An improved peridynamic framework for the accurate solution of multi-physics problems

Fracture phenomena can have severe consequences, such as human casualties and financial losses due to catastrophic failures in aerospace structures. Experimental analysis of fracture phenomenon is costly as it requires the destruction of components under test. This is the reason why, in the last decades, many numerical tools have been developed to virtually simulate crack initiation and propagation. Peridynamics is a nonlocal continuum theory that reformulates the governing equations by replacing the spatial derivatives with integrals, so that cracks can be defined without mathematical inconsistencies. In peridynamic models, fracture is an intrinsic material response, and cracks can initiate, propagate, branch, or coalesce in the most energetically favorable paths, in agreement with experimental observations. Peridynamics has some drawbacks that are typical of nonlocal models, such as the peridynamic surface effect (an undesired variation in the stiffness properties of the material in the region near the boundary of the body), the imposition of boundary conditions on a layer of finite thickness, the numerical integration of the peridynamic operator, and the high computational cost. The main objective of this work is to mitigate all these issues: - The Taylor-based extrapolation method with the nearest-node strategy has been developed to mitigate the peridynamic surface effect in bodies with a possibly complex geometry. - The surface node method has been devised to impose local boundary conditions in peridynamic models. - An efficient algorithm to accurately compute the quadrature weights in 2D and 3D peridynamic models has been developed. Using this algorithm, the numerical results show smaller errors and smoother convergence behavior. - An improved coupling technique between peridynamics and Carrera unified formulation, a very efficient classical model based on the finite element method, has been devised to reduce the computational cost of the simulations. All algorithms and numerical methods mentioned above were validated by many numerical examples. Using this improved peridynamic framework, the mechanism of fracture due to oxidation of zirconium carbide has been analyzed. Zirconium carbide is a very promising candidate for considerably improving the performance of nuclear reactors used in space missions or for green energy production. However, poor knowledge of the behavior of this material under oxidation hinders its use in nuclear applications. This complex multi-physics problem has been solved by means of a peridynamic model, and the main results are the following: - A new stability criterion of an explicit time integration method for the peridynamic diffusion equation has been derived taking into account, unlike previous stability criteria, the influence of the boundary conditions (applied with the surface node method). - Various convergence analyses have been conducted to study the impact of a discontinuity at the boundary in the initial conditions of a peridynamic diffusion problem, which describes the sudden exposure to oxygen of a zirconium carbide. - A peridynamic model of zirconium carbide oxidation, able to predict the growth of the oxide and determine the shape and dimensions of the remaining unoxidized carbide, has been developed. The same modeling approach can also be used, after the appropriate recalibration of material properties, to simulate phenomena similar to zirconium carbide oxidation, such as oxidation of transition metal carbides of group IV and lithiation in solid-state batteries.