Multi-Material Model

To have multiple material types, "regions" in a mesh and material properties in an input file must correspond to each other in terms of the number of material kinds and the order by which the materials and parameters are listed.

This technical requirement is illustrated by a multi-material 2D rifting example. A pair of input parameter files are provided:

1. DynEarthSol/examples/rifting-2d.cfg: input file for DynEarthSol.
2. DynEarthSol/examples/rifting-2d.poly: input file for the mesh generator, triangle.

In .cfg file

1. In [mesh] section, specify poly_filename: e.g.,

poly_filename = rifting-2d.poly

2. In [mat] section, specify num_materials: e.g.,

num_materials = 4

• Provide as many values as num_materials for all the material properties (e.g. rho0, lambda, mu, etc): e.g.,

rho0 = [ 2800, 2900, 3210, 3300 ]

• We recommend you draw a schematic such as the one in rifting-2d.poly to illustrate your layers with labeled nodal points (shown below):

In .poly file

In this file, you will define

• node coordinates
• segments connecting coordinates
• regions

1. Node coordinates As in the example .poly file, specify the number of total nodes and number of dimensions. Then specify the node number (starting from 0) and the x- and y-coordinates.

#### node coordinates ####
# npoints ndims 0 0
  13      2     0 0
# i    xi       yi
  0    0.0      0.0
  1    0.0    -35.0e3 
  2    0.0   -150.0e3 
  3  500.0e3 -150.0e3 
  4  500.0e3  -35.0e3
  5  500.0e3    0.0
  6  150.0e3 -150.0e3 
  7  350.0e3 -150.0e3
  8  380.0e3  -35.0e3
  9  250.0e3  -39.0e3
 10  120.0e3  -35.0e3
 11  300.0e3  -35.0e3
 12  200.0e3  -35.0e3

2. Segments As in the example .poly file, specify the number of total segments connecting any 2 nodes. Then specify the segment number (starting from 0) and the nodes it connects (e.g. in the picture of rifting-2d.poly's scheme above, segment 0 connects nodes 0 and 1. Segment 9 connects nodes 10 and 12.) Finally, assign a boundary flag. Flags:

• 0: not a boundary
• 1: left boundary (x0)
• 2: right boundary (x1)
• 16: bottom boundary (z0)
• 32: top boundary (z1)

#### segments ####
# nsegments 1
  16        1
# j  pj0  pj1  bdry_flag
  0   0    1    1  #  1: left (x0)
  1   1    2    1
  2   2    6   16  # 16: bottom (z0)
  3   6    7   16
  4   7    3   16
  5   3    4    2  #  2: right (x1)
  6   4    5    2
  7   5    0   32  # 32: top (z1)
  8   1   10    0  #  0: not a boundary
  9  10   12    0
 10  12    9    0
 11   9   11    0
 12  11    8    0
 13   8    4    0
 14  10    6    0
 15   8    7    0

3. Holes In tectonic moeling, there is no reason to deal with an undergroun empty space.

#### holes, must be 0 ####
0

4. Regions As in the example .poly file, specify the number of total regions. Then specify the region number (starting from 0) and a point within that region (we recommend choosing a fairly central node here). The mattype specifies which value in the .cfg file [mat] paramter should be applied to the region. Finally, specify the max element size (m^2) for the region. If there is no upper limit on element size, use -1.

#### regions ####
# nregions
  4
# k  xk    zk   mattype  size
  0 250e3 -20e3 0        2e7  # max. element size (in m^2)
  1 250e3 -80e3 1        4e7
  2   1e3 -80e3 1        -1   # no upper limit on elem size
  3 450e3 -80e3 1        -1