simple_shear.prm

# This parameter file reproduces an analytical benchmark for the evolution
# of finite strain in a model of simple 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 simple shear deformation is:
#
# F_xx = 1.0
# F_xy = u_x,y * t
# F_yx = 0
# F_yy = 1.0,
#
# where u is the velocity, t is time, and a comma represents a derivative
# in that particular direction.
# Because u_x,y = 2.0 / 1.0 is constant in the whole domain (and over time) we expect
# a constant F at any given time, and in particular:
# F_xy (t=1.0) = 2.0
#
# 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 in the center of the domain.
# The results should of course be the same.
#
# Numerical results for particle tracking and compositional fields
# show equally excellent agreement:
# F_xy (t=1.0) = 2.0

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

subsection Geometry model
  set Model name = box

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

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

  subsection Function
    set Function expression = if (y < 0.5, -1, 1); 0
  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

############### Parameters describing the discretization

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
    set Time between graphical output = 0.05
  end

  subsection Particles
    set Number of particles = 1
    set Time between data output = 0.05
    set Data output format = vtu
    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 = simple_shear_particle.dat
      end
    end
  end
end