Coupled field damage structural dynamics

by Li, Qiang.

This work aims to develop a class of coupled field, microstructural/macrostructural (damage/structural) models that can be used to study the dynamics of damage evolution. Since the phenomena of failure and fracture span several spatial scales, from atomic to macro scales, and is very complex, our intention is to emphasize the development of a coupled field model with the simplest possible form while including key features of the dynamics. More specifically, we will use our model to study the relationship between initial microstructural damage state uncertainty and dynamic variability in both space and time domains. We will also examine fundamental properties of damage dynamics, such as the dimensionality over time, and the importance of slow flow dynamics. To develop our coupled field damage dynamics model, we define our damage variable and relate it to material properties. We also consider the existence and forms of generalized forces which are work conjugate to the damage variable. The damage field variable we consider represents the microstructural state, and is not limited to a single or several macro cracks. It is natural, therefore, to adopt the methodology and concepts of continuum damage mechanics to aid in defining our damage variable. Then the coupled field differential equations are obtained by iii extending the application of Hamilton’s principle to materials with microstructure. We incorporate the most important observations in the field of fatigue, such as the existence of a fatigue threshold and sensitivity to initial microstructural state. We also extend the concept of the Griffith energy release rate to the problem with generalized damage, and show that our model is a generalization of a Paris-type damage evolution law. iv