Mechanics

• Deformation


  When forces cause an object to change shape
• Types of deformation

  • Extension
  • Compression
  • Bending
• Extension

  The object increases in length, defined as a positive change in length caused by tensile forces (tension)
• Compression


  The object decreases in length, defined as a negative change in length caused by compressive forces
• Bending

  The object does not change overall size but is distorted, requires two forces applied on the same side
• An object can only be deformed when two forces are applied as one force would only accelerate the object in the direction of the force
• Hooke's Law

  The change in length of an object is directly proportional to the force applied up until the limit of proportionality
• Hooke's Law can be applied to both extension and compression, and applies most accurately to metal springs and wires, but can also be approximated to other materials or used for small deformations
• Spring constant (K)


  A constant specific to the spring/wire, not the material, with units N/m
• Hooke's Law mathematically

  F = KAL
• Hooke's Law graph

  Linear relationship, gradient = K
• Springs in series

  • Both carry the full weight of the load, same force F applied to both springs
  • 1/K_total = 1/K_1 + 1/K_2
• Springs in parallel

  • Share the weight of the load, both have the same extension x
  • K_total = K_1 + K_2
• A number of springs in parallel has a higher total spring constant than the same springs in series arrangement
• Elastic deformation

  Material returns to original shape and size when forces are removed, atoms can move small distances without permanent change
• Plastic deformation

  Material does not return to original dimensions, is permanently deformed, atoms do not return to original positions
• Force-extension graph

  • P = limit of proportionality (Hooke's Law)
  • E = elastic limit (elastic deformation)
  • Beyond E = plastic deformation
• Elastic strain energy

  Work done in deforming the object, stored as potential energy, given by area under force-extension graph
• Calculating elastic strain energy

  Elastic strain energy = 1/2 * K * (AL)^2
• During unloading, work is done by the material to regain its shape, and energy is recovered and dissipated to the surroundings, equal to the area under the unloading curve
• During loading, work is done by the force on the material, and this energy is stored in the material, equal to the area under the loading curve
• The difference between the energy transferred to the material during loading and the energy lost by the material during unloading is stored as internal energy, causing the material to heat up
• What is deformation?


  When forces cause an object to change shape