Integrity basis of polyconvex invariants for modeling hyperelastic orthotropic materials — Application to the mechanical response of passive ventricular myocardium

Cai, Renye; Holweck, Frédéric; Feng, Zhi-Qiang; Peyraut, François

doi:10.1016/j.ijnonlinmec.2021.103713

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…By a suitable construction of polynomials of these invariants, constitutive models can be created which fulfill all of the former mentioned restrictions. By using polyconvex invariants instead of non-polyconvex invariants, constitutive models can be improved [11]. Subsequently, also finite strain finite element methods tailored to In the present work, two polyconvex constitutive models are introduced, which are both based on input convex neural networks (ICNNs), see [2], and formulated for hyperelastic, anisotropic material behavior and finite deformations.…”

Section: Introductionmentioning

confidence: 99%

Polyconvex anisotropic hyperelasticity with neural networks

Klein

Fernández

Martín

et al. 2022

Journal of the Mechanics and Physics of Solids

116

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Section: Introductionmentioning

confidence: 99%

Polyconvex anisotropic hyperelasticity with neural networks

Klein

Fernández

Martín

et al. 2022

Journal of the Mechanics and Physics of Solids

116

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“…However, to the best of our knowledge, the invariants introduced by Cai et al [20] have not yet been widely applied in practice. Currently, the application of this set of invariants is primarily seen in the simulation of orthotropic biological soft tissues, such as the responses of the peripheral arteries and the passive ventricular myocardium [20,23]. Given the incompressibility of the considered materials, how could the proposed SEF be incorporated into a finite element code?…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Hyperelastic Strain Energy Function for Carbon Fiber Woven Fabrics

Cai,

Zhang,

Lai

et al. 2024

Materials

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The present paper introduces an innovative strain energy function (SEF) for incompressible anisotropic fiber-reinforced materials. This SEF is specifically designed to understand the mechanical behavior of carbon fiber-woven fabric. The considered model combines polyconvex invariants forming an integrity basisin polynomial form, which is inspired by the application of Noether’s theorem. A single solution can be obtained during the identification because of the relationship between the SEF we have constructed and the material parameters, which are linearly dependent. The six material parameters were precisely determined through a comparison between the closed-form solutions from our model and the corresponding tensile experimental data with different stretching ratios, with determination coefficients consistently reaching a remarkable value of 0.99. When considering only uniaxial tensile tests, our model can be simplified from a quadratic polynomial to a linear polynomial, thereby reducing the number of material parameters required from six to four, while the fidelity of the model’s predictive accuracy remains unaltered. The comparison between the results of numerical calculations and experiments proves the efficiency and accuracy of the method.

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“…By a suitable construction of polynomials of these invariants, constitutive models can be created which fulfill all of the former mentioned restrictions. By using polyconvex invariants instead of non-polyconvex invariants, constitutive models can be improved [9]. Subsequently, also finite strain finite element methods tailored to the discretization of polyconvex material models were developed [8,62].…”

Section: Introductionmentioning

confidence: 99%

Polyconvex anisotropic hyperelasticity with neural networks

Klein,

Fernández,

Martin

et al. 2021

Preprint

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In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. Thus, in particular the second model presents a highly flexible constitutive modeling approach, that leads to a mathematically well-posed problem.

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Integrity basis of polyconvex invariants for modeling hyperelastic orthotropic materials — Application to the mechanical response of passive ventricular myocardium

Cited by 6 publications

References 13 publications

Polyconvex anisotropic hyperelasticity with neural networks

Polyconvex anisotropic hyperelasticity with neural networks

Anisotropic Hyperelastic Strain Energy Function for Carbon Fiber Woven Fabrics

Polyconvex anisotropic hyperelasticity with neural networks

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