A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress.

[1]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[2]  O. C. Zienkiewicz,et al.  On the principle of repeatability and its application in analysis of turbine and pump impellers , 1972 .

[3]  R M Rose,et al.  A structural model for the mechanical behavior of trabecular bone. , 1973, Journal of biomechanics.

[4]  E. Sanchez-Palencia.  Non-Homogeneous Media and Vibration Theory , 1980 .

[5]  Jacques-Louis Lions,et al.  Some Methods in the Mathematical Analysis of Systems and Their Control , 1981 .

[6]  J. Lewis,et al.  Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis. , 1982, Journal of biomechanical engineering.

[7]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[8]  T. Hughes,et al.  An element-by-element solution algorithm for problems of structural and solid mechanics , 1983 .

[9]  M. Kleerekoper,et al.  Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis. Implications for the microanatomic and cellular mechanisms of bone loss. , 1983, The Journal of clinical investigation.

[10]  W. Hayes,et al.  Finite element analysis of a three-dimensional open-celled model for trabecular bone. , 1985, Journal of biomechanical engineering.

[11]  L. Gibson.  The mechanical behaviour of cancellous bone. , 1985, Journal of biomechanics.

[12]  G. Carey,et al.  Element‐by‐element linear and nonlinear solution schemes , 1986 .

[13]  S. Goldstein.  The mechanical properties of trabecular bone: dependence on anatomic location and function. , 1987, Journal of biomechanics.

[14]  D P Fyhrie,et al.  Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. , 1987, Journal of biomechanics.

[15]  P. Suquet,et al.  Elements of Homogenization Theory for Inelastic Solid Mechanics, in Homogenization Techniques for Composite Media , 1987 .

[16]  H. Grootenboer,et al.  Adaptive bone-remodeling theory applied to prosthetic-design analysis. , 1987, Journal of biomechanics.

[17]  A. Parfitt.  Bone remodeling and bone loss: understanding the pathophysiology of osteoporosis. , 1987, Clinical obstetrics and gynecology.

[18]  L. Mosekilde.  Age-related changes in vertebral trabecular bone architecture--assessed by a new method. , 1988, Bone.

[19]  W H Harris,et al.  Limitations of the continuum assumption in cancellous bone. , 1988, Journal of biomechanics.

[20]  L. Mosekilde.  Iliac crest trabecular bone volume as predictor for vertebral compressive strength, ash density and trabecular bone volume in normal individuals. , 1988, Bone.

[21]  J. M. Crolet,et al.  A numerical model of anisotropic elastic properties of osteons , 1988 .

[22]  N. Bakhvalov,et al.  Homogenisation: Averaging Processes in Periodic Media , 1989 .

[23]  S. Goldstein,et al.  The direct examination of three‐dimensional bone architecture in vitro by computed tomography , 1989, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[24]  David B. Burr,et al.  Structure, Function, and Adaptation of Compact Bone , 1989 .

[25]  J. Lewis,et al.  Experimental method for the measurement of the elastic modulus of trabecular bone tissue , 1989, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[26]  S C Cowin,et al.  The fabric dependence of the orthotropic elastic constants of cancellous bone. , 1990, Journal of biomechanics.

[27]  S. Goldstein,et al.  The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. , 1990, Journal of biomechanics.

[28]  S. Goldstein,et al.  Evaluation of a microcomputed tomography system to study trabecular bone structure , 1990, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[29]  L. Mosekilde,et al.  Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). , 1990, Bone and mineral.

[30]  G S Beaupré,et al.  An approach for time‐dependent bone modeling and remodeling—theoretical development , 1990, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[31]  L. Mosekilde.  Age-Related Loss of Vertebral Trabecular Bone Mass and Structure — Biomechanical Consequences , 1990 .

[32]  S. Goldstein,et al.  Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography , 1991, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[33]  H. Weinans,et al.  Mechanically induced bone adaptations around orthopaedic implants , 1991 .

[34]  S. Goldstein,et al.  Application of homogenization theory to the study of trabecular bone mechanics. , 1991, Journal of biomechanics.

[35]  N. Kikuchi,et al.  A comparison of homogenization and standard mechanics analyses for periodic porous composites , 1992 .

[36]  J M Crolet,et al.  Compact bone: numerical simulation of mechanical characteristics. , 1993, Journal of biomechanics.

[37]  Scott J. Hollister,et al.  Digital-image-based finite element analysis for bone microstructure using conjugate gradient and Gaussian filter techniques , 1993, Optics & Photonics.

[38]  S A Goldstein,et al.  The relationship between the structural and orthogonal compressive properties of trabecular bone. , 1994, Journal of biomechanics.