@Article{icces.2023.09499,
AUTHOR = {Yang Liu, Luis Dorfmann},
TITLE = {Localized Necking and Bulging of Finitely Deformed Residually Stressed  Solid Cylinder},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {27},
YEAR = {2023},
NUMBER = {4},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v27n4/55206},
ISSN = {1933-2815},
ABSTRACT = {In this talk, we present some analytical results concerning localized instabilities in stretched soft cylinders 
with residual-stress effect. Within the framework of finite elasticity, a bifurcation analysis is carried out 
based on the incremental theory. It is found that with the residual stress effect taken into consideration 
additional singularities of the incremental equations appear. To overcome this difficulty we apply the Stroh 
formulism and an expansion methodology and derive a bifurcation condition. Then we consider three 
loading scenarios and perform a detailed analysis of the bifurcation behaviors. It turns out that the zero 
mode, giving rise to localization, is always preferred. In particular, an explicit bifurcation condition, namely, 
the derivative of the axial force with respect to the axial stretch is zero, is obtained. Furthermore, there exists 
a threshold of the residual stress or the specified resultant axial force, and below which no bifurcation is 
possible. Finally, some analytical insight is provided for the propagation of localized bulging or necking in 
light of Maxwell’s equal area rule.},
DOI = {10.32604/icces.2023.09499}
}