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SUMMARY:Modeling of Materials with Flexible Nanoplatelets with  Complex Va
 riables - Sonia Mogilevskaya (University of Minnesota)
DTSTART:20230727T090000Z
DTEND:20230727T100000Z
UID:TALK202804@talks.cam.ac.uk
DESCRIPTION:Emerging generations of nanomaterials and biomaterials use ult
 rathin nanoplatelets or membrane sheets as reinforcements. In the talk\, w
 e discuss the use of the theories of material surfaces for modeling such m
 aterials. The theories describe an infinite isotropic elastic medium that 
 contains a material surface treated as either a membrane or a shell of van
 ishing thickness. The material surface is characterized by its own elastic
  stiffness as well as residual surface tension The governing equations of 
 the theories are reviewed and challenges associated with the theoretical a
 nalysis and numerical solutions of resulting non-classical boundary value 
 problems are discussed. For solving the problems in the plane strain setti
 ng\, the displacements in the matrix are sought in the complex variables f
 orm of a single layer elastic potential. The density of the potential repr
 esents the jump in complex tractions across the surface. Exact expressions
  for the elastic fields in the matrix are provided in terms of complex int
 egral representations. We present solutions for the two-dimensional case o
 f a surface along a straight segment. The dimensionless parameters that go
 vern the problems are identified and the numerical examples\, that illustr
 ate their influence on the local elastic &ensp\;fields in the material\, a
 re discussed.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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