Recent Developments in High-Performance Computational Vibro-Acoustics in the Medium Frequency Regime

Structural acoustics applications in the medium frequency regime are computationally challenging. One avenue of research pursues higher-order discretization methods that can deliver both accuracy and computational efficiency at smaller mesh resolutions. The Discontinuous Enrichment Method (DEM) is one example which distinguishes itself from competing approaches in the additional information it incorporates in the approximation method. It has shown a significant promise for acoustic and structural acoustic applications and therefore is reviewed here, together with new applications to shell problems. Frequency sweeps, which are almost inevitable in many vibro-acoustic engineering problems, present an additional challenge as they significantly increase the already high computational cost. Therefore, interpolatory model reduction techniques that successfully address this challenge and enable real-time frequency sweep analyses are also discussed in this paper.

Simulating Atomic-Scale Defects with Atomic Methods and Extended Finite Elements

A finite element method is developed for dislocations in arbitrary, three-dimensional bodies, including micro-/nano-devices, and layered materials, such as thin films. The method is also compatible with anisotropic materials, and can readily be applied to nonlinear media. In this method, dislocations are modeled by adding discontinuities to extend the conventional finite element basis. Two approaches for adding discontinuities to the conventional finite element basis are proposed. In the first, a simple discontinuous enrichment imposes a constant jump in displacement across dislocation glide planes. In the second approach, the enrichments more accurately approximate the dislocations by capture the singular asymptotic behavior near the dislocation core. A basis of singular enrichments is formed from analytical solutions of straight dislocation lines, which are shown to be applicable for more general, curved dislocation configurations. Methods for computing the configurational forces on dislocation lines within the XFEM framework have also been developed. For jump enrichments, an approach based on an energy release rate or J-integral is proposed. When singular enrichments are available, it is shown that the Peach-Koehler equation can be used to compute forces directly. This new approach differs from many existing methods for studying dislocations because it does not rely on superposition of solutions derived analytically or through Green's functions. This extended finite element approach is suitable to study dislocations in micro- and nano-devices, and in specific material micro-structures, where complicated boundaries and material interfaces are pervasive.

Correction force for releasing crack tip element with XFEM and only discontinuous enrichment

This paper deals with numerical crack propagation and makes use of the extended finite element method in the case of explicit dynamics. The advantage of this method is the absence of remeshing. The use of XFEM with Heaviside functions only gives a binary description of the crack tip element: cut or not. Here, we modify the internal forces with a correction force in order to smoothly release the tip element while the virtual crack tip travels through an element. This avoids creating non physical stress waves and improves the accuracy of the evaluation of the stress intensity factors during propagation.