Strain gradient and generalized continua obtained by homogenizing frame lattices

By Houssam Abdoul-Anziz, Pierre Seppecher. Mathematics and Mechanics of Complex Systems, 2018

183 citations recorded by the source corpus.

We determine the effective behavior of periodic structures made of welded elastic bars. Taking into account the fact that flexural and torsional stiffnesses are much smaller than the extensional one we overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0ea82d75acc7bbeccdcc9162c772b3e6d38fc379

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In Computational Theory and Mathematics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Pantographic metamaterials: an example of mathematically driven design and of its technological challenges (2018, methodology): “[24], formal asymptotic expansion procedures, already employed [11,13], are systematically considered in the framework of linear elasticity in order to determine the effective behavior of periodic structures”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, background): “Name Oblique Rectangular Digonal Orthotropic Trichiral Trigonal Tetrachiral [GL] [1] [Z2 ] [Z2] [D2] [Z3] [D3] [Z4] #indep(L) 45 (44) 27 36 (35) 16 15 (14) 10 13 (12) Name Tetragonal Pentachiral Pentagonal Hexachiral Hexagonal Hemitropic Isotropic [GL] [D4] [Z5] [D5] [Z6] [D6] [SO(2)] [O(2)] #indep(”