Solid mechanics developed in the outpouring of mathematical and physical studies by the great achievement of Sir. Isaac Newton’s (1642-1727) laws of motion. Leonardo da Vinci (1452-1519) sketched in his notebooks about the possible test of the tensile strength of a wire. The Italian experimental scientist Galileo Galilei (1564-1642) had investigated the breaking loads of rods in tension and concluded that the load was independent of length and proportional to the cross section area, this being a first step towards a concept of stress. He also investigated how the breaking of heavy stone columns, laid horizontally in storage as beams, depended on the number and condition of their supports.
The English scientist Robert Hooke discovered in 1660, but published only in 1678, the observation that for many materials that displacement under a load was proportional to force, thus establishing the motion of (linear) elasticity but not yet in a way that was expressible in terms of stress and strain. E. Mariotte in France published similar discoveries in 1680 and reached an understanding of how beams like those studied by Galileo resisted transverse loading by developing extensional and compressive deformations. It was for Swiss mathematician and mechanician James Bernoulli (1654-1705) to observe that the proper way of describing deformation was to give force per unit area, or stress, as a function of the elongation per unit length, or strain, of a material fiber under tension.
Swiss mathematician and mechanician Leonhard Euler (1707-1783) proposed a linear relation between stress and strain in 1727. The notion that there is internal tension acting across surfaces in a deformed solid was expressed by German mathematician and physicist Gottfried Wilhelm Leibniz in 1684 and James Bernoulli in 1691. Also, Bernoulli and Euler introduced the idea that at a given section along the length of a beam there were internal tensions amounting to a net force and a net torque. Euler introduced the idea of compressive normal stress as the pressure in a fluid in 1752.
The French engineer and physicist Charles-Augustine Coulomb (1736-1806) was apparently the first to relate the theory of a beam as a bent elastic line to stress and strain in an actual beam. The French mathematician Parent introduced the concept of shear stress in 1713, but Coulomb was the one who extensively developed the idea in connection with beams and with the stressing and failure of soil in 1773, and studies of frictional slip in 1779. It was the great French mathematician Augustin Louis Cauchy (1789-1857), originally educated as an engineer, who in 1822 formalized the stress concept in the context of a general three-dimensional theory, showed its properties as consisting of a 3 by 3 symmetric array of numbers that transform and gave the specific development of the theory of linear elastic response for isotropic solids.
The 1700’s and early 1800’s were a productive period in which the mechanics of simple elastic structural elements were developed well before the beginnings in the 1820’s of the general three-dimensional theory. The development of beam theory by Euler, who generally modeled beams as elastic lines which resist bending, and by several members of the Bernoulli family and by Coulomb, remains among the most immediately useful aspects of solid mechanics, in part for its simplicity and in part because of the pervasiveness of beams and columns in structural technology. James Bernoulli proposed in his final paper of 1705 that the curvature of a beam was proportional to bending moment.
The middle and late 1800’s were a period in which many basic elastic solutions were derived and applied to technology and to the explanation of natural phenomena. French mathematician Barre de Saint-Venant derived in the 1850’s solutions for the torsion of non-circular cylinders, which explained the necessity of warping displacement of the cross section in the direction parallel to the axis of twisting. The German physicist Heinrich Rudolph Hertz developed solutions for the deformation of elastic solids as they are brought into contact, and applied these to model details of impact collisions.
Poisson, Cauchy and George G. Stokes showed that the equations of the theory predicted the existence of two types of elastic deformation waves which could propagate through isotropic elastic solids. These are called body waves. Lord Rayleigh (John Strutt) showed in 1887 that there is a wave type that could propagate along surfaces, such that the motion associated with the wave decayed exponentially with distance into the material from the surface. This type of surface wave, now called a Rayleigh wave, propagates typically at slightly more than 90% of the shear wave speed, and involves an elliptical path of particle motion that lies in planes parallel to that defined by the normal to the surface and the propagation direction.
In 1898 G. Kirsch derived the solution for the stress distribution around a circular hole in a much larger plate under remotely uniform tensile stress. The same solution can be adapted to the tunnel-like cylindrical cavity of circular section in a bulk solid. His solution showed a significant concentration of stress at the boundary, by a factor of three when the remote stress was uniaxial tension. Then in 1907 the Russian mathematician G. Kolosov, and independently in 1914 the British engineer Charles Inglis, derived the analogous solution for stresses around an elliptical hole. Their solution showed that the concentration of stress could become far greater as the radius of curvature at an end of the hole becomes small compared to the overall length of the hole.
The Italian elastician and mathematician V. Volterra introduced in 1905 the theory of the elastostatic stress and displacement fields created by dislocating solids. This involves making a cut in a solid, displacing its surfaces relative to one another by some fixed amount, and joining the sides of the cut back together, filling in with material as necessary. The mathematical techniques advanced by Volterra are now in common use by Earth scientists in explaining ground displacement and deformation induced by tectonic faulting. Also, the first elastodynamic solutions for the rapid motion of a crystal dislocations by South African materials scientist F. R. N. Nabarro, in the early 1950’s, were quickly adapted by seismologists to explain the radiation from propagating slip distributions on faults.
Austrian-American civil engineer Karl Terzaghi in the 1920’s developed the concept of effective stress, whereby the stresses which enter a criterion of yielding or failure are not the total stresses applied to the saturated soil or rock mass, but rather the effective stresses, which are the difference between the total stresses and those of a purely hydrostatic stress state with pressure equal to that in the pore fluid. German applied mechanician Ludwig Prandtl developed the rudiments of the theory of plane plastic flow in 1920 and 1921.
The finite element method and other computational techniques (finite differences, spectral expansions, boundary and integral equations) have made a major change in the practice of and education for, engineering in the various areas that draw on solid mechanics. Previously, many educators saw little point in teaching engineers much of the subject beyond the techniques of elementary beam theory developed in the 1700’s by Bernoulli, Euler and Coulomb. More advanced analyses involved sufficiently difficult mathematics as to be beyond the reach of the typical practitioner and were regarded as the domain of advanced specialists who would, themselves, find all but the simpler cases intractable. The availability of software incorporating the finite element method and other procedures of computational mechanics and design analysis has placed the advanced concepts of solid mechanics into the hands of a far broader community of engineers. At the same time, it has created a necessity for them and other users to have a much deeper education in the subject, so that the computational tools are used properly and at full effectiveness.
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