Chapter 1
Elasticity
1.1 Introduction
Elasticity is a fascinating subject that deals with determination of stresses, strains
and displacement distribution in an elastic body under the influence of external
forces. If the external forces producing deformation do not exceed a certain limit, the
deformation disappears with the removal of the forces. Thus, the elastic behaviour
implies the absence of any permanent deformation. Elasticity has been developed
following the great achievement of Newton in stating the laws of motion, although it
has earlier roots. The need to understand and control the fracture of solids seems to
have been a first motivation. Leonardo da Vinci sketched in his notebooks a possible
test of the tensile strength of a wire. Galileo had investigated the breaking loads
of rods under tension and concluded that the load was independent of length and
proportional to the cross-sectional area, this being the first step towards a concept of
stress.
Every engineering material possesses a certain extent of elasticity. The common
materials of construction would remain elastic only for very small strains before
exhibiting either plastic straining or brittle failure. However, natural polymeric materials show elasticity over a wider range (usually with time or rate effects, thus they
would more accurately be characterized as viscoelastic), and the widespread use
of natural rubber and similar materials motivated the development of finite elasticity. While many roots of the subject were laid in the classical theory, especially in
the work of Green, Gabrio Piola and Kirchhoff in the mid-1800s, the development
of a viable theory with forms of stress–strain relations for specific rubbery elastic
materials, as well as an understanding of the physical effects of the nonlinearity in
simple problems such as torsion and bending, was mainly the achievement of the
British-born engineer and applied mathematician Ronald S. Rivlin in the 1940s and
1950s.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
T. G. Sitharam and L. Govindaraju, Theory of Elasticity,
https://doi.org/10.1007/978-981-33-4650-5_1
1
Elasticity
1.1 Introduction
Elasticity is a fascinating subject that deals with determination of stresses, strains
and displacement distribution in an elastic body under the influence of external
forces. If the external forces producing deformation do not exceed a certain limit, the
deformation disappears with the removal of the forces. Thus, the elastic behaviour
implies the absence of any permanent deformation. Elasticity has been developed
following the great achievement of Newton in stating the laws of motion, although it
has earlier roots. The need to understand and control the fracture of solids seems to
have been a first motivation. Leonardo da Vinci sketched in his notebooks a possible
test of the tensile strength of a wire. Galileo had investigated the breaking loads
of rods under tension and concluded that the load was independent of length and
proportional to the cross-sectional area, this being the first step towards a concept of
stress.
Every engineering material possesses a certain extent of elasticity. The common
materials of construction would remain elastic only for very small strains before
exhibiting either plastic straining or brittle failure. However, natural polymeric materials show elasticity over a wider range (usually with time or rate effects, thus they
would more accurately be characterized as viscoelastic), and the widespread use
of natural rubber and similar materials motivated the development of finite elasticity. While many roots of the subject were laid in the classical theory, especially in
the work of Green, Gabrio Piola and Kirchhoff in the mid-1800s, the development
of a viable theory with forms of stress–strain relations for specific rubbery elastic
materials, as well as an understanding of the physical effects of the nonlinearity in
simple problems such as torsion and bending, was mainly the achievement of the
British-born engineer and applied mathematician Ronald S. Rivlin in the 1940s and
1950s.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
T. G. Sitharam and L. Govindaraju, Theory of Elasticity,
https://doi.org/10.1007/978-981-33-4650-5_1
1