Enhancing Biomechanical Simulations Based on a Posteriori Error Estimates: The Potential of Dual-Weighted...

Area of Science:

• Computational mechanics
• Biomechanics
• Finite element analysis

Background:

• The finite-element method (FEM) is crucial for solving engineering problems governed by partial differential equations.
• Quantifying discretization error using a posteriori error estimates is standard practice in FEM.
• The application and relevance of these error estimates in biomechanics, particularly for large-strain soft tissues, remain underexplored.

Purpose of the Study:

• To implement and validate a posteriori error estimates for biomechanical applications using the dual-weighted residual (DWR) technique.
• To tailor DWR for user-defined quantities of interest in complex, nonlinear soft tissue simulations.
• To leverage automatic differentiation for generic error estimation across various models and constitutive laws.

Main Methods:

• Implementation of the dual-weighted residual (DWR) technique for a posteriori error estimation.
• Adaptation of DWR for three-dimensional geometries and nonlinear hyperelastic soft tissue models.
• Utilization of automatic differentiation in finite-element software for generic error computation.

Main Results:

• Validation of the DWR methodology using experimental data from silicone samples.
• Demonstration of the method's applicability to patient-specific biomechanical computations.
• Successful computation of error estimates for a human heel pressure ulcer model.

Conclusions:

• The proposed DWR-based a posteriori error estimation is effective for nonlinear biomechanical problems.
• This technique enhances the accuracy and reliability of finite-element analysis in soft tissue mechanics.
• The approach is suitable for both general biomechanical modeling and patient-specific clinical applications.