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SUMMARY:Soft elasticity by domain formation in reinforced and magneto-acti
 ve composites - Pedro Ponte Castañeda\, Department of Mechanical Engineer
 ing and Applied Mechanics and Graduate Program in Applied Mathematics and 
 Computational Science\, University of Pennsylvania\,
DTSTART:20231027T130000Z
DTEND:20231027T140000Z
UID:TALK205453@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:Reinforced elastomeric composites with periodic microstructure
 s can undergo both microscopic (pattern changing) and macroscopic (long wa
 velength) instabilities. This presentation is concerned with the response 
 of magneto-active elastomeric composites after the possible development of
  a macroscopic instability\, which have been previously characterized in t
 erms of loss of strong ellipticity of the incremental homogenized response
  of the composite material and can also occur when the microstructures are
  random.  Building on earlier work in the purely mechanical context\, it i
 s shown by means of a generalized Maxwell construction that the composite 
 loses stability by the formation of lamellar domains\, on a scale much lar
 ger than that of the fibers\, and where the orientation of the fibers chan
 ges abruptly from domain to domain in a chevron-type pattern. Mathematical
 ly\, this corresponds to the relaxation or quasiconvexification of the pri
 ncipal solution for the homogenized energy function and is associated with
  soft modes of deformation that can be controlled by externally applied ma
 gnetic fields. For analytical ease\, we consider the application to simple
  laminate composites consisting of two isotropic neo-Hookean phases with l
 inear magnetic responses and obtain estimates for the homogenized relaxed 
 response under combined magneto-mechanical loadings. One important finding
  is that an externally applied magnetic field can be used to trigger the i
 nstability without the application of mechanical loads. Another very inter
 esting finding is that there are perfectly soft modes of deformation where
  the deformation can be accommodated purely by appropriate changes in the 
 domain microstructures — without changes in the applied stress. At the m
 ore theoretical level\, it is found that strict global rank-one convexity 
 of the principal solution is generally lost prior to local rank-one convex
 ity\, or strong ellipticity. This suggest a new definition of macroscopic 
 instabilities in terms of loss of global rank-one convexity.
LOCATION:Department of Engineering - LR5
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