Estimating Constraint Parameter in 3D Models of Specimens Based on $T$-Stress and Fully Plastic Analysis

With constraint parameters (e.g.
$\boldsymbol{A}(\boldsymbol{A}_{2}), \boldsymbol{Q}$
, etc.), two parameter approaches (e.g.
$\boldsymbol{J}-\boldsymbol{A} (\boldsymbol{A}_{2}), \boldsymbol{J}-\boldsymbol{Q}$
, etc.) are proposed, to more accurately analyze the crack front fields, especially for the low constraint cases which are more common in practical engineering structures. Currently, no theoretical solutions of the constraint parameters in two parameter approaches are available. Moreover, numerical methods for the constraint parameter determination are not practical because of the significant resource and time consumption, especially for 3D solid models or engineering structures. Therefore, based on T-stress and fully plastic analysis, estimation theory and formulae for constraint parameter
$\boldsymbol{A}$
in 3D models are developed in current work through theoretical and numerical analyses, to make it possible to apply the two parameter approaches in practical engineering structures.