Modern Methods for Multiscale Simulation: The Love Life of Lobsters in the Light of Quantum Mechanics and Continuum Theory
1. Moderne Methoden der Multiskalensimulation: Das Liebesleben der Hummer im Lichte von Quantenmechanik und Kontinuumstheorie M. Friak,S. Nikolov, D. Ma, F. Roters, J. Neugebauer, D. Raabe Hier: Mechanik der Kristalle 19. Juni 2009, Kolloquium, TU Darmstadt
2. performance large products Motivation: Basics of crystal mechanics processes Understand macromechanics in terms of micromechanics Micromechanics for products
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6. [111] [-110] [11-2] Motivation: Basics of crystal mechanics Small scale experiments Complex microstructures
7. 6 Scales: exampleofmechanicalproperties Length [m] Top down 100 10-3 Mean field and boundary conditions (FE, FD, FFT) Bottom up Crystals (CPFEM, YS, HT) 10-6 Dislocations (DD, CA, KMC) 10-9 Structure of defects (DFT, MD) Structure of matter (DFT) Time [s] 10-9 103 10-15 10-3
36. 20 Az= 2 C44/(C11 − C12) Young‘s modulus surface plots Ti-18.75at.%Nb Ti-25at.%Nb Ti-31.25at.%Nb Pure Nb [001] [100] [010] Az=3.210 Az=2.418 Az=1.058 Az=0.5027 Elastic properties: Ti-Nb system Hershey FEM FFT D. Ma, M. Friák, J. Neugebauer, D. Raabe, F. Roters: phys. stat. sol. B 245 (2008) 2642
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39. 22 Homogeneity and boundary conditions – meso-scale 8% 3% 15% M. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81
40. 23 5mm equivalent strain 5mm equivalent strain Crystal plasticity FEM, grain scale mechanics (3D) exp., grain orientation, side B exp., grain orientation, side A 8mm 21mm 1mm FE mesh Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe (IJP, 2008)
41. 24 Discrete FFTs, stress and strain; different anisotropy stress strain
42. 25 323 points, 200 grains, FEM (surface), FFT (periodic), tensile strain distribution stress distribution CEFEM CEFEM strain distribution stress distribution FFT FFT
52. 30 Structure hierarchy of arthropods Al-Sawalmih, C. Li, S. Siegel, H. Fabritius, S.B. Yi, D. Raabe, P. Fratzl, O. Paris: Advanced functional materials 18 (2008) 3307 H. Fabritius, C. Sachs, P. Romano, D. Raabe, Advanced materials 21 (2009) 391.
53. 31 Epicuticle Cuticle hardened by mineralization with CaCO3 Exocuticle Exocuticle and endocuticle display different stacking density of twisted plywood layers Endocuticle
72. 50 Ab initio prediction of α-chitin elastic properties c b
73. 51 Hierarchical coarse graining Hierarchical modelling of the lobster cuticle: (I), (II) -chitin properties via ab initio calculations; (III) representative volume element (RVE) for a single chitin-protein fibre; (IV a) RVE for chitin-protein fibres arranged in twisted plywood and embedded in mineral-protein matrix; (IV b) RVE for the mineral-protein matrix. Level (V): homogenized twisted plywood without canals; (VI) homogenized plywood pierced with hexagonal array of canals; (VII) 3-layer cuticle.
75. 53 Results and comparison with experiments Young’s modulus as a function of the mineral content for different in-plane area fractions of the pore canals.