Mechanisms Governing the Inelastic Deformation of Cortical Bone
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Mechanisms Governing the Inelastic Deformation of Cortical Bone C. Mercer1, R. Wang2 and A. G. Evans1 1
Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106, U.S.A. 2 Department of Materials Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada. ABSTRACT To understand the inelastic response of bone, a two-part investigation has been conducted. In the first, a flexural test protocol has been designed and implemented that monitors the axial and transverse strains on both the tensile and compressive surfaces of cortical bone. The results are used to assess the relative contributions of dilatation and shear to the inelastic deformation. Unload/reload tests have characterized the hysteresis and provided insight about the mechanisms causing the strain. These tests reveal strain healing attributed to sacrificial bonds. The second part devises a model for the stress/strain response, based on a recent assessment of the nanoscale organization of the collagen fibrils and mineral platelets. The model rationalizes the inelastic deformation in tension, as well as the permanent strain and hysteresis.
INTRODUCTION Mammalian bone is a relatively tough composite consisting of aligned, compliant, collagen fibrils with attached platelets of a stiff hydroxyapatite (Ca10(PO4)6(OH)2) mineral phase. It is composed of two spatially distinct topologies [Ref. 1 (2nd Edition), p. 430, figure 11.1b]. The outside consists of relatively dense, hard layer of cortical bone. The interior is cellular, referred to as cancellous or trabecular bone, consisting of inter-connected struts and faces. Its open cell topology resembles that found in synthetic cellular materials, such as open-cell metallic and polymer foams [1]. Both types of bone contain collagen fibrils arranged in bundles, aligned along the longitudinal axis. The mineral phase, located primarily on the outside of the collagen, is resistant to fragmentation because it consists of tiny, nano-scale platelets [2-4]. Parallel to the collagen fibrils, the inelastic responses of cortical bone differ in tension and compression [1, 510] (figure 1). In tension, it yields, followed by (linear) hardening up to a failure strain of order 2.5%. In compression, it also yields, but at higher stress. It strain hardens rapidly to a peak, then softens and fails at strains of about 1.5%. To characterize the inelastic deformation, the following two-part protocol is adopted. Part I. Design and conduct fully instrumented flexure tests on cortical bone with three subobjectives. (a) Measure the inelastic strains and parse these strains between plasticity (volume conserving permanent strain) and dilatation. (b) Deduce the hysteresis and measure changes in stiffness with permanent strain.
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Figure 1. Schematic of the tensile and compressive stress/strain curves for cortical bone along the axis of the collagen fibrils [1].
Part II. Develop a model capable of characterizing the inelastic deformation in cortical bone (figure 2). The mo
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