Consistent mass scaling for multi-patch and trimmed isogeometric explicit dynamics
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Explicit dynamics is the main workhorse for simulating impact and crash tests, often involving thin-walled components such as shells. Isogeometric analysis offers various advantages for such simulations: the boundary representation of CAD is the natural geometric description of shells and the high-order smoothness of splines naturally accommodates the higher-order partial differential equations governing shell mechanics. Additionally, the higher-order smoothness of the basis eliminates the so-called optical branch observed in the discrete spectrum of conventional finite elements [1], enabling larger stable time-step sizes. In practice, however, the latter point is hindered on three fronts: (i) the reduction of basis continuity on multipatch interfaces introduces outliers in the spectrum [2], (ii) similar outliers appear at domain boundaries due to repeating knots in the knot vector [3], (iii) CAD representations often make use of trimming, effectively leading to (potentially very small) cut elements, detrimental to the permissible critical time-step size [4]. In this talk, we propose a class of variationally consistent mass scaling techniques capable of suppressing outliers of all these forms.