Damaged-bone adaptation under steady homogeneous stress.

In this work an extension of the adaptive-elasticity theory is proposed in order to include the contribution of bone microdamage as a stimulus. Some aspects of damaged-bone tissue adaptation, brought about by a change of the daily loading history, are investigated. In particular, under the assumption of a small strain approximation and isothermal conditions, the solution of the remodeling rate equation for steady homogeneous stress is discussed and the damage effect upon the remodeling time constant is shown. The result is both theoretical and numerical, based on a recent theory of internal damaged-bone remodeling (Ramtani, S., and Zidi, M., 1999, "Damaged-Bone Remodeling Theory: Thermodynamical Approach, " Mechanics Research Communications, Vol. 26, pp. 701-708. Ramtani, S., and Zidi, M., 2001, "A Theoretical Model of the Effect of Continum Damage on a Bone Adaption Model," Journal of Biomechanics, Vol. 34, pp. 471-479) and motivated by the works of Cowin, S. C., and Hegedus, D. M., 1976, "Bone Remodeling I: Theory and Adaptive Elasticity," Journal of Elasticity, Vol. 6, pp. 471-479 and Hegedus, D. H., and Cowin, S. C., 1976, "Bone Remodeling II: Small Strain Adaptive Elasticity," Journal of Elasticity, Vol. 6, pp. 337-352.

[1]  M Zidi,et al.  A theoretical model of the effect of continuum damage on a bone adaptation model. , 2001, Journal of biomechanics.

[2]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[3]  R. Pidaparti,et al.  En bloc staining of bone under load does not improve dye diffusion into microcracks. , 1997, Journal of biomechanics.

[4]  D B Burr,et al.  Increased intracortical remodeling following fatigue damage. , 1993, Bone.

[5]  P J Prendergast,et al.  Prediction of bone adaptation using damage accumulation. , 1994, Journal of biomechanics.

[6]  Percy Williams Bridgman,et al.  The Nature of Thermodynamics , 1941 .

[7]  W C Hayes,et al.  Compact bone fatigue damage--I. Residual strength and stiffness. , 1977, Journal of biomechanics.

[8]  Sumio Murakami,et al.  Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics , 1997 .

[9]  E. Radin,et al.  Bone remodeling in response to in vivo fatigue microdamage. , 1985, Journal of biomechanics.

[10]  R. Huiskes,et al.  Simulation of self-organization and functional adaptation in bone , 1997 .

[11]  S C Cowin,et al.  Devolution of inhomogeneities in bone structure--predictions of adaptive elasticity theory. , 1980, Journal of biomechanical engineering.

[12]  M Zidi,et al.  Bone remodeling theory applied to the study of n unit-elements model. , 1999, Journal of biomechanics.

[13]  Stephen C. Cowin,et al.  Bone remodeling II: small strain adaptive elasticity , 1976 .

[14]  Wl,et al.  Experimental stress fractures of the tibia: biological and mechanical aetiology in rabbits , 1990, The Journal of bone and joint surgery. British volume.

[15]  Joseph Kestin.  Metal Plasticity as a Problem of Thermodynamics , 1988 .

[16]  D T Davy,et al.  A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. , 1984, Journal of biomechanical engineering.

[17]  S. Ramtani,et al.  Damaged-bone remodeling theory: Thermodynamical approach , 1999 .

[18]  J. Chaboche.  Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth , 1988 .

[19]  Frost Hm,et al.  Tetracycline staining of newly forming bone and mineralizing cartilage in vivo. , 1960 .

[20]  Dusan Krajcinovic,et al.  The Continuous Damage Theory of Brittle Materials, Part 1: General Theory , 1981 .

[21]  S. Cowin,et al.  Bone remodeling I: theory of adaptive elasticity , 1976 .

[22]  Gérard A. Maugin,et al.  THERMODYNAMICS WITH INTERNAL VARIABLES , 1999 .

[23]  Bernard D. Coleman,et al.  Thermodynamics of materials with memory , 1964 .

[24]  W. Muschik.  Thermodynamical Constitutive Laws - Outlines - , 1988 .

[25]  B. Manthey,et al.  Three-dimensional confocal images of microdamage in cancellous bone. , 1998, Bone.