On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws

We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this context. To do so, we introduce discontinuous-Galerkin-like interface terms for multi-block upwind SBP methods applied to nonlinear conservation laws. We investigate the behavior of the upwind SBP methods for flux vector splittings of varying complexity on Cartesian as well as unstructured curvilinear multi-block meshes. Moreover, we analyze the local linear/energy stability of these methods following Gassner, Svärd, and Hindenlang (2022, doi:10.1007/s10915-021-01720-8). Finally, we investigate the robustness of upwind SBP methods for challenging examples of shock-free flows of the compressible Euler equations such as a Kelvin-Helmholtz instability and the inviscid Taylor-Green vortex

On the approximation of vector-valued functions by volume sampling

Given a Hilbert space H and a finite measure space Ω, the approximation of a vector-valued function f : Ω → H by a k-dimensional subspace U ⊂ H plays an important role in dimension reduction techniques, such as reduced basis methods for solving parameter dependent partial differential equations. For functions in the Lebesgue–Bochner space L2 (Ω; H), the best possible subspace approximation error d (2) k is characterized by the singular values of f. However, for practical reasons, U is often restricted to be spanned by point samples of f. We show that this restriction only has a mild impact on the attainable error; there always exist k samples such that the resulting error is not larger than √ k + 1 · d (2) k . Our work extends existing results by Binev at al. (SIAM J. Math. Anal., 43(3):1457–1472, 2011) on approximation in supremum norm and by Deshpande et al. (Theory Comput., 2:225–247, 2006) on column subset selection for matrices

Investigation on the recycling potential of additively manufactured carbon fiber reinforced PA 6.6

Carbon fiber reinforced polymers (CFRP) are already used in a wide range of applications such as automotive, aerospace and renewable energy industries and demand on this material class is increasing steadily. As demand increases, the amount of CFRP waste, either from production or at the end of life of components, increases simultaneously and sustainable solutions such as disposal, reuse or recycling of fiber reinforced materials getting more and more important. In this paper one possibility for recycling short carbon fiber reinforced polyamide 6.6 (CF/PA 6.6) is presented. The recycling process includes shredding of the material, drying and filament extrusion to enable a reuse of the material with an additive manufacturing process. The focus of this investigation is on the mechanical properties of the recycled filaments itself as well as on the 3D printed specimen considered recycled filaments. The properties at different stages of the short carbon fiber reinforced polyamide 6.6 recycling process were investigated, including the juvenile CF/PA 6.6 as well as specimens made from one- or two-times recycled material. Mechanical performance was evaluated by tensile, bending and impact testing. Experimental results pointed out that no significant difference in performance of juvenile and recycled materials was observed for tensile and flexural loads. The impact strength of the recycled specimen decreased to a small extent

Combination of in-/and ex-situ damage detection methods to investigate the forming behavior of fiber-metal-laminates

In this study, the forming behavior of fiber-metal laminates (FML) is investigated by a combination of different (in- and ex-situ) measurement techniques. Using FML-samples consisting of aluminum and carbon fiber reinforced polyamide-6, deep-drawing tests were employed at high temperatures. It can be concluded a conventional approach based on the forming limit curve (FLC) is not suitable to predict the failure initiated in the multi-material setup as principal strains cannot differentiate the strain in aluminum and CFRP and lack sensitivity to detect other relevant failure modes, such as debonding as well as debonding in between layers. To better understand the failure behavior due to forming of FML, an experimental setup, that based on the Nakajima-test, was developed, using in-situ acoustic emission testing, 3D digital image correlation as well as ex-situ X-ray computed tomography. The combined results from all methods helped to gain a deeper insight into how thermoplastic FML behave during deep drawing at elevated temperatures especially focusing on evolving damage inside the hybrid material