BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vít Průša DTSTART:20250402T070000Z DTEND:20250402T080000Z DTSTAMP:20260422T122035Z UID:MathMAC/32 DESCRIPTION:Title: Effective models for mechanical response of metamaterials\nby Vít Pr ůša as part of Modelling of materials - theory\, model reduction and eff icient numerical methods (UNCE MathMAC)\n\n\nAbstract\nWe propose a thermo dynamically based approach for constructing effective rate-type constituti ve relations describing finite deformations of metamaterials. The effectiv e constitutive relations are formulated as second-order in time rate-type Eulerian constitutive relations between only the Cauchy stress tensor\, th e Hencky strain tensor and objective time derivatives thereof. In particul ar\, there is no need to introduce additional quantities or concepts such as ``micro-level deformation''\,``micromorphic continua''\, or elastic sol ids with frequency dependent material properties.\n\nMoreover\, the linear isation of the proposed fully nonlinear (finite deformations) constitutive relations leads\, in Fourier/frequency space\, to the same constitutive r elations as those commonly used in theories based on the concepts of frequ ency dependent density and/or stiffness. From this perspective the propose d constitutive relations reproduce the behaviour predicted by the frequenc y dependent density and/or stiffness models\, but yet they work with const ant---that is motion independent---material properties. This is clearly mo re convenient from the physical point of view. Furthermore\, the linearise d version of the proposed constitutive relations leads to the governing pa rtial differential equations that are particularly simple both in Fourier space as well as in physical space.\n\nFinally\, we argue that the propose d fully nonlinear (finite deformations) second-order in time rate-type con stitutive relations do not fall into traditional classes of models for ela stic solids (hyperelastic solids/Green elastic solids\, first-order in tim e hypoelastic solids)\, and that the proposed constitutive relations embod y a new class of constitutive relations characterising elastic solids.\n LOCATION:https://researchseminars.org/talk/MathMAC/32/ END:VEVENT END:VCALENDAR