General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity

Mei, Ying; Gao, Xu; Zimmerman, Brandon; Nguyen, Thao D.; Avril, Stéphane

doi:10.1007/s10659-021-09842-8

Cited by 15 publications

(11 citation statements)

References 49 publications

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“…With the increasing number of unknown material parameters, the total number of virtual fields should be increased accordingly to ensure the uniqueness of the inverse solution. To address this issue, RE-VFM method was firstly proposed in [14] and can be used to solve for the regional material properties without introducing artificial virtual fields. However, the virtual fields in [14] are obtained by solving another constructed forward problem, which requires more time.…”

Section: Discussionmentioning

confidence: 99%

“…To address this issue, RE-VFM method was firstly proposed in [14] and can be used to solve for the regional material properties without introducing artificial virtual fields. However, the virtual fields in [14] are obtained by solving another constructed forward problem, which requires more time.…”

Section: Discussionmentioning

confidence: 99%

“…It is assumed that the boundaries of these regions are known when the VFM is applied. Accordingly, only the biomechanical property of each region needs to be determined [13], [14]. However, if the boundary of each homogeneous region is unknown, the inverse problem becomes highly challenging to solve due to the large number of unknown elastic parameters.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

Deng

Mei

et al. 2023

Advances in Engineering Software

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

Deng

Mei

et al. 2023

Advances in Engineering Software

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“…A DNN serves as a regularizer so that the material parameter distribution will not be irregular (Table 8, Table 9, and Figure 4). The Virtual Fields Method (VFM) [35] has been proposed for heterogeneous material parameter identification, and it needs to repeatedly solve the forward problem given an estimation of the material parameters, which is not needed by our method.…”

Section: Discussionmentioning

confidence: 99%

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications for Biomechanical Analysis of Human Aorta

Liang

Liu

Elefteriades

et al. 2023

Preprint

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Motivation: Patient-specific finite element analysis (FEA) has the potential to aid in the prognosis of cardiovascular diseases by providing accurate stress and deformation analysis in various scenarios. It is known that patient-specific FEA is time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) techniques, including deep neural networks (DNNs), have been developed to construct fast FEA surrogates. However, due to the data-driven nature of these ML models, they may not generalize well on new data, leading to unacceptable errors. Methods: We propose a synergistic integration of DNNs and finite element method (FEM) to overcome each other's limitations. We demonstrated this novel integrative strategy in forward and inverse problems. For the forward problem, we developed DNNs using state-of-the-art architectures, and DNN outputs were then refined by FEM to ensure accuracy. For the inverse problem of heterogeneous material parameter identification, our method employs a DNN as regularization for the inverse analysis process to avoid erroneous material parameter distribution. Results: We tested our methods on biomechanical analysis of the human aorta. For the forward problem, the DNN-only models yielded acceptable stress errors in majority of test cases; yet, for some test cases that could be out of the training distribution (OOD), the peak stress errors were larger than 50%. The DNN-FEM integration eliminated the large errors for these OOD cases. Moreover, the DNN-FEM integration was magnitudes faster than the FEM-only approach. For the inverse problem, the FEM-only inverse method led to errors larger than 50%, and our DNN-FEM integration significantly improved performance on the inverse problem with errors less than 1%.

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“…The governing physics-based model in ultrasound imaging modality is introduced by PDEs, as the system equilibrium equations, which unveil the relationship between speckle displacement and tissue elasticity . To have a simplified representation of the governing PDEs, finite element methods (FEM) [15] is employed to discretize the medium cross-section. The resulting global stiffness equation of ultrasound elastography problem can be represented by [9]:…”

Section: Forward Model Formulationmentioning

confidence: 99%

Combining physics-based modeling and deep learning for ultrasound elastography

Mohammadi¹,

Doyley²,

Çetin³

2021

Preprint

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Ultrasound elasticity images which enable the visualization of quantitative maps of tissue stiffness can be reconstructed by solving an inverse problem. Classical model-based approaches for ultrasound elastography use deterministic finite element methods (FEMs) to incorporate the governing physical laws resulting in poor performance in noisy conditions. Moreover, these approaches utilize fixed regularizers for various tissue patterns while appropriate data-adaptive priors might be required for capturing the complex spatial elasticity distribution. In this regard, we propose a joint model-based and learning-based framework for estimating the elasticity distribution by solving a regularized optimization problem. We present an integrated objective function composed of a statistical physics-based forward model and a data-driven regularizer to leverage deep neural networks for learning the underlying elasticity prior. This constrained optimization problem is solved using the gradient descent (GD) method and the gradient of regularizer is simply replaced by the residual of the trained denoiser network for having an explicit objective function with reduced computation time.

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General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity

Cited by 15 publications

References 49 publications

FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications for Biomechanical Analysis of Human Aorta

Combining physics-based modeling and deep learning for ultrasound elastography

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