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SUMMARY:New 1D models for localisation in slender structures - Claire Lest
 ringant\, Structural Engineering\, Cambridge
DTSTART:20201023T130000Z
DTEND:20201023T140000Z
UID:TALK140308@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:Slender structures are subject to various localised instabilit
 ies: necking of bars under traction\, bulging of cylindrical party balloon
 s\, beading in cylinders made up of soft gels\, or folding of tape-springs
 . In all these examples\, distinct states of deformation may coexist and c
 lassical one-dimensional (1D) models predict singular solutions. In partic
 ular\, classical 1D models fail to describe interfaces or finite size effe
 cts. The most common remedy is to use full structural models based on 3D f
 inite elasticity or nonlinear shell/membrane equations. However\, this is 
 computationally costly and often impracticable: simpler 1D regularised mod
 els depending on the strain and the strain gradient are therefore attracti
 ve. \nThere is a recent effort to rigorously establish 1D higher-order mod
 els for the analysis of localisation in slender structures. I will introdu
 ce a systematic method to derive such models by a formal expansion\, start
 ing from a variety of full structural models for slender elastic structure
 s. The expansion is performed near a finitely pre-strained state and there
 fore retains all sources of nonlinearity\, coming from the geometry and th
 e constitutive law. I will illustrate the method in the case of bulging an
 d beading\, and demonstrate its accuracy by comparing solutions of the 1D 
 gradient model with solutions of the original structural model.\n
LOCATION:zoom 853 4440 7455 - for password email  hh463@cam.ac.uk 
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