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SUMMARY:A variational structure underpinning higher-order homogenization -
   Manon Thbaut\, Ecole Polytechnique  
DTSTART:20250509T130000Z
DTEND:20250509T140000Z
UID:TALK228820@talks.cam.ac.uk
CONTACT:46601
DESCRIPTION:From an engineering point of view\, it is convenient to descri
 be composite materials using homo- geneous effective properties. When the 
 microstructure is periodic\, asymptotic homogenizationis particularly well
  suited for this aim. Classical homogenization corresponds to the dominant
 \norder model and yields an effective standard Cauchy medium. At next orde
 rs\, we can derive addi- tional corrections that depend on the successive 
 strain gradients. These corrections are typically\nof interest to capture 
 size-effects appearing for microstructures with contrasted stiffness prope
 rties. However\, these higher-order models present two major limitations. 
 First\, the corrections producedby homogenization can handle size-effects 
 that occur in the bulk region\, but are not suited to\nthe analysis of the
  boundaries. In fact\, they miss significant boundary effects which can de
 grade\nsignificantly the quality of the predictions. Secondly\, these high
 er-order models present several mathematical inconsistencies\, including n
 on-positive strain-gradient stiffnesses. As a result\, the\neffective ener
 gy is not necessarily positive and any equilibrium solution is unstable wi
 th respect\nto short-scale oscillations. To handle these two limitations s
 imultaneously\, we elaborate a newhomogenization procedure that includes b
 oundary effects. By contrast with usual approaches\, inour procedure the h
 omogenization is carried at the energy level\, rather than on the strong f
 ormof the equilibrium. Besides\, the positivity of the resulting energy is
  guaranteed by an original\ntruncation method [1]. As an example\, we cons
 ider a 1D spring network. The resulting effective energy contains a bulk\n
 term that is positive\, plus a boundary term that accounts for the energy 
 generated by the boundary\neffects. We show that\, by contrast with usual 
 asymptotic homogenization\, this higher-order model\nis able to capture si
 ze-effects occurring in the interior domain\, as well as near the boundari
 es. 
LOCATION:Oatley 1 Meeting Room\, Department of Engineering
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