BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antonio J. Gil (University of Swansea\, UK) DTSTART:20210308T144000Z DTEND:20210308T161000Z DTSTAMP:20260405T174941Z UID:NSCM/24 DESCRIPTION:Title: On the use of mixed formulations for computational polyconvexity and multi -variable convexity\nby Antonio J. Gil (University of Swansea\, UK) as part of Nečas Seminar on Continuum Mechanics\n\n\nAbstract\nThe computat ional modelling of large strain multi-physics problems is nowadays an area of intensive research by numerous scientists. Among problems of this kind \, two pressing applications underpin the motivation behind this presentat ion. On the one hand\, the in-silico design of highly flexible dielectric elastomers for soft robotics applications and\, on the other hand\, the re alistic simulation of the electromechanical interactions of the cardiac mu scle from the physiological and pathological standpoints. In both applicat ions\, the requirement for extremely accurate and stable results at\, poss ibly\, large values of the field variables (i.e. strains and electric/card iac potential) proves very challenging from the computational point of vie w.\nThe presentation starts by revisiting the now well-accepted requiremen t of polyconvexity (a sufficient condition for rank-one convexity) in the case of reversible hyperelasticity\, where the strain energy functional is described by a convex combination of the minors of the deformation gradie nt tensor. We then extend this concept to the case of energies which depen d on non-strain based variables\, for instance\, other physical measures s uch as the electric displacement\, leading to the introduction of a new co mputational paradigm\, Multi-Variable Convexity. Crucially\, this new defi nition of the internal energy enables ellipticity to be extended to the en tire range of deformations and electric fields and\, thus\, spurious numer ical instabilities can then effectively be removed from the model whilst m aintaining real physical instabilities.\nThe polyconvexity of the energy f unctional with respect to its set of arguments guarantees the definition o f well-posed counterpart work conjugates\, where a one to one (invertible) relationship can be established. This ensures the existence of alternativ e energy potentials via the use of partial or total Legendre transforms an d opens up the possibility for new extended Hu–Washizu-type variational principles in terms of using various interpolation spaces for the differen t unknown fields\, leading to enhanced type of formulations. A series of e xamples will be presented demonstrating the potential of this new paradigm when coupled with the use of Finite Element type discretisation technique s.\n LOCATION:https://researchseminars.org/talk/NSCM/24/ END:VEVENT END:VCALENDAR