This study develops a consistent phase-field framework for dynamic ductile fracture in curved shells. It integrates transverse shear deformation, plane-stress plasticity, and coupled geometric and material nonlinearities within a robust shell formulation.

Numerical benchmarks reproduce published fracture responses under static and dynamic loading. The framework captures crack initiation, propagation, curving, branching, and crack-tip velocities in thin and moderately thick shells.

To resolve numerical instabilities in conventional buckling analyses, this study introduces the SPLR scheme. This maintains the positive definiteness of the stiffness matrix throughout the optimization process and suppresses complex eigenvalues, ensuring reliable and physically meaningful buckling evaluations.

The Refined Adaptive Continuation Method (RACM) is extended to multimaterial systems to enhance convergence and numerical robustness. Furthermore, using the MITC4 element eliminates shear locking, thereby optimizing the thermomechanical buckling performance of complex curved shell structures.

The paper introduces TET4E, a refined element using the Partition of Unity method to enrich displacement fields and eliminate volumetric locking in nearly incompressible materials. It integrates Mooney-Rivlin and Neo-Hookean models within a Total Lagrangian framework to accurately handle large deformations without adding nodes.

This study validates TET4E using a new iterative procedure for nonlinear modal analysis to capture amplitude-dependent frequencies and mode shapes. Numerical examples, such as soft robots and distorted plates, demonstrate its superior accuracy and convergence over traditional elements, even with coarse meshes.

This review chronologically examines computer-aided design (CAD) software designed to overcome limitations of manual design. It categorizes design methodologies into bottom-up and top-down strategies, encompassing tile-based and frame-based architectures.

The study classifies simulation tools into finite-element and coarse-grained molecular dynamics models. It highlights future needs, including unified automation platforms and deep learning integration to conserve time and effort.