Hierarchical multi-scale modelling of the nonlinear deformation of fibre reinforced composites by means of general anisotropic constitutive models

Composite materials are made from a combination of two or more materials. Due to their high stiffness-to-weight ratio, they are highly desirable in lightweight construction. However, the effective use of these materials depends on the ability to predict the ultimate load and residual strength of the structures for which they are employed. To achieve this, an accurate representation of the constitutive response of the composite material is required. The present dissertation seeks to address some aspects of this issue by developing and implementing several constitutive models for various composite materials. To this end, a multi-surface constitutive model is developed for woven tungsten fibre reinforced copper matrix composite. Plastic anisotropy is modelled based on the concept of structural tensors by employing three different yield functions for three different load scenarios in the plane of the composite sheet. A finite element model of a plain weave repeating unit cell is set-up for parameter identification and validation. The applicability of the constitutive model is demonstrated by performing a simulation of drawing a thin circular plate with a hole and a cylindrical roof subjected to a line load. A second material model, based on the multi-surface constitutive model, is developed to model the in-plane anisotropic elastoplastic behaviour of paper and paperboard. The model is calibrated from a set of simple uniaxial tension tests carried out in various directions of the material and is validated against loading in other directions. The accuracy as well as the numerical performance of the constitutive model is accessed against a non-quadratic counterpart of the model. Furthermore, a constitutive model for the unidirectional tungsten fibre reinforced copper matrix composite is also developed. The constitutive model employs a Hill type yield function as well as multiple hardening functions to describe the anisotropic hardening behaviour of the composite. A finite element model of the composite is set-up for parameter identification and validation. Finally, a non-associative viscoelastic-viscoplastic constitutive model for unidirectional fibre reinforced polymer composites is developed. As a case study, flax fibre reinforced epoxy matrix is considered. The model adopts an anisotropic linear viscoelastic solid expressed in terms of Boltzmann hereditary form coupled with an anisotropic viscoplastic formulation to describe the deformation behaviour of the material. The yield surface of the model is constructed based on the concept of structural tensors. The anisotropic evolution of the yield surface is described by means of multiple non-linear isotropic and kinematic hardening functions. A finite element model of the unidirectional composite is also setup for calibration and validation. The developed constitutive model is assigned to the tows of a plain weave flax fibre/epoxy composite and the deformation behaviour of the composite is studied as well as the identification of the composite yield surface through virtual experiments