A comprehensive analysis of dynamic indentation and impact behavior in viscoelastic solids

Viscoelastic materials exhibit complex, time-dependent mechanical behaviour, which is one of their fundamental properties and is widely used in engineering and biomedical applications. The accurate characterisation and predictive modelling of their complex behaviour, particularly under various loading conditions such as indentation and impact, remains a key challenge. In this dissertation, an experimental, numerical and theoretical combined framework is developed to investigate the contact mechanics of viscoelastic solids. Two important complementary problems are addressed: dynamic indentation and normal impact. First, the viscoelastic response of nitrile butadiene rubber (NBR) under sinusoidal deformation is investigated. Such indentation plays a key role as an alternative standard technique for the reliable, rapid, and non-destructive characterisation of materials in practical applications, particularly in sensitive fields such as biotechnology, as well as in viscoelastic dampers. In this study, experimental measurements obtained with specially designed sinusoidal indenters are compared with numerical simulations based on the Boundary Element Method (BEM) and a simplified theoretical formulation. The experimental, numerical, and theoretical predictions closely match one another, with only minor differences in the peak force and the relaxation phases. These findings validate the proposed multi-disciplinary methodology and highlight its effectiveness in the characterisation of viscoelastic materials and the estimation of dissipated energy. In the next stage, the dynamic behaviour of spheres such as PTFE, acrylic, PEEK and Nylon is investigated on a hard sapphire surface under normal impact. A custom-designed experimental setup combines controlled drop tests, a laser distance sensor, and high-speed imaging to record both the sphere’s motion and the evolution of the contact area at room temperature and at elevated temperatures. A numerical model based on linear viscoelastic contact mechanics, which incorporates the normal dynamics of the system, has been developed. Comparisons between the simulations and experiments show that under various impact conditions, the reduction of the gap during the initial impact events closely follows the measured contact-radius profiles. Despite its simplified formulation, the model successfully captures the main features of contact dynamics. In conclusion, the results of this thesis suggest that the integration of experimental techniques with advanced numerical modelling provides a fast, robust and reliable framework for the analysis of viscoelastic contact problems. The proposed methodologies contribute to a deeper understanding of the quasi-static and dynamic responses of viscoelastic materials. At the same time, they provide practical tools for their reliable characterisation and design in engineering applications.