Multiscale Modeling of the Evolution of Damage in Heterogeneous Viscoelastic Solids
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It has long been recognized that one of the primary failure modes in solids is due to crack growth, whether it be a single or multiple cracks. It is known, for instance, that Da Vinci [14] proposed experiments of this type in the late fifteenth century. Indeed, modern history is replete with accounts of events wherein fracture-induced failure of structural components has caused the loss of significant life. Such events are common in buildings subjected to acts of nature, such as earthquakes, aircraft subjected to inclement weather, and even human organs subjected to aging. Therefore, it would seem self-evident that cogent models capable of predicting such catastrophic events could be utilized to avoid much loss of life. However, despite the fact that such events occur regularly, the ability to predict the evolution of cracks, especially in inelastic media, continues to elude scientists and engineers. This appears to be at least due, in part, to two as yet unresolved issues (1) there is still no agreed upon model for predicting crack extension in inelastic media and (2) the prediction of the extension of multiple cracks simultaneously in the same object is as yet untenable. While it would be presumptuous to say that the authors have resolved these two outstanding issues, there is at least a glimmer of hope that these two issues may be resolved by using an approach not unlike that proposed herein. This chapter outlines an approach for predicting the evolution of multiple cracks in heterogeneous viscoelastic media that ultimately leads to failure of the component to perform its intended task. 2008 Springer Science+Business Media, LLC.
