Solid mechanics
Solid mechanics is the part of mechanics that studies how solid materials respond to the forces, or loads, placed on them: how they stretch, bend, twist and eventually break. Two of its most important ideas are stress and strain.[1]
Elastic materials
Many materials are elastic, though not all are. An elastic material changes shape as soon as a load is put on it, keeps the same shape while the load stays the same, and goes straight back to its original shape when the load is taken away.[2]
The scientist Robert Hooke (1635–1703) measured how long wires stretched under different loads. He found that, as long as the loads were small enough, the stretch was roughly proportional to the load. This rule is known as Hooke's law.[3] A related quantity, Young's modulus or the modulus of elasticity, is named after the English physicist Thomas Young (1773–1829). It describes how stiff a material is, and it is one of the most important ways of describing a material's mechanical behaviour.[4] In general, the strain in a material is in direct proportion to the stress only when the stress is low enough; the constant linking them is called the elastic modulus.[5]
Testing materials
One of the simplest ways to find out a material's mechanical properties is the tension test. A strip or rod of the material is fixed at one end and pulled along its length at the other.[6] As the pull is increased, the specimen stretches further, until it eventually breaks, often suddenly snapping into two or more pieces.[7]
Topics studied
University courses in solid mechanics usually cover stress and strain in more than one direction, how materials fail, the bending of beams and how far they bend, the twisting of shafts (torsion), and methods based on energy.[8]
References
- ↑ Roylance, David. "1.1: Introduction to Elastic Response". Mechanics of Materials. LibreTexts (MIT OpenCourseWare). Retrieved 20 October 2026.
This module will also introduce two essential concepts in Mechanics of Materials: stress and strain.
- ↑ Roylance, David. "1.1: Introduction to Elastic Response". Mechanics of Materials. LibreTexts (MIT OpenCourseWare). Retrieved 20 October 2026.
An elastic material is one that deforms immediately upon loading, maintains a constant deformation as long as the load is held constant, and returns immediately to its original undeformed shape when the load is removed.
- ↑ Roylance, David. "1.1: Introduction to Elastic Response". Mechanics of Materials. LibreTexts (MIT OpenCourseWare). Retrieved 20 October 2026.
made a number of such measurements on long wires under various loads, and observed that to a good approximation the load P and its resulting deformation δ were related linearly as long as the loads were sufficiently small. This relation, generally known as Hooke's Law
- ↑ Roylance, David. "1.1: Introduction to Elastic Response". Mechanics of Materials. LibreTexts (MIT OpenCourseWare). Retrieved 20 October 2026.
or the modulus of elasticity, is one of the most important mechanical descriptors of a material.
- ↑ Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). "12.3 Stress, Strain, and Elastic Modulus". University Physics Volume 1. OpenStax. Retrieved 20 October 2026.
Only when stress is sufficiently low is the deformation it causes in direct proportion to the stress value. The proportionality constant in this relation is called the elastic modulus.
- ↑ Roylance, David. "1.1: Introduction to Elastic Response". Mechanics of Materials. LibreTexts (MIT OpenCourseWare). Retrieved 20 October 2026.
Perhaps the most natural test of a material's mechanical properties is the tension test, in which a strip or cylinder of the material, having length L and cross-sectional area A, is anchored at one end and subjected to an axial load P – a load acting along the specimen's long axis – at the other.
- ↑ Roylance, David. "1.1: Introduction to Elastic Response". Mechanics of Materials. LibreTexts (MIT OpenCourseWare). Retrieved 20 October 2026.
Eventually the test specimen breaks or does something else catastrophic, often fracturing suddenly into two or more pieces.
- ↑ "2.001 Mechanics & Materials I, Fall 2006: Lecture Notes". MIT OpenCourseWare. Massachusetts Institute of Technology. Retrieved 20 October 2026.
Multiaxial Stress ... Stress Transformations and Principal Stress ... Failure of Materials and Examples ... Pure Bending ... Beam Deflection ... Torsion and Twisting ... Energy Methods