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

Deng, Jianwei; Xu, Guowang; Mei, Ying; Avril, Stéphane

doi:10.1016/j.advengsoft.2022.103343

Cited by 9 publications

(5 citation statements)

References 20 publications

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“…Finite element analysis has been widely used in clinical medicine [11][12][13], as it saves a lot of time as well as economic costs, and the results obtained are very close to the real experimental results, regardless of the spatial constraints of the site [14,15]. Thus, the FE model analysis is an effective alternative method for interventional stent studies.…”

Section: Introductionmentioning

confidence: 72%

Numerical Study of the Biomechanical Behavior of a 3D Printed Polymer Esophageal Stent in the Esophagus by BP Neural Network Algorithm

Wu,

Huang,

Liu

et al. 2024

CMES

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Esophageal disease is a common disorder of the digestive system that can severely affect the quality of life and prognosis of patients. Esophageal stenting is an effective treatment that has been widely used in clinical practice. However, esophageal stents of different types and parameters have varying adaptability and effectiveness for patients, and they need to be individually selected according to the patient's specific situation. The purpose of this study was to provide a reference for clinical doctors to choose suitable esophageal stents. We used 3D printing technology to fabricate esophageal stents with different ratios of thermoplastic polyurethane (TPU)/(Polyε-caprolactone) PCL polymer, and established an artificial neural network model that could predict the radial force of esophageal stents based on the content of TPU, PCL and print parameter. We selected three optimal ratios for mechanical performance tests and evaluated the biomechanical effects of different ratios of stents on esophageal implantation, swallowing, and stent migration processes through finite element numerical simulation and in vitro simulation tests. The results showed that different ratios of polymer stents had different mechanical properties, affecting the effectiveness of stent expansion treatment and the possibility of postoperative complications of stent implantation.

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Section: Introductionmentioning

confidence: 72%

Numerical Study of the Biomechanical Behavior of a 3D Printed Polymer Esophageal Stent in the Esophagus by BP Neural Network Algorithm

Wu,

Huang,

Liu

et al. 2024

CMES

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“…[1][2][3] Besides, some natural materials with similar properties can also be regarded as rubber-like materials, including biological tissues and organs. [4][5][6] Although these materials are able to deformed extremely under mechanical loading, they also suffer from fracture similar to other solids, especially the dynamic fracture within extreme deformation. 7,8 The numerical simulation of fracture behavior is an effective method to predict the crack propagation and structural failure for rubber-like polymeric materials, which is helpful for the structural safety assessment in engineering and of great significance in the fields of biology and medicine.…”

Section: Introductionmentioning

confidence: 99%

“…Rubber and rubber‐like polymeric materials (e.g., hydrogels and other elastomeric polymers) play an important role in industrial engineering because of their high extensibility and powerful reversible deformation abilities 1–3 . Besides, some natural materials with similar properties can also be regarded as rubber‐like materials, including biological tissues and organs 4–6 . Although these materials are able to deformed extremely under mechanical loading, they also suffer from fracture similar to other solids, especially the dynamic fracture within extreme deformation 7,8 .…”

Section: Introductionmentioning

confidence: 99%

A mixed three‐field total Lagrangian material point method for phase‐field fracture modeling of nearly incompressible rubber‐like solids

Zhang

et al. 2023

Numerical Meth Engineering

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The rubber‐like solids, as commonly observed materials in nature and engineering areas, often show high extensibility and weak compressibility, which lead to difficulties for modeling the fracture behavior of these materials. In this paper, we propose a mixed three‐field total Lagrangian material point method (TLMPM) to deal with the fracture of nearly incompressible rubber‐like solids. In this method, the phase‐field method combining with perturbed Lagrangian approach is developed to describe the fracture of nearly incompressible materials. Based on the Lagrangian equation, the governing equations of the displacement, pressure and phase fields are derived for the system considering dynamic effect. Then, a mixed three‐field TLMPM discrete formulation with a remapping strategy is then built to solve the problem involving large deformation. Besides, a staggered solving scheme with explicit time integration is developed for the three‐field problem. The accuracy and capabilities of the proposed method for dealing with the fracture of incompressible materials are demonstrated by modeling several quasi‐static and dynamic numerical problems and comparing the results with other numerical methods and experiments. Moreover, the applicability of the method is further proved by an out‐of‐plane tearing case.

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“…For instance, Avril et al applied the VFM to identify the hyperelastic behavior of artery walls in vitro (Avril et al, 2010;Kim et al, 2012). Since the law parameters cause nonlinear responses of the hyperelastic domain (Deng et al, 2023), the implemented VFM leads to a cost function by using the sum of the squared residual between internal and external virtual works and then minimizing this function with respect to constitutive objective parameters.…”

Section: Introductionmentioning

confidence: 99%

“…These con gurations includes magnetic resonance elastography (MRE) (Connesson et al, 2015) and laser doppler velocimetry (LDV) (Berry et al, 2014) for dynamic loading and displacement, magnetic resonance imaging for static loading (Avril et al, 2008), coherence tomography imaging (Zhang et al, 2017), and the study of vibrating thin plates (Giraudeau & Pierron, 2005). VFM is well-suited for FE implementation in nonlinear elasticity (Mei et al, 2021), leading to the identi cation of nonlinear hyperelastic solids (Deng et al, 2023). In order to contribute to VFM studies in soft tissue, we proposed a VFM-based inverse framework to identify the nonlinear hyperelastic properties of ventricular tissue, particularly in personalized LVs affected by ventricular geometric remodeling (Aissiou et al, 2016;Aissiou et al, 2013;Gamba, 2019).…”

Section: Introductionmentioning

confidence: 99%

Identification of hyperelastic properties of CMR patient-specific left ventricle by finite elements and virtual fields method

Ghafarinatanzi,

Perie,

Mahalatchimy

2023

Preprint

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Detection of left ventricle (LV) myocardial dysfunction after doxorubicin-based chemotherapy is investigated by determining myocardial stiffness, which is a potential clinical biomarker for the monitoring of heart failure (HF). The combination of cardiac magnetic resonance (CMR) imaging and the finite element method (FEM) was used to estimate anisotropic elastic stiffness in the LV. The myocardium also has a complex geometry with nonlinear hyperelastic properties leading to large deformation. Within the proposed framework, which generates the LV mesh and reconstructs the strain field from the existing CMR data, we apply the virtual field method (VFM) to determine the hyperelastic material parameters. Minimizing an energy-based objective function obtained from VFM identifies the unknown parameters coupled in nonlinear constitutive law considering passive myocardial behavior. While Full-field characterization using VFM is valuable for studying regular-shaped models, we propose applying this method when particularly looking into ventricular remodeling caused by doxorubicin, in the context of cardiotoxicity. In the cardiac diastolic phase, the estimated stiffness of VFM results with FEM validation is compared for a case study of leukemia cancer survivors separated into three groups.

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

Cited by 9 publications

References 20 publications

Numerical Study of the Biomechanical Behavior of a 3D Printed Polymer Esophageal Stent in the Esophagus by BP Neural Network Algorithm

Numerical Study of the Biomechanical Behavior of a 3D Printed Polymer Esophageal Stent in the Esophagus by BP Neural Network Algorithm

A mixed three‐field total Lagrangian material point method for phase‐field fracture modeling of nearly incompressible rubber‐like solids

Identification of hyperelastic properties of CMR patient-specific left ventricle by finite elements and virtual fields method

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