Theory of elasticity and consolidation for a porous anisotropic solid

Biot, M. A.

Affiliations

¹Shell Development Company, New York City, New York

Abstract

The author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.

Links

DOI: 10.1063/1.1721956

WoS: A1955WF80700006

History

Received: 1954-05-05

Cited By (28)

Year	Entry
2001	Knothe Tate ML. Bone poroelasticity. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:22-1–22-29.
1990	Mow VC, Hou JS, Owens JM, Ratcliffe A. Biphasic and quasilinear viscoelastic theories for hydrated soft tissues. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:215-260.
1984	Johnson MW. Behavior of fluid in stressed bone and cellular stimulation. Calcif Tiss Int. March 1984;36(suppl 1):S72-S76.
1976	Torzilli PA, Mow VC. On the fundamental fluid transport mechanisms through normal and pathological articular cartilage during function, I: the formulation. J Biomech. 1976;9(8):541-552.
1982	Johnson MW, Chakkalakal DA, Harper RA, Katz JL, Rouhana SW. Fluid flow in bone in vitro. J Biomech. 1982;15(11):881-885.
1995	Kim Y-J, Bonassar LJ, Grodzinsky AJ. The role of cartilage streaming potential, fluid flow and pressure in the stimulation of chondrocyte biosynthesis during dynamic compression. J Biomech. September 1995;28(9):1055-1066.
1997	Khalsa PS, Eisenberg SR. Compressive behavior of articular cartilage is not completely explained by proteoglycan osmotic pressure. J Biomech. June 1997;30(6):589-594.
2002	Smit TH, Huyghe JM, Cowin SC. Estimation of the poroelastic parameters of cortical bone. J Biomech. June 2002;35(6):829-835.
2003	Knothe Tate ML. “Whither flows the fluid in bone?” an osteocyte's perspective. J Biomech. October 2003;36(10):1409-1424.
2011	Brynk T, Hellmich C, Fritsch A, Zysset P, Eberhardsteiner J. Experimental poromechanics of trabecular bone strength: role of Terzaghi's effective stress and of tissue level stress fluctuations. J Biomech. 2011;44(3):501-508.
1997	Li L. Theory of Poroelastic Structures With Diffusion in the Longitudinal Directions [PhD thesis]. Ben-Gurion University of the Negev; 1997.
2001	Smith CL. Some Aspects of the Biomechanics of Articular Cartilage Repair [PhD thesis]. Cleveland, OH: Case Western Reserve University; May 2001.
2020	Zimmerman BKL. Mechanically Mediated Fatigue Failure in Articular Cartilage: Experimental, Theoretical, and Computational Models [PhD thesis]. Columbia University; 2020.
2005	Yoon YJ. Estimates of Bone Elastic Constants At Sequential Hierarchical Levels [PhD thesis]. New York, NY: The City University of New York; 2005.
2009	Gailani G. Russian Doll Poroelasticity [PhD thesis]. New York, NY: The City University of New York; 2009.
2012	Benalla M. Experimental Detrmination of the Lacunar-Canalicular Permeability Using Cyclic Loading [PhD thesis]. New York, NY: The City University of New York; 2012.
1983	Eisenberg SR. Nonequilibrium Electromechanical Interactions in Cartilage: Swelling and Electrokinetics Cambridge, MA: Massachusetts Institute of Technology; February 1983.
1987	Sachs JR. A Mathematical Model of an Electromechanically Coupled Poroelastic Medium [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 1987.
1996	Berkenblit SI. Spatial Localization of Cartilage Degradation Using Electromechanical Surface Spectroscopy With Variable Wavelength and Frequency [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 1996.
1999	Treppo S. Physical Diagnostics of Cartilage Degeneration [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; February 1999.
2013	Verbruggen SW. Mechanobiological Origins of Osteoporosis [PhD thesis]. National University of Ireland Galway; September 2013.
2006	Yao J. Finite Element Modeling of the Meniscus in the Anterior Cruciate Ligament Deficient Knee With Magnetic Resonance Imaging Based Experimental Validation [PhD thesis]. University of Rochester; 2006.
2002	Loboa Polefka EG. Mechanobiology of Multipotent Mesenchymal Tissue Differentiation [PhD thesis]. Stanford University; June 2002.
1992	Van der Voet AF. Finite Element Modelling of Load Transfer Through Articular Cartilage [PhD thesis]. Calgary, AB: University of Calgary; August 1992.
1999	Whyne CM. Development of Guidelines for the Prophylactic Treatment of Metastatically Involved Vertebral Bodies [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1999.
2018	Jafari S. Biomechanics of Articular Cartilage: Osteoarthritis and Tissue Engineering [PhD thesis]. San Diego (UCSD), University of California; 2018.
2006	Cheng S. The Role of Brain Tissue Mechanical Properties and Cerebrospinal Fluid Flow in the Biomechanics of the Normal and Hydrocephalic Brain [PhD thesis]. University of New South Wales; 2006.
1996	Panneton R. Modélisation numérique tridimensionnelle par éléments finis des milieux poroélastiques: Application au problème couplé élasto-poro-acoustique [PhD thesis]. Université de Sherbrooke; August 1996.