An In Silico-Based Investigation on Anisotropic Hyperelastic Constitutive Models for Soft Biological Tissues

Dal, Hüsnü; Açan, Alp Kağan; Durcan, Ciara; Hossain, Mokarram

doi:10.1007/s11831-023-09956-3

Cited by 8 publications

(3 citation statements)

References 91 publications

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“…The lack of sufficient understanding and the difficulty in selecting the appropriate model resulted in tens of papers comparing the predictive power of different models when parameters are characterized by a multitude of approaches. Some well-known comparative studies are [ 10 , 12 , 14 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ].…”

Section: Introductionmentioning

confidence: 99%

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers

Moreno-Corrales,

Sanz-Gómez,

Benítez

et al. 2024

Materials

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The formulation of the entropic statistical theory and the related neo-Hookean model has been a major advance in the modeling of rubber-like materials, but the failure to explain some experimental observations such as the slope in Mooney plots resulted in hundreds of micromechanical and phenomenological models. The origin of the difficulties, the reason for the apparent need for the second invariant, and the reason for the relative success of models based on the Valanis–Landel decomposition have been recently explained. From that insight, a new micro–macro chain stretch connection using the stretch tensor (instead of the right Cauchy–Green deformation tensor) has been proposed and supported both theoretically and from experimental data. A simple three-parameter model using this connection has been suggested. The purpose of this work is to provide further insight into the model, to provide an analytical expression for the Gaussian contribution, and to provide a simple procedure to obtain the parameters from a tensile test using the Mooney space or the Mooney–Rivlin constants. From different papers, a wide variety of experimental tests on different materials and loading conditions have been selected to demonstrate that the simple model calibrated only from a tensile test provides accurate predictions for a wide variety of elastomers under different deformation levels and multiaxial patterns.

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Section: Introductionmentioning

confidence: 99%

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers

Moreno-Corrales,

Sanz-Gómez,

Benítez

et al. 2024

Materials

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“…Therefore, when analyzing the mechanical behavior of liver tissue under loads, it is essential to adapt equilibrium equations for its incompressibility and ensure coherence with the load system and internally generated stresses [4,5]. There is a limitation in finding a solution because the relationship between stresses and deformations in biological tissues is unknown.…”

Section: Introductionmentioning

confidence: 99%

Fractal Analysis and FEM Assessment of Soft Tissue Affected by Fibrosis

Prieto-Vázquez,

Cuautle-Estrada,

Grave-Capistrán

et al. 2023

Fractal Fract

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This research shows an image processing method to determine the liver tissue’s mechanical behavior under physiological damage caused by fibrosis pathology. The proposed method consists of using a liver tissue CAD/CAE model obtained from a tomography of the human abdomen, where the diaphragmatic surface of this tissue is compressed by a moving flat surface. For this work, two tools were created—the first to analyze the deformations and the second to analyze the displacements of the liver tissue. Gibbon and MATLAB® were used for numerical analysis with the FEBio computer program. Although deformation in the scenario can be treated as an orthogonal coordinate system, the relationship between the total change in height (measured) and the deformation was obtained. The outcomes show liver tissue behavior as a hyperelastic model; the Mooney–Rivlin mathematical characterization model was proposed in this case. Another method to determine the level of physiological damage caused by fibrosis is fractal analysis. This work used the Hausdorff fractal dimension (HFD) method to calculate and analyze the 2D topological surface.

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“…These tissues exhibit highly nonlinear mechanical responses under large deformations. The literature is replete with efforts to capture their nonlinear behavior, which can be broadly categorized into three approaches: those based on Green-Lagrange strain components, principal invariants, and fiber dispersion [1].…”

Section: Introductionmentioning

confidence: 99%

A data‐driven constitutive model for soft biological tissues

Açan,

Tikenoğullari,

Dal

2023

Proc Appl Math and Mech

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Constitutive modeling of soft biological tissues is crucial for biomedical simulations and a deep understanding of tissue mechanics. Classical constitutive models have a fixed mathematical expression, however, the microstructure and the corresponding macro‐mechanical response of different tissue types can vary significantly. A model that works for one tissue may not work for another kind of tissue, and choosing the right model may become challenging. To solve this issue, this study introduces a new data‐driven approach to creating a unified model for predicting the mechanical response of various tissue classes. The proposed model is based on B‐Spline approximations and assumes the strain energy function can be divided into volumetric, isotropic, and anisotropic components. The B‐Spline ansatz replaces partial derivatives of free energy energy function with respect to invariants with control points and polynomial degree, and allows the use of existing dispersion models. The model adapts its control point values to reduce the error between data and prediction until a threshold is reached, and is thermodynamically consistent through the use of optimization constraints. The model is demonstrated on various biological tissues, showing excellent fitting capabilities with a minimal number of control points. The outcome is a generic framework that can model any tissue given the data from experiments and imaging techniques.

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An In Silico-Based Investigation on Anisotropic Hyperelastic Constitutive Models for Soft Biological Tissues

Cited by 8 publications

References 91 publications

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers

Fractal Analysis and FEM Assessment of Soft Tissue Affected by Fibrosis

A data‐driven constitutive model for soft biological tissues

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