BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mykola Tkachuk (Karlstad University) DTSTART:20240923T111500Z DTEND:20240923T120000Z DTSTAMP:20260417T004337Z UID:cam/36 DESCRIPTION:Title: Var iational approaches to the analysis of structural response of fiber networ k microstructures\nby Mykola Tkachuk (Karlstad University) as part of CAM seminar\n\nLecture held in MV:L14.\n\nAbstract\nTwo approaches to stat ic equilibrium of fiber network microstructures will be presented.\nOrient ation-based averaging of network microstructures with non-affine kinematic s associates the ensemble of fibers at a given material point with a unit sphere of initial orientations (called also microsphere or representative orientation space). A special micro-macro relation between these microscop ic deformations and the macroscopic deformation gradient is derived by the concept of maximal advance paths in the network. The averaged microscopic free energy of the fibers is minimized subjected to this kinematic constr aint. The derived model can be applied to networks of flexible polymer cha ins (as found in elastomers)\, semiflexible or stiff filaments (elastin\, collagen and other biopolymers and soft tissues). The model has been recen tly extended to composite networks consisting of two or more distinguished components. \nSliding of inextensible fibers in discrete network microstr ucture of nonwoven materials is defined as a nonsmooth convex optimization problem. The rate-independent sliding and the quasi-static equilibrium lo ading of such network structure are constituted within the theory of stand ard dissipative systems. A minimum principle for incremental potential is formulated with respect to the displacement-based variables as a second-or der cone programming (SOCP) problem. A pure complementary energy principle is derived as the dual formulation in terms of stress-like variables. Bot h SOCP problems can be solved numerically by interior-point methods.\n LOCATION:https://researchseminars.org/talk/cam/36/ END:VEVENT END:VCALENDAR