2021/04/09 by Deison Préve, Andrea Bacigalupo, Préve, Deison +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2104.04343
openalex publication_date 2021/04/09 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/01
A multiscale asymptotic homogenization method for periodic microstructured\nmaterials in presence of thermoelasticity with periodic spatially dependent one\nrelaxation time is introduced. The asymptotic expansions of the\nmicro-displacement and the micro-temperature fields are rewritten on the\ntransformed Laplace space and expressed as power series of the microstructural\nlength scale, leading to a set of recursive differential problems over the\nperiodic unit cell. The solution of such cell problems leads to the\nperturbation functions. Up-scaling and down-scaling relations are then defined,\nand the latter allow expressing the microscopic fields in terms of the\nmacroscopic ones and their gradients. Average field equations of infinite order\nare also derived. The efficiency of the proposed technique was tested in\nrelation to a bi dimensional orthotropic layered body with orthotropy axis\nparallel to the direction of the layers, where the mechanical and temperature\nconstitutive properties were well stabilised. The dispersion curves of the\nhomogenized medium, truncated at the first order are compared with the\ndispersion curves of the heterogeneous continuum obtained by the Floquet-Bloch\ntheory. The results obtained with the two different approaches show a very good\nagreement.\n