Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids

Cheviakov, Alexei F.; Ganghoffer, Jean‐François; Jean, S. St.

doi:10.1016/j.ijnonlinmec.2015.01.006

Cited by 21 publications

(20 citation statements)

References 44 publications

(71 reference statements)

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“…Thus, further developments are expected considering composite fiber-reinforced models and the interaction between the steel bars and the concrete based on suitable homogenizations (see e.g. [1,50,34,16,27,42]).…”

Section: Discussionmentioning

confidence: 99%

Multi-scale concrete model with rate-dependent internal friction

Giorgio

Scerrato

2016

European Journal of Environmental and Civil Engineering

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International audienceIn this paper, a micromorphic, non-linear 3D model aiming to describe internal friction phenomena in concrete is considered. A reduced two-degrees-of-freedom model is employed for the sake of easy handling to explain dissipative loops which have been observed in some concrete specimens tested under cyclic uniaxial compression loading with different frequencies and having various amplitudes but never inducing large strains. As (linear or non-linear) viscoelastic models do not seem suitable to describe neither qualitatively nor quantitatively the measured dissipation loops, we propose to introduce a multi-scale micro-mechanism of Coulomb-type internal dissi-pation associated to the relative motion of the faces of the micro-cracks present in the material and to the asperities inside the micro-cracks. We finally present numerical simulations showing that the proposed model is suitable to describe some of the available experimental evidence

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Section: Discussionmentioning

confidence: 99%

Multi-scale concrete model with rate-dependent internal friction

Giorgio

Scerrato

2016

European Journal of Environmental and Civil Engineering

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“…. , I 9 are pseudo-invariants involving fiber direction vectors (for details, see, e.g., [62,63], and references therein). A wide class of materials is described using Mooney-Rivlin isotropic energy part and the standard reinforcement anisotropic model [63]:…”

Section: Application: Construction Of the Master Curve Of A Dry Polyamentioning

confidence: 99%

“…In [63], it has been shown that for a shear wave propagating in X 1 -direction, i.e., with finite displacements G(X 1 , t) arising from the incompressibility-compatible ansatz…”

Section: Application: Construction Of the Master Curve Of A Dry Polyamentioning

confidence: 99%

Symmetry analysis and equivalence transformations for the construction and reduction of constitutive models

Ganghoffer

Rahouadj

Cheviakov

2021

Adv. Model. and Simul. in Eng. Sci.

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A methodology based on Lie analysis is proposed to investigate the mechanical behavior of materials exhibiting experimental master curves. It is based on the idea that the mechanical response of materials is associated with hidden symmetries reflected in the form of the energy functional and the dissipation potential leading to constitutive laws written in the framework of the thermodynamics of irreversible processes. In constitutive modeling, symmetry analysis lets one formulate the response of a material in terms of so-called master curves, and construct rheological models based on a limited number of measurements. The application of symmetry methods leads to model reduction in a double sense: in treating large amounts number of measurements data to reduce them in a form exploitable for the construction of constitutive models, and by exploiting equivalence transformations extending point symmetries to efficiently reduce the number of significant parameters, and thus the computational cost of solving boundary value problems (BVPs). The symmetry framework and related conservation law analysis provide invariance properties of the constitutive models, allowing to predict the influence of a variation of the model parameters on the material response or on the solution of BVPs posed over spatial domains. The first part of the paper is devoted to the presentation of the general methodology proposed in this contribution. Examples of construction of rheological models based on experimental data are given for setting up a reduced model of the uniaxial creep and rupture behaviour of a Chrome-Molybdenum alloy (9Cr1Mo) at different temperatures and stress levels. Constitutive equations for creep and rupture master responses are identified for this alloy, and validated based on experimental data. Equivalence transformations are exemplified in the context of parameter reduction in fully nonlinear anisotropic fiber-reinforced elastic solids.

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“…. , I 9 are pseudo-invariants involving fiber direction vectors (for details, see, e.g., [13,14], and references therein).…”

Section: Equivalence Transformations Of a Family Of Nonlinear Equatiomentioning

confidence: 99%

Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models

Cheviakov

2017

Computer Physics Communications

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An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software package GeM for Maple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. First computational example of a generalized equivalence transformation where the transformation of the dependent variable involves the arbitrary constitutive function is presented.As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelasic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements.The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements.

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Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids

Cited by 21 publications

References 44 publications

Multi-scale concrete model with rate-dependent internal friction

Multi-scale concrete model with rate-dependent internal friction

Symmetry analysis and equivalence transformations for the construction and reduction of constitutive models

Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models

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