In the elastic range stress is proportional to strain, σ=Eε.
Within the elastic region stress is proportional to strain, σ=Eε, and the material returns to its original shape when unloaded. For springs F=kx. Generalised Hooke's law relates all stress and strain components with E and ν.
Steel with E=200 GPa under 100 MPa strains by 0.05%.
Hooke's law is valid in the elastic range and lets you predict deformation from load with a simple proportion.
In the elastic range stress is proportional to strain, σ=Eε.
Hooke's law is valid in the elastic range and lets you predict deformation from load with a simple proportion.
It stops at the proportional limit and yield point, where permanent deformation starts and the stress is no longer proportional to strain.
Most metals and ceramics are linear in the elastic range, but rubbers and soft tissues are strongly nonlinear.
Typical applications include predicting the stretch of a spring under a known load, calculating the stress in a bar for a measured strain and modelling the response of a rubber mount in the linear region.
Study "Stress-strain curve" first (topic 45 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Linear elasticity assumption. Superposition valid. Fails beyond yield.
Steel with E=200 GPa under 100 MPa strains by 0.05%.
The next topic is "Young's modulus", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 46 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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