A cluster-based incremental potential approach for reduced order homogenization of bones

Area of Science:

• Computational Mechanics
• Biomaterials Science
• Finite Element Analysis

Background:

• Accurate computational modeling of bone tissue is crucial for understanding its mechanical behavior.
• Existing homogenization techniques can be computationally intensive, limiting their application.
• Generalized Standard Material (GSM) models offer a robust framework for describing material behavior, including bone.

Purpose of the Study:

• To develop a computationally efficient model order reduction (MOR) approach for bone homogenization.
• To extend the proper generalized decomposition (pGPD) based MOR (pRBMOR) to a clustered version (C-pRBMOR).
• To ensure compatibility with various GSM models for bone microstructure analysis.

Main Methods:

• Development of a cluster-based proper generalized decomposition based model order reduction (C-pRBMOR) approach.
• Extension of the pRBMOR method, based on a mixed incremental potential formulation, to a clustered version.
• Offline phase involving clustering analysis for spatial decomposition and space-time decomposition of microscopic plastic strain fields.
• Online phase utilizing a cluster-enhanced version of evolution equations for reduced variables derived from an incremental variational formulation.

Main Results:

• The C-pRBMOR approach achieves significant improvements in computational efficiency for bone homogenization.
• Demonstrated acceleration rates exceeding 10^4 compared to conventional Finite Element (FE) computations.
• Achieved acceleration rates over 10^3 compared to the original pRBMOR approach.
• Comparative study evaluated different clustering approaches and mode identification algorithms.

Conclusions:

• The C-pRBMOR method provides a highly effective and computationally efficient strategy for bone homogenization.
• The approach enables the solution of a reduced set of nonlinear equations, drastically cutting down computation time.
• This technique is compatible with a wide range of GSM models, enhancing its applicability in biomaterial research.