TY - JOUR

T1 - An exact finite deformation elasto-plastic solution for the outside-in free eversion problem of a tube of elastic linear-hardening material

AU - Gao, Xin Lin

AU - Atluri, Satya N.

N1 - Funding Information:
The support for this work from the US FAA, through a grant to the Center of Excellence for Computational Modeling of Aircraft Structures at the Georgia Institute of Technology, is greatly appreciated. Grateful acknowledgement is also made to two referees for their very helpful comments on an earlier version of this paper.

PY - 1997/6

Y1 - 1997/6

N2 - An exact solution is obtained in this paper for the elasto-plastic outside-in free eversion problem of a tube of elastic linear-hardening material using a tensorial formulation. The solution is based on a finite-strain version of Hencky's deformation theory, the von Mises yield criterion, and the assumptions of volume incompressibility and axial length constancy. All expressions for the stress, strain distributions and the eversion load are derived in an explicit form. In addition, with both the linear-elastic and strain-hardening-plastic responses of the material being included and with the thickness effect of the tube being incorporated, this solution provides a rigorous and complete theoretical analysis of the elasto-plastic eversion problem, unlike existing solutions. Two specific solutions are also presented as limiting cases of the solution. Also provided are some numerical results and the related observations to show quantitatively applications of the solution.

AB - An exact solution is obtained in this paper for the elasto-plastic outside-in free eversion problem of a tube of elastic linear-hardening material using a tensorial formulation. The solution is based on a finite-strain version of Hencky's deformation theory, the von Mises yield criterion, and the assumptions of volume incompressibility and axial length constancy. All expressions for the stress, strain distributions and the eversion load are derived in an explicit form. In addition, with both the linear-elastic and strain-hardening-plastic responses of the material being included and with the thickness effect of the tube being incorporated, this solution provides a rigorous and complete theoretical analysis of the elasto-plastic eversion problem, unlike existing solutions. Two specific solutions are also presented as limiting cases of the solution. Also provided are some numerical results and the related observations to show quantitatively applications of the solution.

UR - http://www.scopus.com/inward/record.url?scp=0031167343&partnerID=8YFLogxK

U2 - 10.1093/imamat/58.3.259

DO - 10.1093/imamat/58.3.259

M3 - Article

AN - SCOPUS:0031167343

SN - 0272-4960

VL - 58

SP - 259

EP - 275

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 3

ER -