Implicit sub-stepping scheme for critical state soil models

Area of Science:

• Geotechnical Engineering
• Computational Mechanics
• Soil Mechanics

Background:

• Implicit Euler algorithm and return mapping are standard for critical soil models.
• Large load steps can cause convergence issues in local nonlinear systems.
• Sub-stepping schemes improve convergence but increase tangent operator complexity.

Purpose of the Study:

• To develop a consistent tangent operator formulation for implicit sub-stepping integration.
• To address convergence challenges in critical soil models under large load steps.
• To enhance the efficiency of numerical simulations for geotechnical problems.

Main Methods:

• Developed a formulation for the consistent tangent operator.
• Applied the formulation to implicit sub-stepping integration.
• Validated the approach for modified Cam-Clay and unified Clay and Sand models.

Main Results:

• The proposed formulation is highly efficient.
• Achieved convergence for arbitrary large load steps.
• Successfully integrated with modified Cam-Clay and unified Clay and Sand models.

Conclusions:

• The developed consistent tangent operator formulation overcomes convergence issues in large load steps.
• This method is efficient and applicable to complex geotechnical simulations, including tunnel analysis.
• Enhances the robustness of numerical integration for critical soil models.