Simulation Of Thin Shells Research Articles

Hydrocode simulation of Ganymede and Europa cratering trends – How thick is Europa’s crust?

One of the continuing debates of outer Solar System research centers on the thickness of Europa’s ice crust, as it affects both the habitability and accessibility of its sub-surface ocean. Here we use hydrocode modeling of the impact process in layered ice and water targets and comparison to Europan cratering trends and Galileo-derived topographic profiles to investigate the crustal thickness. Full or partial penetration of the ice crust by an impactor occurred in simulations in which the ice thickness was less than 14 times the projectile radius. Craters produced in these thin-shell simulations were consistently smaller than for larger ice thicknesses, which will complicate inference of large impactor population sizes. Simulations in which the resultant crater was 3 times the ice layer thickness resulted in summit-pit morphology. This work supports that summit pit craters noted on both rocky and icy bodies, can be created by the presence of a weaker layer at depth. We suggest that floor pits, seen only on ice-rich bodies, require a different formation mechanism to summit pits.Pristine craters formed in a target with high heat flow were shallower than for the same impact into a target of lesser heat flow, suggesting that the ‘starting’ crater morphology for viscous relaxation, isostatic readjustments and erosion rate studies is different for craters formed in times of different heat flow. We find that the crater depth–diameter trend of Europa can only be recreated when simulating impact into an upper brittle ice layer of 7km depth, with a corresponding geothermal gradient of 0.025K/m. As this ice thickness estimate is below ∼10km, results from this work suggest that convective overturn of the surface ice may occur, or have occurred, on Europa making the development of indigenous life a possibility.

One-point quadrature ANS solid-shell element based on a displacement variational formulation Part I – Geometrically linear assessment

A demonstration of a computationally efficient, physically stabilised one point-quadrature solid-shell finite element in pure displacement variational formulation and within the context of hierarchical displacement modes is presented in this paper. The displacement field of the 24 degree of freedom 8-node solid finite element is enhanced by a hierarchical, thickness-wise, quadratic displacement field and associated single displacement degree of freedom. The displacement enhancements expand the covariant element strain space resolving thickness locking and in combination with the assumed natural strain approach, attenuates shear and trapezoidal locking in thin shell simulations. Formulated within the recent framework of the reduced integration element technology and hourglass physical stabilisation, a locking free, 8-node solid-shell element for general three dimensional shell analysis is obtained. The theoretical relevance and applicability of the proposed displacement-kinematics 8-node solid-shell element offering comparable accuracy and performance flexibility as physically stabilised reduced integration solid-shell elements based on mixed and EAS variational statements is demonstrated in selected linear numerical benchmark problems.

A virtual node algorithm for changing mesh topology during simulation

We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This results in elements that contain both real material and empty regions. The missing material is contained in another copy (or copies) of this element. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material in a fashion consistent with the embedded geometry. This approach enables efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small CFL time step restrictions since they are embedded in well shaped larger elements. To enable robust simulation of embedded geometry, we propose new algorithms for handling rigid body and self collisions. In addition, we present several mechanisms for influencing and controlling fracture with grain boundaries, prescoring, etc. We illustrate our method for both volumetric and thin-shell simulations.