Bifurcation of fiber reinforced inflated membranes with different natural configurations of the constituents

Topol, Heiko; Demirkoparan, Hasan; Stoffel, Marcus; Markert, Bernd; Merodio, J.

doi:10.1002/pamm.202200004

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Some works have been accomplished regarding fiber-reinforcement materials models in recent decades. (for instance [43], [89], [97], [98], [112], [113], [114], [116], [137], [139], [159], and [177]). In this chapter, the sensitivity analysis (SA) on input parameters in the fiber-reinforced materials models in the presence of internal pressure has been considered in two types natural configurations: the fiber natural configuration remains constant throughout the considered deformation, and when the fiber natural configuration varies when the deformation of the fibers.…”

Section: Discussionmentioning

confidence: 99%

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Asghari

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This thesis deals with applying the sensitivity analysis methods that consideration of different functions on the non-linear elastic constitutive models in particular a circular cylindrical tube with radial and circumferential residual stresses and in some different types of pressure-inflation relation in a pressurized and axially stretched tube.Considering the inflation of hyperelastic cylinders in the framework of non-linear elastic constitutive models imposed to an axial stretch and torsion in the presence of residual stress has been done in this work. The constitutive relation of the material depends on various parameters such as the cylinder geometry, the different loading parameters, the prescribed stretches, and the magnitude of the residual stresses. Applying sensitivity analysis methods with attention to a statistical approach determined how the variations of the input variables affect the output variables.After reviewing on applied sensitivity analysis and recapping on basic contents of the non-linear elastic constitutive models, through the implementation of Sobol and the Fourier Amplitude Sensitivity Test (FAST) methods, the most important parameters of the system under the applied pressure and axial force such as the thickness of the tube or axial and azimuthal stretch are gained in the first part of the thesis. Then, the complicated form of the mechanical problem is expressed which is the problem of mixed extension, inflation, and torsion of a circular cylindrical tube in the presence of residual stress which the input parameters in the material model are distributed according to three probability distribution methods, namely the uniform, the gamma, and the normal distribution. In other words, the relation between various parameters as they relate to the inflation pressure, the moment, and the reduced axial force is studied with the help of two sensitivity analysis methods, namely, the Sobol method and FAST method. Both methods found their application in relatively complex models, especially when these models show a non-linear and non-monotonic behaviour. After that, the pressure-inflation relation in a pressurized and axially stretched tube is studied in fiber-reinforcement materials with different natural configurations. The material consists of an isotropic ground substance that is reinforced by two families of fibers. The natural configuration of the fibers may differ from that of the ground substance and the fibers are taken to be dispersed. The sensitivity analysis is applied by means of statistical simulation in the "R" program to determine how the uncertainties of the cylinder stretch, the fiber dispersion, and the fiber natural configuration affect the required inflation pressure. The V implementation of the Sobol and FAST methods allows us to account for the interplay of different parameters and to identify the most influential parameters in the pressure-inflation relation.

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Section: Discussionmentioning

confidence: 99%

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Asghari

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Instabilities of an inflated and extended doubly fiber-reinforced cylindrical membrane under damage processes and different natural configurations of its constituents with application to abnormal artery dilation

Topol,

Nazari,

Stoffel

et al. 2024

Thin-Walled Structures

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On the inflation, bulging/necking bifurcation and post-bifurcation of a cylindrical membrane under limited extensibility of its constituents

Topol,

Font,

Melnikov

et al. 2024

Mathematics and Mechanics of Solids

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We consider the bifurcation and post-bifurcation of an extended and inflated circular cylindrical membrane under limited extensibility of its constituents. First, for illustration of the limited extensibility effect, a membrane made of the (isotropic) Gent model is briefly analyzed. Second, the membrane is considered to be made of an isotropic ground substance reinforced with fibers symmetrically arranged in two helically distributed families which are mechanically equivalent. The mechanical behavior of the fibers in a similar way to the (isotropic) Gent model is taken to reflect fiber limited extensibility. In particular, the materials under consideration are NH models augmented with two functions called reinforcing models, each one accounting for unidirectional reinforcement. For a specific material, since both families are mechanically equivalent, the reinforcing models are equal. The nature of the anisotropy considered, i.e., the reinforcing model, can depend only on the stretch in the fiber direction or can depend on the fiber stretch and also can have an influence on the shear response of the material (i.e., it also captures shearing in the fiber direction). The limitation associated with the material anisotropic deformability as well as the arrangement of the material constituents is discussed with respect to the initiation of bulging and necking for the membrane. The subsequent consequences for configurations in equilibrium during post-bifurcation are also studied in detail and a variety of results are given in terms of the limited extensibility (deformability) of the fibers as well as their mechanical response and arrangement (fiber winding angle).

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Bifurcation of fiber reinforced inflated membranes with different natural configurations of the constituents

Cited by 3 publications

References 23 publications

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Instabilities of an inflated and extended doubly fiber-reinforced cylindrical membrane under damage processes and different natural configurations of its constituents with application to abnormal artery dilation

On the inflation, bulging/necking bifurcation and post-bifurcation of a cylindrical membrane under limited extensibility of its constituents

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