pure_shear.prm

# This parameter file reproduces an analytical benchmark for the evolution
# of finite strain in a model of pure shear as described (for a specific
# application) in McKenzie & Jackson (1983): "The relationship between
# strain rates, crustal thickening, paleomagnetism, finite strain and
# fault movements within a deforming zone." They show that the analytical
# solution for the deformation gradient tensor F in pure shear deformation is:
#
# F_xx = e^(u_x,x * t)
# F_xy = 0
# F_yx = 0
# F_yy = e^(-u_x,x * t),
#
# where u is the velocity, t is time, and a comma represents a derivative
# in that particular direction. u_x,x in this example is equivalent to
# -u_y,y so that also: F_yy = e^(u_y,y * t) which is intuitive.
# For this benchmark it is important to recognize that the deformation in
# this model is actually only "pure" pure shear at the origin, since the
# deformation field around is a mixture of pure shear and a rotational
# component. Also the value of u_x,x at the origin is not prescribed
# directly, but is a model output, because we only know velocity profiles
# for the top and right boundaries. Using the computed velocity field we
# can calculate u_x,x approximately at the origin to be 1.253, and therefore
# expect:
# F_xx (t=1.0) = 3.501
# F_yy (t=1.0) = 0.2856
# This parameter file tracks the finite strain in two ways, once by using
# compositional fields as illustrated in the finite strain cookbook, and
# once by using a particle particle that sits and remains at the origin.
# The results should of course be the same.
#
# Numerical results for particle tracking show excellent agreement:
# F_xx (t=1.0) = 3.50088
# F_yy (t=1.0) = 0.285643
#
# Numerical results for compositional fields also show good results.
# F_xx (t=1.0) = 3.49776
# F_yy (t=1.0) = 0.286723
# The compositional field results are slightly less accurate, probably due to
# numerical diffusion, but were found to converge against the analytical
# values with increasing resolution.

set Additional shared libraries            = ./libfinite_strain.so
set Dimension                              = 2
set End time                               = 1.0
set Use years instead of seconds           = false
set Output directory                       = output-pure_shear

subsection Geometry model
  set Model name = box

  subsection Box
    set X extent  = 1.0
    set Y extent  = 1.0
  end
end

subsection Boundary velocity model
  set Tangential velocity boundary indicators = left, bottom
  set Prescribed velocity boundary indicators = top:function, right:function

  subsection Function
    set Function expression = 1-y; x-1
  end
end

subsection Material model
  set Model name = finite strain

  subsection Simple model
    set Reference density             = 1010
    set Viscosity                     = 1e2
    set Thermal expansion coefficient = 0
  end
end

subsection Gravity model
  set Model name = vertical

  subsection Vertical
    set Magnitude = 10
  end
end

subsection Compositional fields
  set Number of fields = 4
  set Names of fields = strain_xx, strain_xy, strain_yx, strain_yy
end

subsection Boundary composition model
  set List of model names = initial composition
end

subsection Initial composition model
  set Model name = function

  subsection Function
    set Function expression = 1.0;0.0;0.0;1.0
  end
end

############### Parameters describing the temperature field
# Note: The temperature plays no role in this model

subsection Initial temperature model
  set Model name = function

  subsection Function
    set Function expression = 0
  end
end

subsection Mesh refinement
  set Initial adaptive refinement        = 0
  set Strategy                           = strain rate
  set Initial global refinement          = 4
  set Time steps between mesh refinement = 0
end

############### Parameters describing what to do with the solution

subsection Postprocess
  set List of postprocessors = particles, visualization

  subsection Visualization
    set List of output variables = strain rate, shear stress
    set Time between graphical output = 0.05
  end

  subsection Particles
    set Time between data output = 0.05
    set Data output format = vtu
  end
end

subsection Particles
  set List of particle properties = integrated strain
  set Particle generator name = ascii file

  subsection Generator
    subsection Ascii file
      set Data directory = ./
      set Data file name = pure_shear_particle.dat
    end
  end
end