AIFlow Non-diagonal Fabric Variables

Extension of Elmer in computational glaciology

AIFlow Non-diagonal Fabric Variables

Postby kate.hruby » 09 Feb 2018, 23:36

Hello,

This question is regarding the a_12, a_23 and a_13 values (Fabric 3-5) in the AIFlow Solver. When needing to rotate, say, a single-maximum fabric not in an x, y, z plane into a single maximum in the x direction, does one input a single maximum fabric in the x direction, but with values in Fabrics 3-5 as well?

For example:
Fabric 1 = Real 0.998 !a2_11
Fabric 2 = Real 0.001 !a2_22
Fabric 3 = Real 0.66 !a2_12
Fabric 4 = Real 0.56 !a2_23
Fabric 5 = Real 0.49 !a2_13

Where the single maximum is hypothetically off the x-axis by 40˚, off the y-axis by 30˚ and off the z-axis by 50˚, thus making the fabric parameters
Fabric 3 = cos(40)*cos(30) = 0.66
Fabric 4 = cos(30)*cos(50) = 0.56
Fabric 5 = cos(40)*cos(50) = 0.49
according to the orientation tensor specified in Watson, 1965 and Woodcock, 1977. Is this a correct assumption for the use of the Fabric variables 3, 4 and 5?

Best,
Kate
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Re: AIFlow Non-diagonal Fabric Variables

Postby gagliar » 04 Apr 2018, 10:18

Dear Kate,

Sorry for the late reply.

The term in Fabric 3 to Frabric 5 are the non-diagonal terms of the second order orientation tensor. If you want to prescribe a single maximum fabric which is not orientated along one of the axis of the global reference frame, you then have to rotate the orientation tensor of the single maximum fabric expressed in the orthotropy reference frame into the global reference frame.

In the orthotropy reference frame a2 = | (0.998 0 0 ) (0 0.001 0) (0 0 0.001) |, and then using the rotation matrix R to go from the orthotropy reference frame to the global reference frame, you have to evaluate the 5 fabric terms fi as | (f1 f3 f5) (f3 f2 f4) (f5 f4 1-f1-f2) | = R^T a2 R.

Hope it helps
Olivier
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