Three-dimensional peridynamic modelling of quasi-brittle structural elements

Abstract

The peridynamic theory provides a promising theoretical framework for developing robust numerical models capable of simulating the complex fracture processes in quasi-brittle materials. However, there is a lack of detailed validation studies in the literature, and significant work remains to quantify the predictive accuracy and generality of a peridynamic model.

This thesis presents the development and validation of a three-dimensional bond-based peridynamic framework for modelling quasi-brittle structural elements. By following a rigorous validation process and carefully selecting validation problems that test a wide range of fundamental behaviours, a robust examination of the model is provided, and new insights into the capabilities of the bond-based model are gained.

This thesis begins with an examination of existing constitutive laws and a new non-linear softening model is introduced. Predictions with the newly proposed non-linear model improve upon existing laws. In an attempt to explain the cause of discrepancies between experimental and numerical results, it was determined that the application of surface correction factors increases the energy required to produce a fracture surface. This is the first time that this effect has been described, and a correction scheme is proposed that is simple to implement and yields improved results.

It is demonstrated that a bond-based peridynamic model can accurately capture the size effect in quasi-brittle materials. This is the first time that a peridynamic model has been used to examine the size effect and provides an important check on the validity of the numerical model. The thesis ends with an examination of the predictive accuracy and generality of the model against nine reinforced concrete beams that exhibit a wide range of failure modes. The shear-span-to-depth ratio is systematically varied from 1 to 8 to facilitate a study of different load-transfer mechanisms and failure modes. This is the first study to rigorously validate the predictive capability of a peridynamic model against a series of problems.

The model is validated using published experimental data, and the predictive accuracy is equivalent to well-established numerical methods whilst offering several benefits that justify further research and development.