Sciences & Société
Soutenance de thèse : Fahmi GRINE
Initially-stressed hyperelastic materials: modeling, mechanical and numerical analysis of singular problems and identification of residual stress.
Doctorant : Fahmi GRINE
Laboratoire INSA : LaMCos
Ecole doctorale : ED162 Mécanique, Energétique, Génie Civil, Acoustique de Lyon
The presence of initial stress in natural and manufactured materials and structures has been known for a long term and it is experimentally well attested in diverse scopes from biomechanics, geophysics, to welded structures and industrial manufacturing. This internal stress has a substantial effect on the material and structural behaviour and can be the origin of heterogeneous and anisotropic behaviour.
This thesis aims to contribute to the development of different formulations and theoretical results in the theory of initially-stressed hyperelasticity. A first contribution is the development of constitutive models for initially stressed hyperelastic materials which has permitted to identify the kind of anisotropy generated by the initial stress field based on the analogy with the constitutive formulation for fibrous materials. The exploitation of this analogy for linear transverse isotropic elasticity has provided some insight into the use of anisotropy and fibre orientation to design some elastic machines by coupling different deformation modes in a continuum boundary value problem.
In addition, the identification of the residual stress and material parameters of an initially stressed linear elastic model is addressed and an analysis of the different parameters influencing the quality of the reconstructed fields is carried out.
Furthermore, two singular boundary value problems are considered and analyzed. The first problem is dedicated to the rigidity contrast (discontinuity) influence on the asymptotic mechanical field near a crack tip subjected to an anti-plane transformation. Whereas in the second one, a particular generalization of the three-dimensional Linear Elastic Fracture Mechanics (LEFM) to a model for an initially-stressed hyperelastic material is developed. A numerical analysis of the second singular problem using an XFEM formulation is realized accompanied by tests of convergence and stability.
Informations complémentaires
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INSA Lyon - Salle Bellecour-Terreaux (bâtiment Sophie Germain) (Villeurbanne)