extends the small strains homogenization method developed with special emphasis on textile structures in [the second author et al., “Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization”, J. Mech. Phys. Solids 61, No. 12, 2537–2565 (2013; doi:10.1016/j.jmps.2013.07.014)]. A systematic methodology is established, allowing the prediction of the overall mechanical properties of these structures in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the chosen equivalent continuum. Internal scale effects of the initially discrete structure are captured by the consideration of a micropolar effective continuum model. Applications to the large strain response of 3D hexagonal lattices and dry textiles exemplify the powerfulness of the proposed method. The effective mechanical responses obtained for different loadings are validated by FE simulations performed over a representative unit cell.

MSC:

74B20 Nonlinear elasticity
74A35 Polar materials
74Q15 Effective constitutive equations in solid mechanics
74E30 Composite and mixture properties
74K99 Thin bodies, structures
74A60 Micromechanical theories
74M25 Micromechanics of solids
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