Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical...

Area of Science:

• Computational mechanics
• Materials science
• Finite element analysis

Background:

• Accurate modeling of crack propagation in materials under coupled thermal-mechanical loads is crucial for structural integrity.
• Existing methods often face challenges in handling arbitrary evolving cracks and ensuring numerical efficiency.

Purpose of the Study:

• To propose, implement, and validate a novel thermal-mechanical augmented finite-element method (TM-AFEM).
• To enable precise analysis of steady-state and transient coupled thermal-mechanical problems with evolving cracks.

Main Methods:

• Development of an augmented finite-element method incorporating thermal-mechanical coupling.
• Derivation of explicit, fully condensed thermal-mechanical equilibrium equations.
• Implementation using 4-node quadrilateral (2D) and 4-node tetrahedron (3D) elements.

Main Results:

• The TM-AFEM provides mathematically exact solutions in a piecewise linear sense.
• Demonstrated significant improvements in numerical accuracy and efficiency for crack propagation problems.
• Successfully applied to both 2D and 3D solids under coupled thermal-mechanical loading.

Conclusions:

• The TM-AFEM is a robust and efficient tool for analyzing crack propagation in complex materials.
• The method offers enhanced accuracy for coupled thermal-mechanical analyses involving evolving cracks.
• This work contributes to multiscale modeling of structural integrity in composite materials.