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Justification for use of Riks method to investigate gross plastic deformation

Hi, my question is on the use of Riks and other Arc length methods when analysing  a system for gross plastic deformation. ASME B&PV code , in its investigation for Gross plastic deformation as a Load at which convergence does not take place. Now, as far as I understand, Newton Raphson method fails at locations of singularity in the stiffness matrix and also at Bifurcation points, it can trace the unstable primary paths. Both these issues can be overcome ( provided the limit point is not too sharp) by Riks and other Arc length methods.

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