Elastic and Plastic Thin Strip Deformations under their Compression between Plane Rigid Stamps

Authors: Tretyakov Ye.M. Published: 19.06.2015
Published in issue: #3(102)/2015  

DOI: 10.18698/0236-3941-2015-3-103-118

Category: Mechanics | Chapter: Mechanics of Deformable Solid Body  
Keywords: solid, elastic deformations, plastic deformations, thin strip, planar deformation

The paper discusses the results of the research into the plasticity theory of thin strip deformations. It presents a solution to the two-dimensional elasto-plastic problem of compressing a thin strip between the plane rigid stamps. The load is estimated which causes plastic deformations within a rigid thin strip. The forms of plastic areas and their dimensions were delineated. Their dependence on an external load is determined. If the Poisson’s ratio is v = 0.5, the lines parallel to the stamp plains prove to be the boundary lines between the elastic and plastic areas. When a thin plane becomes completely plastic, the formulae of the classical Prandtl’s equation for compression of a thin fully plastic strip are derived as a particular solution to the two-dimensional elasto-plastic problem.


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