Prof.-Dr.-Ing. Kerstin Weinberg
Department of Mechanical Engineering
University of Siegen

Non-Local Models for Dynamic Fracture Simulations (Phase-Field and Peridynamics)

ABSTRACT: Recently, non-local methods have gained attention for computing fracturing solids. Two such methods are the phase-field fracture approach and peridynamic modeling. While, in reality, cracks in a solid are sharp two-dimensional hypersurfaces, the phase-field fracture approach regularizes the material discontinuities with smooth transitions between broken and unbroken states. Otherwise, it relies on the classical Boltzmann continuum model. In contrast, peridynamics describes the material in a non-local form with a similar regularizing effect on cracks. One significant issue in the simulation of dynamic fracture and spallation is the correct handling of elastic waves, such as the pressure and tension waves inside a body induced by dynamic boundary conditions from an impact or impulse. This contribution investigates different peridynamic and phase-field fracture formulations. By studying longitudinal pressure waves inside an elastic body, this work compares the propagation and reflection of linear and non-linear waves at cracks in different peridynamic models. With numerical examples, the efficiency of the chosen methods for dynamic crack propagation and spallation is illustrated.

BIOGRAPHY: Kerstin Weinberg is a full professor of solid mechanics at the University of Siegen, Germany. She has a background in mechanical engineering and received her Ph.D. from the University of Magdeburg in 1996. After appointments at other German universities and at the California Institute of Technology, she received her Habilitation in Mechanics from the Technical University of Berlin. Kerstin Weinberg works mainly numerically, but also experimentally, on topics ranging from nonconventional discretization methods and investigations of dynamic fracture to microstructured materials, soft polymers, and data-driven numerical approaches. She has published more than 120 articles in international journals on the mechanics and physics of materials and structures. Kerstin Weinberg has been an associate editor of Mechanics of Materials since 2019 and is on the editorial boards of the journals European Journal of Mechanics A, Technische Mechanik, and Continuum Mechanics and Thermodynamics. She has organized international workshops and colloquia and serves, for example, as a member of the review board, Section Mechanics and Constructive Mechanical Engineering, at the German Research Foundation. Since 2024, Kerstin Weinberg has been treasurer of the European Mechanics Society. She has long been an active member of the German Association of Applied Mathematics and Mechanics (GAMM). Presently, Kerstin Weinberg is the president of GAMM.