A Road Map for Nonlinear Elastodynamics

Abstract: Nonlinear elastodynamics lies at the core of many contemporary challenges in mechanics, ranging from wave propagation in complex media to the modeling of soft materials and biological tissues. Despite significant advances, the current theoretical and computational frameworks often remain rooted in classical continuum assumptions, which may be inadequate to capture key phenomena such as dispersion, multiscale interactions, and the influence of microstructural discreteness. This talk presents a critical overview of the state of the art in nonlinear elastodynamics and proposes a forward-looking research agenda. After revisiting the main achievements of classical and weakly nonlinear theories, particular emphasis is placed on their limitations in describing strongly nonlinear wave phenomena and materials with complex internal structure. The discussion will highlight several open problems, including the role of microstructure in macroscopic wave dynamics, the identification and validation of constitutive models beyond the classical paradigm, and the interplay between nonlinearity, dispersion, and dissipation. The talk concludes by outlining a possible roadmap for future developments. The aim is to stimulate a more unified and rigorous framework for nonlinear elastodynamics, capable of addressing emerging applications in engineering and applied science.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)