Some computational and algorithmic developments in computational mechanics of discontinua

Area of Science:

• Computational mechanics
• Computational science
• Geomechanics

Background:

• Computational mechanics of discontinua is an emerging sub-discipline.
• Discrete-element methods (DEM), combined finite-discrete-element methods (FEM-DEM), and discontinuum deformation analysis (DDA) are key methods.
• Common algorithmic procedures include contact detection, explicit solvers, fracture/fragmentation models, 3D contact kinematics, and fluid coupling.

Purpose of the Study:

• To review recent algorithmic breakthroughs in computational mechanics of discontinua.
• To bridge the gap between specialized publications and researchers in different fields.
• To facilitate the application of compatible developments across various discontinuum problems.

Main Methods:

• Review of key algorithmic breakthroughs in discontinuum simulations.
• Focus on advancements in contact detection, explicit solvers, fracture/fragmentation models, and fluid coupling.
• Discussion of 3D explicit solvers with finite rotations and fluid pressure-driven fracture.

Main Results:

• Significant breakthroughs have occurred in contact detection (e.g., NBS, C-grid), contact solutions, and fracture/fragmentation models.
• Advancements include fluid pressure-driven fracture processes and 3D explicit solvers incorporating finite rotations.
• Many breakthroughs remain underutilized across the full spectrum of discontinuum problems.

Conclusions:

• Recent algorithmic advancements in computational mechanics of discontinua offer significant potential.
• Dissemination of these breakthroughs across diverse research fields is crucial for broader application.
• This review aims to enable researchers to apply compatible developments to their specific discontinuum problems.