An innovative multi-component variate that reveals hierarchy and evolution of structural damage in a solid:...

A major limitation of solid mechanics is the inability to take into account the influence of hierarchy and evolution of the inherent microscopic structure on evaluating the performance of materials. Irreversible damage and fracture in solids, studied commonly as cracks, flaws, and conventional material properties, are by no means descriptive of the subsequent responses of the microstructures to the applied load. In this work, we addressed this limitation through the use of a novel multi-component variate. The essence of this variate is that it allows the presentation of the random damage in the amplitude spectrum, probability space, and probabilistic entropy. Its uniqueness is that it reveals the evolution and hierarchy of random damage in multi- and trans-scales, and, in addition, it includes the correlations among the various damage features. To better understand the evolution and hierarchy of random damage, we conducted a series of experiments designed to test three variants of a poly (methyl methacrylate) (PMMA) bone cement, distinguished by the methods used to sterilize the cement powder. While analysis of results from conventional tension tests and scanning electron microscopy failed to pinpoint differences among these cement variants, our multi-component variate allowed quantification of the multi- and trans-scale random damage events that occurred in the loading process. We tested the statistical significance of damage states to differentiate the responses at the various loading stages and compared the damage states among the groups. We also interpreted the hierarchical and evolutional damage in terms of the probabilistic entropy (s), the applied stress (σ), and the trajectory of damage state. We found that the cement powder sterilization method has a strong influence on the evolution of damage states in the cured cement specimens when subjected to stress in controlled mechanical tests. We have shown that in PMMA bone cements, our damage state variate has the unique ability to quantify and discern the history and evolution of microstructural damage.