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Fix speed of sound calculation for elastic solids #688

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@FabienPean-Virtonomy FabienPean-Virtonomy commented Nov 22, 2024

This pull request includes a change to the ElasticSolid class in the src/shared/materials/elastic_solid.cpp file. The change modifies the calculation of the sound speeds to ensure accuracy for three-dimensional solids.

The pressure wave speed for isotropic elastic solids is (see Wikipedia)

$$ c_p = \sqrt{\frac{K + \frac{4}{3}G} { \rho}} $$

@FabienPean-Virtonomy
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This fix triggers (regression) failure for all those cases:

The following tests FAILED:
	  9 - test_2d_anisotropic_beam (Failed)
	 14 - test_2d_collision (Failed)
	 50 - test_2d_oscillating_beam (Failed)
	 52 - test_2d_oscillating_beam_cauchy (Failed)
	 59 - test_2d_self_contact (Failed)                      self_contact solid_dynamics
	 64 - test_2d_sliding (Failed)
	 74 - test_2d_stretching (Failed)
	 77 - test_2d_three_ring_impact (Failed)                 contact solid_dynamics
	 88 - test_2d_VP_same_sink_optimization (Failed)
	 90 - test_2d_T_pipe_VIPO_shell (Failed)                pressure boundary
	 97 - test_3d_passive_cantilever_LG (Failed)
	132 - test_3d_muscle_soft_body_contact (Failed)
	138 - test_3d_passive_cantilever (Failed)
	163 - test_3d_taylor_bar (Failed)                        contact solid_dynamics

I will leave it to you from here @Xiangyu-Hu

@Xiangyu-Hu
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@FabienPean-Virtonomy It seems that we need update the regression test data set the failures are due to mismatched data.

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