Prof. Ugo Galvanetto
Department of Industrial Engineering
University of Padua

Recent Developments in Numerical Peridynamic Methods for Solid Mechanics

ABSTRACT: Initially, this seminar will cover several contributions by the author and his co-workers that may be applicable to the most recent works discussed in the second half of the talk. A coupling approach between numerical discretizations of classical continuum mechanics and peridynamics (PD) [1] naturally lends itself to a more efficient numerical solution procedure, as well as to simpler imposition of boundary conditions (BC). A second method for locally imposing BC on a PD model will also be presented [2]. The seminar will then address the numerical solution of multiphysics problems and some common aspects of such problems [3]. The focus will include fully saturated porous media, where fluid pressure or flow can deform the solid or generate cracks within it. The main topic of the presentation will be a PD model designed for large strain in nearly incompressible materials. This work utilizes a correspondence model [4, 5] based on classical hyperelastic constitutive laws. Finally, the seminar will explain an efficient numerical procedure for solving PD problems, adapted from the work of Bobaru et al. [6].

REFERENCES:

[1] Ongaro, G., Seleson, P., Galvanetto, U., Ni, T., & Zaccariotto, M.  "Overall Equilibrium in the Coupling of Peridynamics and Classical Continuum Mechanics." Computer Methods in Applied Mechanics and Engineering, vol. 381, 2021, 113–515.

[2] Scabbia, F., Zaccariotto, M., & Galvanetto, U.  "A New Surface Node Method to Accurately Model the Mechanical Behavior of the Boundary in 3D State-Based Peridynamics." Journal of Peridynamics and Nonlocal Modeling, vol. 5, 2023, 521–555.

[3] Ni, T., Fan, X., Zhang, J., Zaccariotto, M., Galvanetto, U., & Schrefler, B.A.  "A Peridynamic-Enhanced Finite Element Method for Thermo-Hydro-Mechanical Coupled Problems in Saturated Porous Media Involving Cracks." Computer Methods in Applied Mechanics and Engineering, vol. 417, 2023, 116–376. 

[4] Warren, T.L., Silling, S.A., Askari, A., Weckner, O., Epton, M.A., & Xu, J.  "A Non-Ordinary State-Based Peridynamic Method to Model Solid Material Deformation and Fracture."  International Journal of Solids and Structures, vol. 46, 2009, 1186–1195.

[5] Scabbia, F., Diana, V., Fantoni, F., Zaccariotto, M., & Galvanetto, U. "Peridynamic Correspondence Model for Nearly-Incompressible Finite Elasticity." Computer Methods in Applied Mechanics and Engineering, vol. 447, 2025, 118–350.

[6] Jafarzadeh, S., Mousavi, F., Wang, L., & Bobaru, F. "PeriFast/Dynamics: A MATLAB Code for Explicit Fast Convolution-Based Peridynamic Analysis of Deformation and Fracture." Journal of Peridynamics and Nonlocal Modeling, vol. 6, 2024, 33–61.

BIOGRAPHY: Ugo Galvanetto is a professor of aerospace structures in the Department of Industrial Engineering at the University of Padua, Italy. His research interests include various fields of computational mechanics, such as virtual testing and design of personal protective equipment, biomechanics, fracture mechanics, and coupling techniques for local and nonlocal computational methods. He is the author or co-author of more than 125 peer-reviewed journal articles. He spent over ten years in the Department of Aeronautics at Imperial College London, where he was the principal investigator for several research projects funded by the European Union and other institutions. Additionally, he served on the editorial boards of the international journals Structural Health Monitoring and Mechanics of Advanced Materials and Structures. He is an associate editor for the Council of European Aerospace Societies Aeronautical Journal and the Journal of Peridynamics and Nonlocal Modeling. At the University of Padua, he is the Head of Undergraduate and Postgraduate Studies in Aerospace Engineering.