A novel implementation of asymptotic homogenization for viscoelastic composites with periodic microstructures

An approach for modeling non-ageing linear viscoelastic composites with general periodicity

“…Considering 19, it is possible to simplify significantly the problem (17). The following terms are vanishing,…”

“…Many papers have exhibited their potentialities for elastic (see Ramírez-Torres et al 2018 [13]), thermo-elastic (see Chatzigeorgiou et al 2012 [14]) and piezoelectric materials (see Rodríguez-Ramos et al 2014 [15]). Moreover, it gives suitable solution in the case of fibrous viscoelastic composites (see Berger et al 2018 [16] and Li et al 2019 [17]). Actually, the investigation of the effective properties of non-ageing viscoelastic composites are mainly based on the correspondence principle and the Laplace transform (see Hashin 1965 [18], 1970a [19], 1970b [20], Mandel 1966 [21], Christensen 1969 [22], Lahellec & Suquet 2007 [23]).…”

On the effective behavior of viscoelastic composites in three dimensions

“…In addition, the manuscript presents some differences with respect to previous works of some of the authors Rodríguez-Ramos et al, 2020 ) and with others in the literature ( Chen, Wang, Chen, & Geng, 2017;Chen et al, 2020;Li, Chen, Liu, & Wang, 2019;Wang & Pindera, 2016a ). Specifically, the numerical solution of the local problem is tackled by means of the finite element software COMSOL Multiphysics® and LiveLink TM for Matlab® scripting, and the solution's convergence is analyzed through three types of mesh discretization.…”

A numerical homogenization scheme used for derivation of a homogenized viscoelastic-viscoplastic model for the transverse response of fiber-reinforced polymer composites

“…In this method, the inelastic strain field is considered as given eigenstrains, which can be determined from solving linear problems with eigenstrains. Examples can be found for viscoelasticity [24][25][26] and for viscoplasticity [27][28][29][30] In the computational homogenization method, also referred to as micro-macro analysis or FE 2 [31], the local macroscopic constitutive response is derived from the solution of a microstructural boundary value problem in a (statistically equivalent) representative volume element (RVE) and information of the microscale is hierarchically passed to the macroscale by bridging laws. The RVE is a characteristic sample of heterogeneous material that should be sufficiently large to involve enough composite micro-heterogeneities in order to be representative, however it should be much smaller than the macroscopic dimensions [32].…”