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Description
The accurate modeling of soft tissue material behavior remains a challenging task in biomechanics due to its complex, non-linear, and anisotropic characteristics. Traditional methods, such as Finite Element Methods (FEM), while reliable, demand significant computational resources and expert knowledge for implementing physical laws. Machine Learning (ML) techniques, particularly Neural Networks (NN), offer an innovative alternative by automating data-driven tasks, enabling more efficient and scalable modeling frameworks.
This work focuses on evaluating two state-of-the-art ML architectures—Neural Ordinary Differential Equations (N-ODEs) and Unconstrained Monotonic Neural Networks (UMNNs)—for simulating hyperelastic responses in soft tissue materials. Both architectures were implemented in Julia and benchmarked using experimental stress-deformation data. The results indicate that while both approaches deliver high accuracy, UMNNs outperform N-ODEs in computational efficiency and numerical stability. The intrinsic monotonicity of UMNNs allows for robust convergence, even in cases where N-ODEs exhibit instability.
Beyond hyperelastic modeling, this study extends the ML framework to include deteriorated material behavior, focusing on the softening effects observed in one-dimensional fibrous structures. By integrating a data-driven deterioration function into the ML models, the framework accurately captures non-monotonic stress-deformation responses. The deterioration function, validated against experimental data, effectively simulates dissipative material behaviors. This extension enables modeling of both the elastic and deteriorative phases of material response, providing a comprehensive solution for biomechanical simulations.
Key findings emphasize the versatility and efficiency of UMNNs as a computational tool for material modeling. Compared to traditional methods, the ML-based approach demonstrates superior scalability, adaptability, and performance, offering a promising direction for future research in computational biomechanics. By bridging advanced ML techniques with classical continuum mechanics and FEM, this thesis contributes to the development of innovative, data-driven solutions for simulating the complex behavior of soft tissue materials. Apart from this, an artificial deterioration data set shows, that the Machine Learning model does not necessarily need to find the exact virtual elastic representation or deterioration parameters as an intermediate step in order to reach good convergence in the actual response. The question, as to how important the uniqueness of these quantities is to the actual simulation is left for further study.
