Intra-increment Penalty Stiffness Adjustment for Finite Element Simulation
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Solution Overview
Problem
Existing finite element simulation methods, such as the augmented penalty method, face challenges in achieving accurate results due to non-physical numerical effects like contact penetration and pressure issues, which require user judgment and can lead to inaccuracies and confusion in simulation outcomes.
Innovation Solution
The method involves determining a first and second value of a parameter, such as penalty stiffness, through Newton iterations, with different convergence checks to ensure accurate and realistic simulations, allowing for precise enforcement of contact constraints and improved convergence without degrading accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the augmented penalty method is used to improve simulation accuracy, then contact penetration errors are reduced, but non-physical numerical effects like positive contact pressure with positive gap distances occur
Solution Approach 1:
The penalty stiffness parameter is dynamically adjusted during the Newton iteration process rather than remaining constant. The method transitions from a lower penalty stiffness in early iterations to a higher penalty stiffness in later iterations, allowing the system to adapt its constraint enforcement strength based on the convergence state and eliminate non-physical effects like positive pressure with positive gaps
Solution Approach 2:
The invention changes the penalty stiffness parameter value during the solution process. By modifying this key parameter from a lower initial value to a higher final value across different iterations, the method achieves both robust convergence and physically realistic contact behavior, resolving the contradiction between accuracy and physical realism
2Measurement precision
If a higher penalty stiffness is used to reduce contact penetration, then contact constraint accuracy improves, but convergence difficulty increases
Solution Approach 1:
The method performs preliminary iterations with a lower penalty stiffness value to establish initial convergence and reduce numerical instability. This preliminary phase prepares the system for the subsequent phase with higher penalty stiffness, enabling the system to achieve both accuracy and convergence without the trade-off that would exist if high stiffness were applied from the beginning
Solution Approach 2:
The penalty stiffness is dynamically adjusted during the Newton iteration process rather than remaining constant. The method transitions from a lower penalty stiffness in early iterations to a higher penalty stiffness in later iterations, allowing the system to adapt its constraint enforcement strength based on the convergence state and eliminate non-physical effects like positive pressure with positive gaps
Data Source
AI summary
An embodiment of the invention involves increasing the penalty stiffness within a finite element simulation increment, which is more accurate because it avoids following a solution path with significant non-physical penetrations. An embodiment of the present invention begins by determining a first value of a parameter used by a finite element simulation of a load increment. Next, a first solution of the finite element simulation is determined by performing Newton iterations using the first value of the parameter until a first convergence check is satisfied. Then, a second value the parameter is determined wherein the second value of the parameter is unequal to the first value of the parameter. Finally, a second solution of the finite element simulation is determined by continuing the Newton iterations using the second value of the parameter until a second convergence check is satisfied, the first convergence check being different than the second convergence check.