A Study on the Correlation between Nonlocal Damage Mechanics and Hyperelasticity for Modeling Localization in a Slender Cylinder

The evolution of quasi-brittle failure is characterized by the evolution of localized damage (microcracking) that results in the formation and propagation of macrocracks. Higher-order continuum models have been developed by the research community over the last twenty years to predict the evolution of localization. However, there is a lack of analytical solutions in general due to the complexity involved in higher-order governing equations. Usually, numerical solutions are sought with a limited set of experimental data available for the verification of numerical approaches. Based on the previous work of the investigators, the main objective of this international interdisciplinary research project is to find the similarities and differences between the one-dimensional analytical solutions for damage with localization and the three-dimensional analytical solutions for hyperelasticity with necking-like localization. To demonstrate the proposed procedure, a slender cylinder will be considered with a parametric study performed to identify the physics behind each model parameter. As a result, the three-dimensional analytical solutions with simple constitutive models will be obtained to qualitatively predict the evolution of quasi-brittle failure, which could be used to verify numerical solutions with more advanced constitutive models.