2021/07/09 by Pietro Lenarda, Lenarda, Pietro, Marco Paggi +1
Chemical Engineering · Engineering · Mathematics · #Computational Physics (physics.comp-ph) #Elasticity and Material Modeling #FOS: Physical sciences #Fractional Differential Equations Solutions #Rheology and Fluid Dynamics Studies #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2107.08796
openalex publication_date 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fractional calculus has been proved to be very effective in representing the\nvisco-elastic relaxation response of materials with memory such as polymers.\nMoreover, in modelling the temperature dependency of the material functions in\nthermo-visco-elasticity, the standard time-temperature superposition principle\nis known to be ineffective in most of the cases (thermo-rehological\ncomplexity). In this work, a novel finite element formulation and numerical\nimplementation is proposed for the simulation of transient thermal analysis in\nthermo-rehologically complex materials. The parameters of the visco-elastic\nfractional constitutive law are assumed to be temperature dependent functions\nand an internal history variable is introduced to track the changes in\ntemperature which are responsible for the phase transition of the material. The\nnumerical approximation of the fractional derivative is employed via the so\ncalled Gr "unwald-Letnikov approximation. The proposed model is used to\nnumerically solve some test cases related to relaxation and creep tests\nconducted on a real polymer (Etylene Vynil Acetate), which is used as the major\nencapsulant of solar cells in photovoltaics.\n