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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. My question is, how do we justify that using Riks and similar methods, we are not forcing a solution even when gross plastic deforation ( in the language of the code, overall structural instability) is taking place? The model is geometrically non linear. What can be the physical and mathematical arguments in favour of Riks algorithm in investigating gross plastic deformation?

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