Elastic properties of reinforced solids:​ some theoretical principles

Hill, R.

Affiliations

¹Department of Mathematics, University of Nottingham

Abstract

The title problem concerns two isotropic phases firmly bonded together to form a mixture with any concentrations. An elementary account of several theoretical methods of attack is given, among them the derivation of inequalities between various moduli. The approach is completely general and exact. Additionally, the problem is fully solved when the phases have equal rigidities but different compressibilities, the geometry being entirely arbitrary.

Links

DOI: 10.1016/0022-5096(63)90036-X

WoS: A1963WZ82600005

History

Received: 1963-04-04

Cited Works (1)

Year	Entry
1963	Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids. March–April 1963;11(2):127-140.

Cited By (51)

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1996	van Rietbergen B. Mechanical Behavior and Adaptation of Trabecular Bone in Relation to Bone Morphology [PhD thesis]. Nijmegen, Netherlands: Catholic University of Nijmegen; 1996.
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1999	Kabel J, van Rietbergen B, Odgaard A, Huiskes R. Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. Bone. October 1999;25(4):481-486.
1992	Hollister SJ, Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput Mech. March 1992;10(2):73-95.
2021	Sabet FA, Koric S, Idkaidek A, Jasiuk I. High-performance computing comparison of implicit and explicit nonlinear finite element simulations of trabecular bone. Comput Methods Prog Biomed. March 2021;200:105870.
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2018	Deng N, Korkolis YP. Elastic anisotropy of dual-phase steels with varying martensite content. Int J Solids Struct. June 1, 2018;141-142:264-278.
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1999	Cowin SC. Bone poroelasticity. J Biomech. March 1999;32(3):217-238.
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2023	Branni MG. Constitutive Models of Bone: The Human Femur [PhD thesis]. Queensland University of Technology; 2023.
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2003	Pahr DH. Experimental and Numerical Investigations of Perforated FRP-Laminates [PhD thesis]. Vienna University of Technology; February 2003.
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1994	Ko C-C. Mechanical Characteristics of Implant/tissue Interphases [PhD thesis]. University of Michigan; 1994.
1995	Guldberg RE. Mechanical Adaptation of Trabecular Bone Formation in Vivo [PhD thesis]. University of Michigan; 1995.
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