Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials

Abstract

The current work deals with periodic thermomechanical composite media, in which the material constituents are considered to obey the generalized standard materials laws. The aim is to provide a proper homogenization framework that takes into account both the equilibrium and the thermodynamics laws in microscale and macroscale levels. The study is based on the asymptotic expansion homogenization technique, which permits to deduce useful results about the general structure of microscale and macroscale energy potentials and constitutive laws. The paper also proposes an incremental, linearized formulation that allows to identify suitable thermomechanical tangent moduli for the macroscale problem. The capabilities of this framework are illustrated with numerical examples on multilayered composites.

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

“…Such approach can be achieved using the concept of periodic homogenization (Chatzigeorgiou et al, 2015(Chatzigeorgiou et al, , 2016. …”

Phenomenological multi-mechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation

“…ii) The present constitutive equations can be used for the modelling of thermoplastic based composites through a micromechanical scale transition scheme, whether by mean field (Lagoudas et al, 1991;Chaboche et al, 2005;Miled et al, 2013) or full field theories (Chatzigeorgiou et al, , 2016. Indeed, in reinforced thermoplastics, the rheological behaviour of the matrix is known to have coupled effects with the damage mechanisms that occur at the scale of the microstructure (Fitoussi et al, 2013;Arif et al, 2014a,b) and can then be accounted for using such approaches.…”

“…Indeed, because the thermomechanical interactions are known to be important in thermoplastic polymers (Benaarbia et al, 2014(Benaarbia et al, , 2015. Such a coupling requires the integration of the self-heating generated by the dissipation and the thermomechanical coupling sources (Ovalle Rodas et al, 2014Benaarbia et al, 2015;Chatzigeorgiou et al, 2016;Yu et al, 2017a,b).…”

“…Such verification is essential to validate the 3D numerical implementation of the model as well as its applicability for studying the behaviour of thermoplastic based composites through multiscale micromechanical schemes, whether by mean field theories (Lagoudas et al, 1991;Chaboche et al, 2005;Miled et al, 2013) or periodic homogenization (Chatzigeorgiou et al, , 2016). …”

An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture

“…For other models, such a decoupling through homogenization is well‐known. For instance, in the context of fully coupled thermomechanics, the mechanical problem and the heat equation decouple almost entirely upon homogenization …”