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Incompressible elastic problem

Asked by Oleg

Is it possible to solve incompressible elastic problem? All examples in user guide write for incompressible fluid.

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Lutz Gross
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Lutz Gross (l-gross) said : 		#1

Methods for incompressible flow can be applied to incompressible elastic: replace velocity by displacement and
viscosity by modulus of elasticity.

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Oleg (oleg100) said : 		#2

Thank you.

As I understand the Stokes problem is similar to isotropic incompressible elastic problem and I can use the StokesProblemCartesian class to solve the one.

 And what about anisotropic incompressible elastic problem?

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Best Lutz Gross (l-gross) said : 		#3

Obviously StokesProblemCartesian as it exists cannot do this but I would expect that you can modify this class to work for anisotropic problems. You need to modify escript/py_src/flows.py: firstly the operator A is different which requires to change the A tensor in self.__pde_v (line 528) into what ever your elasticity tensor is. You also need to modify getDV (line 614) by replacing 2*self.eta*util.symmetric(util.grad(v)) by what every your stress is. The tricky bit is the coefficient D in self.__pde_prec (see line 527). This PDE is used as a preconditioner for the solver only so the actual value (if >0 everywhere) has no impact on the answer but impacts on the convergence rate. One could try to work through the paper for the stokes problem (eg. http://portal.acm.org/citation.cfm?id=373546) and try to generalize the result (if this is possible). I would try D =1/(C_00+C_11+C_22).

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Oleg (oleg100) said : 		#4

Thanks Lutz Gross, that solved my question.