Concise Summary of Deformation of Solids

Deformation: Stress & Strain

• Deformation: Changes to size and shape due to an applied force.

  • Tensile: Stretching forces.

  • Compressive: Compression forces.

Tensile Strength

• Tensile Strength: Maximum load before the material breaks.

Hooke's Law

• States that extension is proportional to the applied load when within the elastic limit:
  $F = k imes e$
  (where $F$ is the force, $k$ the spring constant, and $e$ the extension).

Young's Modulus

• Measures material's stiffness: $E = \frac{\text{Stress}}{\text{Strain}}$ (where stress = $\frac{F}{A}$ and strain = $\frac{e}{L_0}$).

  • Unit: Pascal (Pa).

Elastic & Plastic Behavior

• Elastic Deformation: Returns to original shape when load is removed.

• Plastic Deformation: Does not return to original shape beyond the elastic limit.

Stress-strain relationship

• Graph shows the linear relationship and helps outline elastic/plastic behaviors.

  • Brittle materials: Little to no plastic deformation; fracture easily.

  • Ductile materials: Significant plastic deformation before breaking.

Energy Stored - Elastic Potential Energy

• Work done in material deformation: Area under force-extension graph.

• Formula for elastic potential energy (for materials obeying Hooke's law):
  $E_{PE} = \frac{1}{2} k x^2$
  (where $k$ is spring constant in N/m and $x$ is extension in meters).