Abstract
The equilibrium equations derived in Chap. 2 must be connected with the kinematic relations developed in Chap. 3. This coupling is accomplished by considering the mechanical properties of the materials for which the theory of elasticity is to be applied and is expressed by constitutive or material laws. Beginning with the generalized Hooke’s Law, the relationships between stress and strain are progressively reduced to the familiar isotropic form. Several modern characterizations, including transverse isotropic and functionally graded materials, are also considered.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Westergaard HM (1964) Theory of elasticity and plasticity. Dover Publications, Inc., New York
Love AEH (1944) The mathematical theory of elasticity. Dover Publications, Inc., New York
Tauchert TR (1974) Energy principles in structural mechanics. (McGraw–Hill Book Company, Inc, New York
Little RW (1973) Elasticity. Prentice–Hall, Inc, Englewood Cliffs, NJ
Sinkus R et al. (2005) Imaging anisotropic and viscous properties of breast tissue by magnetic resonance-elastography. Magn Reson Med, Wiley Interscience. 53:372–387.
Namani R et al. (2012) Elastic Characterization of transversely isotropic soft materials by dynamic shear and asymmetric indentation. J Biomech Eng 136(6):061004
Cooley WG (2005) Application of functionally graded materials in aircraft structures. Masters thesis, AFIT/GAE/ENY/05-M04 Wright-Patterson AFB, OH.
Sankar BV (2001) An elasticity solution for functionally graded beams. Comp Sci Technol 61:689–696
Roylance D (1999) Engineering viscoelasticity, Module for Engineering/3-11, (Massachusetts Institute of Technology, Cambridge, MA, 24 Oct 2001, 2 Dec 2009).
Vinson JR, Sierakowski RL (1986) The behavior of structures composed of composite materials. Martinus Nijhoff, Dordrecht
Chen WF, Saleeb AF (1982) Constitutive equations for engineering materials, vol 1. John Wiley-Interscience, New York
Ohtani YC, Chen WF (1987) Hypoelasticity-perfectly plastic model for concrete materials. J Eng Mech, ASCE 113(12):1840–1860
Meek JL, Lin WJ (1990) Geometric and material nonlinear analysis of thin-walled beam columns. J Struct Eng 116(6):1473–1490
Boresi AP, Chong KP (1987) Elasticity in engineering mechanics. Elsevier, New York
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gould, P.L. (2013). Material Behavior. In: Introduction to Linear Elasticity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4833-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4833-4_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4832-7
Online ISBN: 978-1-4614-4833-4
eBook Packages: EngineeringEngineering (R0)