The brittle strength of orthotropic materials

Hoffman, Oscar<sup>1</sup>

Affiliations

¹Lockheed Palo Alto Research Laboratory, Palo Alto, California

Abstract

A phenomenological fracture condition is proposed for ortho tropic brittle materials. It contains nine material parameters and can account for widely differing compressive and tensile strengths in various directions. The proposed fracture condition is devel oped, purely on formal grounds, by borrowing features of the Mises-Schleicher isotropic yield condition and Hill's orthotropic yield condition. Comparison with experimental data on a fiber- reinforced composite material shows good agreement. The reader is reminded repeatedly that, despite formal similarities, yield conditions and brittle-fracture conditions pertain to unrelated physical phenomena.

Links

DOI: 10.1177/002199836700100210

History

Received: 1966-08-12

Cited Works (1)

Year	Entry
1948	Hill R. A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lon Ser-A. May 27, 1948;193(1033):281-297.

Cited By (15)

Year	Entry
1993	Fung YC. Bone and cartilage. In: Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993:500-544.
2008	Yoon Y-S, Oxland TR, Hodgson AJ, Duncan CP, Masri BA, Choi D. Mechanical aspects of degree of cement bonding and implant wedge effect. Clin Biomech (Bristol, Avon). November 2008;23(9):310-314.
2004	Doblaré M, García JM, Gomez MJ. Modelling bone tissue fracture and healing: a review. Eng Fract Mech. September 2004;71(13-14):1809-1840.
1983	Stone JL, Beaupre GS, Hayes WC. Multiaxial strength characteristics of trabecular bone. J Biomech. 1983;16(9):743-752.
1985	Kaplan SJ, Hayes WC, Stone JL, Beaupré GS. Tensile strength of bovine trabecular bone. J Biomech. 1985;18(9):723-727.
2000	Keyak J, Rossi S. Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories. J Biomech. 2000;33(2):209-214.
1991	Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models, I: linear analysis. J Biomech Eng. 1991;113(4):353-360.
1971	Tsai SW, Wu EM. A general theory of strength for anisotropic materials. J Compos Mater. January 1971;5(1):58-80.
2011	Donaldson FE. On Incorporating Bone Microstructure in Macro-Finite-Element Models [PhD thesis]. Edinburgh, UK: University of Edinburgh; March 2011.
2006	Garcia D. Elastic Plastic Damage Laws for Cortical Bone [PhD thesis]. Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne; 2006.
1988	Lotz JC. Hip Fracture Risk Predictions by X-Ray Computed Tomography [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; August 1988.
1988	Whalen RT. The Influence of the Daily Stress History on the Regulation of Bone Density [PhD thesis]. Stanford University; February 1988.
2013	Sanyal A. Bone Strength Multi-Axial Behavior: Volume Fraction, Anisotropy and Microarchitecture [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2013.
1990	Tenace MA. Optimal Design of Fibre Composite Pressure Vessels [Master's thesis]. University of Ottawa; December 1990.
2020	Bunyamin ATO. Predicting Off-Axis Bone Strength of the Distal Radius Using High-Resolution Peripheral Quantitative Computed Tomography Based Finite Element Modeling [Master's thesis]. University of Saskatchewan; March 2020.