1203 Nonlocal models in computational mechanics: perspectives, challenges, and applications

  • Mirco Zaccariotto, University of Padova
  • Marta D'Elia, Sandia National Laboratories
  • Ugo Galvanetto, University of Padova
  • Pablo Seleson, Oak Ridge National Laboratory

Key words: Nonlocal Models, Discretization, Numerical Analysis, Multiscale Modelling, Local-Nonlocal Coupling Methods, Inverse Problems, Nonlocal models for Industrial applications.

The capability of nonlocal theories to accurately capture phenomena that are difficult or impossible to represent by (local) partial differential equations motivates and drives the interest in nonlocal models. As an example, the full description of damage propagation in structural materials is still a challenge. Although computational methods based on classical local continuum mechanics have produced some useful results, there are various concerns on their applicability and versatility. Nonlocal theories, based on integral-type models, offer alternative approaches that avoid difficulties arising in classical local theories. Furthermore, nonlocal continuum mechanics models can describe microstructure-dependent mechanical response by embedding the length scales in the governing equations. Finally, the possibility to adopt various length scales paves the way for the development of multiscale modelling methods. However, nonlocal models present several computational and modelling challenges that are still subject of open research. These challenges include reduction of the computational cost in the numerical solution; definition of strategies for imposing nonlocal boundary conditions; accurate and higher-order discretizations; study of multiphysics problems; formulation of physically-consistent nonlocal interface problems; and estimation of nonlocal model parameters from experimental data. Advances in these topics would unlock the full potential of nonlocal models for their application in computational mechanics and several other fields. The goal of this minisymposium is to bring together experts on the mathematical, computational, and engineering aspects of nonlocal models to discuss the state-of-the-art of nonlocal modelling, establish new research directions, identify promising research advances, and create synergies between participants.

Topics of interest include but are not limited to:
1. Mathematical and numerical analysis of nonlocal models.
2. Mesh-based and mesh-free discretization of nonlocal models.
3. Software implementation and efficient solvers for nonlocal problems.
4. Peridynamics and nonlocal diffusion modelling.
5. Nonlocal elasticity, nonlocal damage, and nonlocal plasticity models.
6. Nonlocal structural theories, such as beam and shell theories.
7. Multi-scale modelling using nonlocal methods, such as local/nonlocal coupling.
8. Multi-physics modelling in nonlocal problems, such as thermo-mechanical coupling.
9. Inverse nonlocal problems under uncertainty.
10. Scientific, engineering, and industrial applications of nonlocal models, such as subsurface flow, material failure and damage, image denoising, wave propagation, and stochastic processes.

Presentations on topics not included in the list, but in line with the theme of the minisymposium are also welcome.

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