Elasticity

Abstarct

When a force, F, is applied to a specimen with cross-sectional area A =¼πd ², and length l ₀, the length will be increased by Δ l (left Figure in box). With a specimen of larger cross-sectional area the same force will result in a smaller length change. Also, when the starting length of the specimen, l ₀, is longer the same force will result in a larger length change. To be able to give a unique characterization of the material, independent of the sample size, we normalize force by the area and the LaGrangian stress is obtained, σ = F/A. Similarly we normalize the length change to the starting length, l _o , and obtain strain, ε =Δ l/l _o .