Mechanism-based modelling of the viscoelastic response of a unidirectional composite ply: validation of a new transversely isotropic model through analytical and numerical homogenisation
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Federica DAGHIA (FRANCE), Alexandre LAGACHE , Livio DI GENNARO (UNITED KINGDOM)Abstract :
The macroscopic constitutive behaviour of composite materials results from the individual constituents’ behaviour, as well as their geometric arrangement. In particular, the viscoelastic response of long fibres, polymer matrix composites is mainly associated to the deviatoric response of the matrix [1]. This single microscale mechanism, however, results in different amounts of viscous relaxation for the different elastic constants defining the overall transversely isotropic composite behaviour, thus requiring the definition and identification of an increased number of model parameters [2].
In a recent work [3], some of the authors proposed a reformulation of transverse isotropy based on group representation theory, and in particular on an irreducible decomposition of the stress (resp. strain) tensors, also known as the Cartan decomposition. Four terms are retained: the normal stress in the fibres’ direction, the longitudinal shear stress, and finally the hydrostatic and deviatoric components of the stress in the plane of transverse isotropy. The integrity basis and the energy function deriving from this decomposition give rise to a set of five elastic constants which is different from those commonly used in transverse isotropy. In particular, the viscoelastic response was only attributed to the longitudinal and transverse shear moduli in [3], thus reducing the number of model parameters to be identified.
In this work, the pertinence of the model proposed in [3] is evaluated through analytical and numerical homogenisation techniques. Assuming linear elastic isotropic or transversely isotropic fibres, and a matrix whose deviatoric response is viscoelastic, the macroscopic response is investigated. Analytical results from [4] enable us to distinguish two sets of parameters among the five retained: the two shear moduli, whose value goes to zero as the matrix shear modulus goes to zero, and the three remaining parameters, mainly related to the fibres’ and to the bulk matrix responses, which vary by 20% maximum if elastic parameters for typical fibres and matrix in composites are considered. Numerical homogenisation with periodic boundary conditions enabled us to simulate relaxation, as well as creep tests in different directions. They confirmed that the key features of the Representative Volume Element (RVE) response can be captured by the new transversely isotropic model proposed in [3]. The key results discussed here can be found in a recent publication [5].
Acknowledgements: the authors would like to acknowledge Dr. Marc Olive for his key role in the geometrical formulation of the macroscopic transversely isotropic model. This work was motivated and partly funded by Cetim within the framework of the Laboratoire Commun Comp’Innov.
In a recent work [3], some of the authors proposed a reformulation of transverse isotropy based on group representation theory, and in particular on an irreducible decomposition of the stress (resp. strain) tensors, also known as the Cartan decomposition. Four terms are retained: the normal stress in the fibres’ direction, the longitudinal shear stress, and finally the hydrostatic and deviatoric components of the stress in the plane of transverse isotropy. The integrity basis and the energy function deriving from this decomposition give rise to a set of five elastic constants which is different from those commonly used in transverse isotropy. In particular, the viscoelastic response was only attributed to the longitudinal and transverse shear moduli in [3], thus reducing the number of model parameters to be identified.
In this work, the pertinence of the model proposed in [3] is evaluated through analytical and numerical homogenisation techniques. Assuming linear elastic isotropic or transversely isotropic fibres, and a matrix whose deviatoric response is viscoelastic, the macroscopic response is investigated. Analytical results from [4] enable us to distinguish two sets of parameters among the five retained: the two shear moduli, whose value goes to zero as the matrix shear modulus goes to zero, and the three remaining parameters, mainly related to the fibres’ and to the bulk matrix responses, which vary by 20% maximum if elastic parameters for typical fibres and matrix in composites are considered. Numerical homogenisation with periodic boundary conditions enabled us to simulate relaxation, as well as creep tests in different directions. They confirmed that the key features of the Representative Volume Element (RVE) response can be captured by the new transversely isotropic model proposed in [3]. The key results discussed here can be found in a recent publication [5].
Acknowledgements: the authors would like to acknowledge Dr. Marc Olive for his key role in the geometrical formulation of the macroscopic transversely isotropic model. This work was motivated and partly funded by Cetim within the framework of the Laboratoire Commun Comp’Innov.