On Solid Mechanics:
That this branch of physics remains a vital and provocative subject for fundamental study nearly three fourths of the way through the 20th century, is one of the lessons to be learned from perusing the 300 year history of the growth of the experimental foundations of solid mechanics since the inaugural measurements of Robert Hooke in the 17th century.
J.F. Bell, 1973.

On Linear Stress-Strain Response For Small Deformations:
The dilemma of Leibniz in the 17th century over the apparently conflicting experiments of Hooke and James Bernoulli has been resolved in favor of the latter. The experiments of 280 years have demonstrated amply for every solid substance examined with sufficient care, that the strain resulting from small applied stress is not a linear function thereof.
J.F. Bell, 1973.

1678 : Robert Hooke

Discovers that force is a linear function of elongation based on expeiments on long, thin wires and springs. His anagram for this law was "ceiiinosssttuu" (published 1676) which was deciphered as "Ut tensio sic vis" in his 1678 paper.

1720 : Jordan Ricatti

Proposes that elastic properties of a body could be inferred from the frequency of vibration. The first experimental study of elastic E-moduli.

1729 : Pieter Van Musschenbroek

Publishes the first book showing testing machines for tension, compression, and flexure.

1766 : Leonhard Euler

Introduces the concept of "Young's modulus" eighty years before Thomas Young popularized Euler's concepts of the "height of the modulus" and the "weight of the modulus".

1780 : Charles Augustin Coulomb

First to measure the shear modulus in the modern sense.

1787 : Ernst Chladni

Calculates ratios of the velocity of sound in air to that in various solids. This work provided a major impetus for 19th century continuum mechanics.

1807 : Thomas Young

Publishes his "Lectures on Natural Philosophy". This work led to the popularization of the "height of the modulus". The units were in feet.

1809 : Jean Baptiste Biot

First direct measurement of the velocity of sound in a solid.

1813 : Alphonse Duleau

First quasi-static experiments for small deformation linear elasticity (by design). This work provided experimental evidence for numerous theoretical developments in elasticity, including St Venant's principle and the theoretical work of Cauchy, Poisson and Navier.

1841 : Guillaume Wertheim

Presents first definitive study of elastic properties of solids under various conditions to the French Academy. This study included results from Jean Victor Poncelet, Thomas Tregold, Antoin Masson, Felix Savart among others. Linear plots of stress versus strain begin to be widely used.

1848 : Guillaume Wertheim

First experiments showing that the Poisson's ratio of a solid does not have the constant value of 0.25.

1859 : Gustav Robert Kirchhoff

First measurement of Poisson's ratio indepenedent of the elastic modulus and specimen diameter.

1869 : Marie Alfred Cornu

First direct optical measurement of Poisson's ratio.

1882 : Woldemar Voigt

Performs experiments to prove the isotropy or otherwise of solids.

1904 : Arnulph Malloc

Devises a method to determine the quasi-static bulk modulus based on the theory of linear elasticity.

1908 : Eduard August Gruneisen

The Poisson's ratio is first determined experimentally as ratio of lateral and longitudinal strains. Uses Malloc's method to determine the compressibility of solids.