Paper Fiber Network Models for Elastic Wave Simulation

Three-dimensional fiber network models of paper sheets (80 g/m² grammage), represented as node/edge graphs with per-edge mechanical properties. Each archive contains one network in a folder net2/ or net3/: Archive Sheet size Grammage Nodes Edges net2.zip 8 mm × 8 mm 80 g/m² 1,639,153 2,356,560 net3.zip 40 mm × 40 mm 80 g/m² 40,904,969 58,887,384 Units. All quantities are expressed in the base units listed in units.txt: mass in kg, length in µm, time in s. Consequently coordinates and widths are in µm, masses in kg, the force-like stiffness constants (EA, kG_1A, kG_2A) are in kg µm s⁻² (= 1 µN), and the moment-like stiffness constants (G_xI_x, E_1I_1, E_2I_2) are in kg µm³ s⁻² (= 10⁻¹⁸ N m²). nodes.csv contains the nodes of the network: id: the node id x, y, z: node position in µm edges.csv contains the connectivity. Each edge is a straight fiber segment between two nodes: id: the edge id node1, node2: node ids of the two endpoints edgeProperties.csv contains the mechanical properties of each edge (Timoshenko beam constants). All directional quantities are expressed in the edge-local orthonormal basis (tangent, normal 1, normal 2); the cross-section is assumed rectangular: id: the edge id (matches edges.csv) mass: mass of the edge [kg] EA: axial (displacement) stiffness along the edge tangent kG_1A, kG_2A: shear stiffness in the direction of normal 1 and normal 2 (k = shear correction factor) G_xI_x: torsional (rotation) stiffness about the edge axis E_1I_1, E_2I_2: bending stiffness associated with normal 1 and normal 2 n_11, n_12, n_13: normal 1 — first principal direction of the cross-section n_21, n_22, n_23: normal 2 — second principal direction of the cross-section width1, width2: widths of the cross-section in the direction of normal 1 and normal 2 [µm] fiber_id: id of the physical fiber this edge belongs to; -1 for virtual weld edges (see note below) fiber_edge_id: running index of the edge along its fiber; -1 for virtual weld edges Note on virtual weld edges. In addition to fiber segments, the networks contain virtual weld edges (marked by fiber_id = -1 and fiber_edge_id = -1) that bond fibers together at their contact points. These edges are massless (mass = 0); this is intended and correct. info.txt records the sheet grammage, sheet size, and node count. units.txt records the base units (mass, length, time) used for all quantities. The fiber networks were generated at the Fraunhofer-Chalmers Centre for Industrial Mathematics (FCC), Gothenburg, Sweden. We want to thank Morgan Görtz from the FCC for his continued support.