Original title: Constitutive Modelling of Composites with Elastomer Matrix and Fibres with Significant Bending Stiffness
Translated title: Constitutive Modelling of Composites with Elastomer Matrix and Fibres with Significant Bending Stiffness
Authors: Fedorova, Svitlana ; Kotoul, Michal (referee) ; Menzel, Andreas (referee) ; Burša, Jiří (advisor)
Document type: Doctoral theses
Year: 2018
Language: eng
Publisher: Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract: Constitutive modelling of fibre reinforced solids is the focus of this work. To account for the resulting anisotropy of material, the corresponding strain energy function contains additional terms. Thus, tensile stiffness in the fibre direction is characterised by additional strain invariant and respective material constant. In this way deformation in the fibre direction is penalised. Following this logic, the model investigated in this work includes the term that penalises change in curvature in the fibre direction. The model is based on the large strain anisotropic formulation involving couple stresses, also referred to as “polar elasticity for fibre reinforced solids”. The need of such formulation arises when the size effect becomes significant. Mechanical tests are carried out to confirm the limits of applicability of the classical elasticity for constitutive description of composites with thick fibres. Classical unimaterial models fail to take into account the size affect of fibres and their bending stiffness contribution. The specific simplified model is chosen, which involves new kinematic quantities related to fibre curvature and the corresponding material stiffness parameters. In particular, additional constant k3 (associated with the fibre bending stiffness) is considered. Within the small strains framework, k3 is analytically linked to the geometric and material properties of the composite and can serve as a parameter augmenting the integral stiffness of the whole plate. The numerical tests using the updated finite element code for couple stress theory confirm the relevance of this approach. An analytical study is also carried out, extending the existing solution by Farhat and Soldatos for the fibre-reinforced plate, by including additional extra moduli into constitutive description. Solution for a pure bending problem is extended analytically for couple stress theory. Size effect of fibres is observed analytically. Verification of the new constitutive model and the updated code is carried out using new exact solution for the anisotropic couple stress continuum with the incompressibility constraint. Perfect agreement is achieved for small strain case. Large strain problem is considered by finite element method only qualitatively. Three cases of kinematic constraints on transversely isotropic material are considered in the last section: incompressibility, inextensibility and the double constraint case. They are compared with a general material formulation in which the independent elastic constants are manipulated in order to converge the solution to the “constraint” formulation solution. The problem of a thick plate under sinusoidal load is used as a test problem. The inclusion of couple stresses and additional bending stiffness constant is considered as well. The scheme of determination of the additional constant d31 is suggested by using mechanical tests combined with the analytical procedure.
Keywords: hyperelasticita; konstitutivní modelování; Materiály zesílené vlákny; ohybová tuhost vlákna; polární pružnost; constitutive modelling; fibre bending stiffness; Fibre-reinforced materials; hyperelasticity; polar elasticity

Institution: Brno University of Technology (web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library.
Original record: http://hdl.handle.net/11012/137224

Permalink: http://www.nusl.cz/ntk/nusl-391300


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Universities and colleges > Public universities > Brno University of Technology
Academic theses (ETDs) > Doctoral theses