Peridynamic (PD) models are ideally suited for simulating damage (fracture, fragmentation, dissolution, corrosion, erosion, etc.) because nonlocality allows various failure mechanisms to be represented, in an average sense, seamlessly across multiple scales, while maintaining the dominant length-scale in the description. This course presents PD formulations of general material failure/degradation phenomena, including: dynamic brittle fracture, shear banding and ductile failure, corrosion damage, damage in concrete structures, thermomechanical failure, fracture in composite and porous materials, etc.
FFurthermore, strategies to couple classical continuum mechanics and PD will be discussed and applied to the coupling of FEM meshes and PD grids. A special emphasis will be placed on transitioning from a mathematical formulation to numerical solutions.
Participants will gain hands-on experience with open-source Matlab codes implementing FEM-PD coupled models to simulate crack propagation problems, and fast pseudo-spectral solvers for PD models of dynamic fracture and corrosion. Differences from other nonlocal models, and confusing terms used in the published literature will be clarified. Other advanced topis will be addressed. The course is aimed at researchers and graduate students in the fields of mechanical, aerospace, civil and biomedical engineering, applied mathematics, electrochemical engineering, physics, and biophysics.

Dr. Bobaru will introduce the peridynamic formulation as a general continuum/discontinuum theory of mechanics and thermodynamics. PD formulations do not use spatial derivatives, allowing them to handle material failure (fracture, damage, dissolution, etc.) in a mathematically consistent way. He will present two types of numerical methods that are particularly well suited for discretizing PD models: meshfree and pseudo-spectral methods. He will conduct hands-on sessions using Matlab-based implementations of pseudo-spectral methods for solving problems in fracture mechanics and corrosion damage. Dr. Bobaru will also show that analytical solutions for some PD problems in elasticity and heat/mass transfer are no more difficult to find than for classical PDE-based problems.

Dr. Galvanetto will discuss how PD can be used in conjunction with classical methods to study multiphysics problems. He will address problems specific to PD, such as the imposition of the boundary conditions, or to its numerical implementation, such as the accurate computation of the integrals or solution sensitivity to grid orientation.

Dr. Zaccariotto will discuss a strategy to couple classical continuum mechanics and PD. The method will not only be described theoretically but also through practical sessions using Matlab-based codes. Moreover, the often-neglected issue of verifying overall structural equilibrium in coupled FEM-PD models will be discussed. Finally, he will provide an accurate description of an implicit static solution procedure.

Dr. Diana will introduce a unified theoretical and computational scheme for pair-potentials based continuum-molecular modelling of anisotropic elasticity, fracture and diffusion-type problems within the framework of a revised bond-based peridynamic theory with oriented material points. Finally he will propose a general micro-macro moduli correspondence procedure.