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• W3215748102 abstract "We provide in this chapter a synthetic overview of homogenization methods for the setting up of second gradient linear and nonlinear anisotropic continuum media representative of periodic network materials made of beam-type structural elements, considering successively static and dynamic aspects in the context and linear and nonlinear theories. Generalized continuum models accounting for either nodal rotations or strain gradient contributions emerge from the extended asymptotic homogenization schemes taking into account either additional nodal degrees of freedom or long-range interactions between neighboring representative unit cells. The strain energy density of the effective continuum is derived relying either on analytic methods or based on dedicated asymptotic homogenization methods specific to discrete network materials. Strain gradient theories lead to dispersive wave propagation features that are overlooked by classical elasticity and that reflect measurements. Based on these models, we study the dispersion of elastic waves propagating in periodic beam networks, considering the pantographic structures, the re-entrant hexagonal lattice, the diamond chiral lattice, plain weave fabric, and the 3D hexagonal unit cell representative of trabecular bone. In the framework of nonlinear strain gradient theories, different types of waves propagate depending on the degree of nonlinearity; a supersonic mode occurs for a weak nonlinearity, whereas wave propagation changes from a supersonic to an evanescent subsonic mode for a higher degree of nonlinearity." @default.
• W3215748102 created "2021-12-06" @default.
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• W3215748102 date "2021-01-01" @default.
• W3215748102 modified "2023-10-10" @default.
• W3215748102 title "Second Gradient Linear and Nonlinear Constitutive Models of Architectured Materials: Static and Dynamic Behaviors" @default.
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• W3215748102 doi "https://doi.org/10.1007/978-3-030-42707-8_4" @default.
• W3215748102 hasPublicationYear "2021" @default.
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