Giulia Sarego

Examples of applications of the peridynamic theory to the solution of static equilibrium problems

Peridynamics is a recently proposed continuum theory based on a non local approach and formulated with integral equations. The theory is suitable for dealing with crack propagation in solid materials. The original peridynamic formulation regarded dynamic problems and was adapted to the static case mainly using a relaxation method by introducing a substantial amount of numerical damping in the time integration. In the present work the implementation of the theory within an implicit code for static crack propagation phenomena based on the Newton-Raphson method is presented and applied to several examples of static crack propagation equilibrium problems. Results obtained with the newly developed procedure are presented for various structural configurations, with different boundary and load conditions and quantitatively compared to published data.

Mixed-Mode Crack Patterns in Ordinary State-Based Peridynamics

A new nonlocal theory of continuum, called Peridynamics, was introduced in 2000. While the classical theory of solid mechanics employs spatial derivatives in order to solve the motion equation and consequently requires the derivability of the displacement field, Peridynamics employs an integral formulation of the equation of motion which leads to the possibility to analyze structures without specific techniques whenever discontinuities, such as cracks or inhomogeneities, are involved. Peridynamics has proven to be able to handle several phenomena concerning crack propagation. There are two variants of the theory, bond-based and state-based. The former is a particular case of the latter, which can also be found in two versions, the ordinary, in which the interaction force between two nodes is aligned with their current relative position, and the non-ordinary, in which interaction forces can have different directions and classical models can be directly introduced in the formulation, even though in this variant numerical integration problems arise (spurious mode deformation). In this study, fracture patterns for mixed-mode crack propagation cases are investigated while varying two fundamental parameters of Peridynamics, the maximum length of interaction, called horizon, and the ratio between the grid spacing and the horizon, called m-ratio. An ordinary state-based Peridynamics formulation is adopted and numerical results are compared with experimental evidences.