Thesis defense – Rajasekar GOPALSAMY ‘Variational approach to model fracture in viscolelastic materials of bituminous type’

Composition of jury :

• – Rapporteurs :
• Gilles PIJAUDIER-CABOT, Professeur, Université de Pau et des Pays de l’Adour
• Eshan V.DAVE, Professeur, University of New Hampshire, USA
• – Examinateurs
• Véronique LAZARUS, Professeure des universités, ENSTA Paris
• Frédéric DUBOIS, Professeur, Université de Limoges
• Nicolas MOËS, Professeur, École Centrale de Nantes
• -Directeur de thèse :
•  Ferhat HAMMOUM, Directeur de recherche, Université Gustave Eiffel
• – Co-encadrants :
•  Olivier CHUPIN, Chargé de recherché, Université Gustave Eiffel
•  Nicolas CHEVAUGEON, Maître de conférences, École Centrale de Nantes

Summary :

The deterioration of pavement due to the fracturing of layers made of bituminous materials
is a significant challenge, necessitating a deeper understanding of the associated mechanisms
and factors. Addressing this issue involves the development of essential theoretical models and
numerical tools. Bituminous materials are widely acknowledged for their viscoelastic character-
istics, forming the core focus of this thesis. In this context, the present thesis focuses on the
cracking of viscoelastic materials in a quasi-static setting. A novel, thermodynamically consistent
variational approach is introduced to model damage within viscoelastic solids. This approach
enables the integration of local constitutive equations into a global incremental potential, the
minimization of which yields the solution to the mechanical problem. To overcome the spurious
mesh-dependent results associated with softening damage models, the lip-field approach has been
used to regularize the problem. A detailed numerical implementation for both one-dimensional
(1D) and two-dimensional (2D) scenarios is presented, complemented by Python-based finite
element (FE) codes (link to code). The simulation results for the 2D case show the ability of
the model to fit experimental force-displacement curves (for mode-I fracture) and to predict the
crack paths (for mixed mode fracture). This work not only provides a robust theoretical and
numerical foundation for potential future applications in pavement mechanics but also extends
its relevance beyond bituminous materials. The methodology developed here can be applied ef-
fectively to model cracking in various viscoelastic materials.

Keywords : Damage, Fracture, Viscoelasticity, Lip-field approach, Bituminous materials, Vari-
ational approach