text: from directional_clustering.transformations import rigidity_bending_plate
  from directional_clustering.transformations import curvatures_bending_plate
  
  
  __all__ = ["virtual_work_bending"]
  
  
  def virtual_work_bending(m1, m2, m12, height, e_modulus, poisson):
      """
      Computes the virtual work density from bending on a tiny fragment of a plate.
      """
      D = rigidity_bending_plate(height, e_modulus, poisson)
      k1, k2, k12 = curvatures_bending_plate(m1, m2, m12, D, poisson)
  
      work = m1 * k1 + m2 * k2 + 2 * m12 * k12
  
      return work
  
  
  if __name__ == "__main__":
      pass
  