strain energy

Question 1

modulus of toughness and resilience

Answer 1

toughness:
- the amount of energy a material can withstand before breaking

u = ∫ σ dϵ (integrate from 0 to point of failure)

resilience:
- the amount of energy a material can withstand before permanent deformation

u = σ^2 / 2E

*stress (σ)
*strain (ϵ)
*youngs modulus (E)

Question 2

strain energy (U) when elastic deformation is linear (gradually applied with elastic limit)

Answer 2

U = 1/2 Px (area under P x graph)

*load (P)
*deformation (x)

Question 3

strain energy density (u)

Answer 3

= U / V
= ∫ σ dϵ

Measures the energy stored per unit volume of material up to a specific point of strain

*strain energy (U)
*volume (V)
*stress (σ)
*strain (ϵ)

Question 4

strain energy for a uniform rod

Answer 4

U = P^2L / 2AE

*length (L)
*load (P)
*cross-sectional area (A)
*youngs modulus (E)