Peridynamic Modeling of Thin-Film Fracture on a Winkler Foundation

  • Yousefimiab, Elham (Lund University)
  • Salman, Oguz Umut (Lund University)
  • León Baldelli, Andrés Alessandro (CNRS – Sorbonne Université)
  • Ahadi, Aylin (Lund University)

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The mechanical properties of thin films have attracted significant attention due to their expanding applications in technologies such as microelectronics, optics, and protective coatings [1-4]. In this study, we numerically investigate the formation of crack patterns in thin films. The primary aim of this study is to identify the underlying fracture mechanisms and to gain insight into the mechanical behavior of thin films. To achieve this, we employ the peridynamic (PD) model, which, contrary to classical continuum mechanics, is integral-based and offers a non-local framework for capturing fracture dynamics. Peridynamic has the inherent capability of dealing with discontinuities such as damage within a continuum framework without requiring additional assumptions [5]. In this work, we investigate a one-dimensional benchmark problem of a simple composite film-substrate system using PD. In this model, the elastic film is attached to an elastic foundation using a Winkler-type interaction. The energy-based derivation of governing equations reveals an intrinsic length scale arising from the competition between nonlocal elastic interactions and the local Winkler interaction. Numerical simulations are then conducted using an in-house code. For the PD model, we employ a bond-based peridynamic approach with viscous damping to study the quasi-static fracture in the film-substrate system while retaining access to transient dynamic behaviour. The dynamic evolution of mechanical fields and energy measures during the relaxation process is studied. Additionally, the influence of damping on elastic wave propagation and fracture onset is systematically investigated. The study provides a computational basis for further investigations of fracture and dynamic behavior in peridynamic film–substrate models and motivates future investigation of alternative peridynamic interface formulations capable of capturing more complex and spatially heterogeneous crack patterns.