An Implicit Solution for GTN Model by Primal-dual Interior Point Method

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  • GTNモデルのための主双対内点法による陰的解法

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<p>An implicit algorithm in which a primal-dual interior point method (PDIP method) is applied for Gurson-Tvergaard-Needleman model (GTN model) is presented to stabilize the stress update. Although the GTN model widely utilized to realize the change of void volume fraction that dominates ductile fracture in metals, the numerical instability occurs due to the shrinkage of yield surface and the acceleration of void growth. In particular, the conventional return mapping algorithm leads to the misjudgment of yield condition since the yield surface shrinks by the evolution of void volume fraction. In addition, the smoothness of solved equations is required to employ the nonlinear solution method such as the Newton method, whereas the evolution of void volume fraction is approximated as bilinear form to represent the acceleration of void growth. Against these backgrounds, we apply the PDIP method for the stress update of GTN model, in which the inequality constraints in the constitutive model are replaced by an equivalent constrained optimization problem to ensure the numerical stability. Finally, the capability of our proposed PDIP method is demonstrated throughout several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied for only yield function.</p>

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