Vertex Displacement-Based Discontinuous Deformation Analysis Using Virtual Element Method

Area of Science:

• Computational Mechanics
• Geotechnical Engineering
• Numerical Methods

Background:

• Traditional Discontinuous Deformation Analysis (DDA) faces challenges with rotational degrees of freedom.
• Existing methods may lead to inaccuracies or computational inefficiencies.

Purpose of the Study:

• To develop an improved block displacement mode for DDA.
• To enhance the precision and efficiency of DDA simulations by incorporating the Virtual Element Method (VEM).

Main Methods:

• Defined a new block displacement mode where block vertex displacements are the degrees of freedom.
• Utilized the Virtual Element Method (VEM) to define an individual virtual element space for block displacement illustration.
• Formulated and minimized the total potential energy of the block system based on VEM theory to derive global equilibrium equations.

Main Results:

• The new method effectively bypasses the need for explicit displacement expressions.
• Numerical integrations are simplified and readily computable.
• Analysis of four numerical examples demonstrates the method's effectiveness and precision.

Conclusions:

• The proposed VEM-based approach offers a robust alternative for DDA.
• This method successfully addresses limitations of the original DDA, particularly concerning rotational degrees of freedom.
• The findings validate the enhanced accuracy and computational advantages of the new technique.