Seminar in Numerical Analysis: Alexandre Imperiale (CEA Paris-Saclay)

A Gonzalez scheme for smooth nonlinear contact conditions in time-domain wave propagation problems

We consider the problem of transient wave propagation within two domains linked with smooth nonlinear contact conditions at a common interface. While standard linear elastodynamics is assumed within each domain, at the interface we consider continuity of normal stresses, and (more importantly) a smooth finite compressibility law. We propose an energy preserving – thus stable – time scheme based upon [1], and devise an efficient time-marching algorithm. We validate our approach with semi-analytical results, and illustrate typical nonlinear waves phenomena (harmonics, zero-frequency components) in 2D.

References

[1] O. Gonzalez, Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Comput. Methods Appl. Mech. Eng., 2000, 190(13-14), 1763-1783.

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