Crack propagation analysis using a hybrid 2D finite element-peridynamics framework with a residual-based quasi-static...

Area of Science:

• Computational mechanics
• Materials science
• Fracture mechanics

Background:

• Accurate fracture simulation requires robust computational methods.
• Integrating peridynamics (PD) with finite elements (FE) offers a hybrid approach.
• Existing methods for quasi-static analysis of coupled FE-PD systems have limitations.

Purpose of the Study:

• To present a novel hybrid finite element-peridynamics (FE-PD) framework for 2D fracture simulation.
• To develop and implement a residual-based dynamic relaxation (RBDR) solver for quasi-static FE-PD analyses.
• To validate the accuracy and computational efficiency of the proposed FE-PD framework and RBDR solver.

Main Methods:

• Embedding a peridynamic fracture zone within finite element domains using a modified volume-based coupling scheme.
• Developing a damping-free, matrix-free residual-based dynamic relaxation (RBDR) solver for quasi-static equilibrium.
• Utilizing Richardson-type pseudo-time iteration to minimize the residual force field.

Main Results:

• The RBDR solver achieved higher accuracy and was 23 times faster than the standard Adaptive Dynamic Relaxation (ADR) method.
• The hybrid FE-PD framework accurately reproduced crack morphology and kinetic energy evolution in Mode I loading simulations.
• Quasi-static crack propagation simulations showed no crack branching, consistent with fracture mechanics theory.

Conclusions:

• The hybrid FE-PD framework with the RBDR solver provides an efficient and accurate method for 2D fracture simulation.
• The RBDR solver overcomes limitations of traditional damping-based relaxation methods.
• This approach enhances the capability to study complex fracture phenomena under various loading conditions.