Thesis title: Advanced material modeling for virtual tire development
The tire industry is undergoing a significant transformation, shifting towards virtual prototyping to reduce development time, costs, and environmental impact associated with physical testing. This transition to digital twin technology necessitates highly accurate constitutive models capable of capturing the complex behavior of carbon black-reinforced rubber compounds used in tire manufacturing. However, current models often fall short in accurately predicting the nonlinear, viscoelastic, and rate-dependent behavior of filled elastomers across the wide range of loading conditions and frequencies encountered in tire applications. This research addresses this critical gap by developing advanced material models for virtual tire development.
The main research objectives are:
To develop a unified theoretical framework for finite viscoelasticity that extends existing models to capture complex phenomena such as Payne effect;
To implement novel experimental protocols for comprehensive material characterization;
To create robust computational tools for implementing these advanced material models in finite element simulations;
To explore innovative data-driven approaches that complement traditional phenomenological modeling.
This thesis builds upon and extends several key theories in the field of viscoelasticity and rubber mechanics. The foundation is laid with the Generalized Maxwell Model (GMM), which is systematically developed from 1D linear viscoelasticity to 3D nonlinear finite viscoelasticity. Central to this development is the multiplicative decomposition of the deformation gradient (Kröner-Lee split), which allows for a thermodynamically consistent treatment of large deformations. The framework incorporates objective rates of elastic strain measures, such as the Oldroyd derivative, to ensure frame invariance in the constitutive equations. The thesis extends these theories by developing a generalized framework that encompasses various existing models as special cases, including the Reese-Govindjee, Bergström-Boyce, Kumar-Lopez-Pamies, and Yoshida-Sugiyama models. Particular attention is given to the formulation of nonlinear viscosity functions that capture phenomena like shear-thinning and strain-induced softening, crucial for accurately modeling the Payne effect observed in filled rubber compounds.
This unified approach allows for a systematic comparison of different models and provides a flexible structure for developing new constitutive relationships. Experimental work centers on Dynamic Mechanical Analysis (DMA) of filled elastomers, analyzing storage and loss moduli to characterize nonlinear viscoelastic behavior. Model validation involves comparing analytical solutions with 3D finite element simulations, using Particle-Swarm-Optimization for parameter calibration. Furthermore, the theoretical framework is enriched by incorporating concepts from data-driven modeling, particularly in the formulation of the Deep Rheological Element, which combines the structure of the GMM with neural networks to model complex nonlinear viscosity functions. This hybrid approach demonstrated improved accuracy over traditional phenomenological models while maintaining physical consistency.