„… Tensoren Symbol Beschreibung B Approximierte Hesse-Matrix (Gl. 3.15) C Rechts-Cauchy-Green-Tensor (Gl. 6.5 …” „… ) G C Gestaltänderungsanteil von C (Gl. 6.5) D Skalierungsmatrix (Gl. 4.2) D Tensor der …” „… Links-Cauchy-Green-Tensor (Gl. 6.8) P Kovarianzmatrix (Gl. 3.47) Π Permutationsmatrix (Kap. 5.1) T 1 …”

„… Formulierung der Energiedichte Ŵ in Abhängigkeit der Hauptinvarianten des Rechts-Cauchy-Green-Tensors …” „… exp ⎛⎝⎛⎝p7 GLG LT G CT CST ⎞⎠⎞⎠+ p8 GLG LT ⎞⎠ · C 1 . (6.8) Der Tensor G L kann als Lagrangesches …” „… Äquivalent zur Zaremba-Jaumann-Zeitableitung des isochoren Links-Cauchy-Green-Tensor interpretiert werden …”

„… (σ,q) is the plastic flow direction, often assumed as ∂Ψ ∂σ , with the Cauchy stress tensor σ. Ψ …” „… change in the plastic part of the deformation tensor Dp = 0. Considering the stress state on the yield …” „… . Thus the plastic deformation tensor changes – Dp 6= 0 – as well as the internal variables: q̇ 6= 0. The …”

„… bordering elements of a shared node, the mean stress tensor can be build which are essential for the …” „… stress tensors material planes are built with the angles and (Fig. 4 a). The stress tensors can then be …” „… , it is neces-sary to take the whole stress tensor into consideration. In contrast to Böhme’s 2D stress …”

„… tensor components to each element of the structural mesh. In the present study, this information is …” „… gate (figure 10). Fig 10: Moldflow model and predicted fiber orientation tensor (first principal values …” „… ) The local fiber orientation tensor computed for each node of the MOLDFLOW mesh is mapped to the ABAQUS …”

„… Python: A Hands-On Introduction, Apress L. P, Berkeley, CA. [14] TensorFlow, 2021,“TensorFlow …” „… pinion 30% The neuronal network was implemented in PYTHON with the package TENSORFLOW and KERAS[14,15 …” „… ,” https://www.tensorflow.org/. [15] Keras, 2022,“Keras: the Python deep learning API,” https://keras.io/. [16] SciPy, 2023 …”

„… orientation tensors. It can be seen that the main orientation follows the tooth surface due to the flow …”

„… means of the tensor product between univariate bases. By defin-VDI-Berichte Nr. 2422, 2023416 ing …”

„… , the second loading cycle stress tensors for all 335 different contact points of each node in a marked …”

„… . The components of the stress tensor sare evaluated along paths intersecting this point in the …”

„… Ree–Eyring stress, 0 0/ sinh /eq N eq & & &is shear strain rate tensor.The density-pressure-temperature …” „… tensor,sd''is solid gravity acceleration.(3) Fluid-structure coupling equationThe kinematic condition and …” „… Hertzian contact half-width (m) V Tensor of velocity (m/s)teE , ieE , keE Specific total energy, specific …”

„… full stress tensors at any desired location in the gear with the efficiency of the influence number …” „… the local stress calculation on the hexahedron is performed. By averaging the stress tensors of the …” „… adjacent elements, the nodal stress tensors can be calculated from the element stresses. The result of the …”

„… representation. At present, it is an approximation by means of Bézier tensor product surfaces. With this surface …” „… an approxi-mation with Bézier tensor product surfaces. De-pending on the tooth geometry, this surface …” „… represented with separate surface descriptions by Bézier tensor product surfaces. For the purpose of surface …”

„… instantaneous hydrostatic component of the stress tensor; and ? ? is the instantaneous value of the Tresca …” „… mesoscopic scale, obtained by subtracting from the deviatoric stress, ? ? , a constant tensor, ? , , given by …”

„… the local stress tensors is performed in BECAL. The advantage of the fast recalculation of different …”

„… parameters. The acting stress tensor is a superposition of dynamicHertzian, shear, out-of-phase bending …” „… normalstresses τa, τm, σna, σnm, the second invariant of the deviatoric stress tensor J2,a or the hydrostatic …”

„… der inneren Geometrie der Fläche ab, d. h. von der ersten Fundamentalform (bzw. dem metrischen Tensor …” „… lässt sich verallgemeinern auf Mannig faltigkeit beliebiger Dimension mit einem metrischen Tensor. Auf …”