Deformation partitioning provides insight into elastic, plastic, and viscous contributions to bone material behavior

Abstract

The relative contributions of elastic, plastic, and viscous material behavior are poorly described by the separate extraction and analysis of the plane strain modulus, E ′ , the contact hardness, H c (a hybrid parameter encompassing both elastic and plastic behavior), and various viscoelastic material constants. A multiple element mechanical model enables the partitioning of a single indentation response into its fundamental elastic, plastic, and viscous deformation components. The objective of this study was to apply deformation partitioning to explore the role of hydration, tissue type, and degree of mineralization in bone and calcified cartilage. Wet, ethanol-dehydrated, and PMMA-embedded equine cortical bone samples and PMMA-embedded human femoral head tissues were analyzed for contributions of elastic, plastic and viscous deformation to the overall nanoindentation response at each site. While the alteration of hydration state had little effect on any measure of deformation, unembedded tissues demonstrated significantly greater measures of resistance to plastic deformation than PMMA-embedded tissues. The PMMA appeared to mechanically stabilize the tissues and prevent extensive permanent deformation within the bone material. Increasing mineral volume fraction correlated with positive changes in E ′ , H c , and resistance to plastic deformation, H ; however, the partitioned deformation components were generally unaffected by mineralization. The contribution of viscous deformation was minimal and may only play a significant role in poorly mineralized tissues. Deformation partitioning enables a detailed interpretation of the elastic, plastic, and viscous contributions to the nanomechanical behavior of mineralized tissues that is not possible when examining modulus and contact hardness alone. Varying experimental or biological factors, such as hydration or mineralization level, enables the understanding of potential mechanisms for specific mechanical behavior patterns that would otherwise be hidden within a more complex set of material property parameters.