Nonlinear mechanical model -- Model K(x, u)

o Nonlinear model

mx'' + c x' + K(x,u) x = mg sin(angle)

  • K depends on position and velocity
  • K also depends on crystal structure
  • Slope of K at the origin is stiffness
  • Existence of an interior maximum indicates the possiblity of fracture

o u dependence

  • Snow with round crystals is mechanically stiff but fracture prone
  • Snow with square crystals is mechanically weak but not fracture prone

o x dependence

  • At small displacements, K is nearly linear in x
  • At large displacements, fracture occurs

K(x,u) = k u ( 1 - u x )

  • Solid curve models round crystals
  • Dashed curve models square crystals
  • At small displacements, spring stiffness = k u

o Factors ignored

  • Dependence on x'
  • Compression fracture

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