Bulging of inflated membranes made of fiber reinforced materials with different natural configurations

Topol, Heiko; Jha, Niraj Kumar; Demirkoparan, Hasan; Stoffel, Marcus; Merodio, J.

doi:10.1016/j.euromechsol.2022.104670

Cited by 14 publications

(16 citation statements)

References 59 publications

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“…In the membrane treatment, the radial normal component of the Cauchy stress tensor T is negligible, T rr → 0, so that the relation between the inflation pressure P , the radius R, the wall thickness H (with H ≪ R), and the strain energy density function W (λ θ , λ z ) takes the form [13]…”

Section: Inflation and Bulging Of Inflated Membranesmentioning

confidence: 99%

“…Different modeling techniques have been derived in order to account for the fiber dispersion. Here we apply the κ-model [12], which has been modified in order to account for dispersed fibers (see, e.g., Topol et al [13]). In this approach, in order to account for fiber dispersion, the invariants in (2) are replaced by…”

Section: Dispersed Fibersmentioning

confidence: 99%

“…In order to describe fiber pre-stretch, we employ an approach that has been described in [19] for swelling soft tissue constituents, which has then been generalized in [13]. The mapping tensor from the reference configuration Ω 0 into the fiber natural configuration Ω f for the n-th fiber family is now considered in the form…”

Section: Natural Configuration Of Pre-stretched Fibersmentioning

confidence: 99%

“…The article [13] studies bulging initiation for fibers that possess a natural fiber configuration that differs from that of the ground substance, where the fibers are taken to be dispersed. This dispersion is taken into account by a modification of the so-called κ-model.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Topol

Demirkoparan

Stoffel

et al. 2023

Proc Appl Math and Mech

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This article studies the inflation and bulging of fiber‐reinforced hyperelastic membranes. A neo‐Hookean model describes the mechanical behavior of the ground substance, and a relatively standard reinforcing model describes the mechanical behavior of fibers. The natural configuration of the constituents may differ, for example, because the fiber may be pre‐stretched in comparison to the natural configuration of the ground substance. Additionally, the fibers may be dispersed. Both the pre‐stretch and dispersion of the fibers have an effect on the formation of a bulge. The results explore how material stiffness ratios and fiber arrangements are involved in initiating bulging instabilities. The herein presented results may provide a contribution to understanding the formation of aneurysms.

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Section: Inflation and Bulging Of Inflated Membranesmentioning

confidence: 99%

Section: Dispersed Fibersmentioning

confidence: 99%

Section: Natural Configuration Of Pre-stretched Fibersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Topol

Demirkoparan

Stoffel

et al. 2023

Proc Appl Math and Mech

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“…Further invariants may be introduced that may also account for shearing, or to consider multiple fibers families and their interplay [19].…”

Section: F I G U R Ementioning

confidence: 99%

Modeling of mechanosensitive remodeling processes in collagen fibers

Topol,

Stoffel,

Markert

et al. 2023

Proc Appl Math and Mech

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A large number of biochemical processes such as enzymatic collagen degradation are involved in the remodeling of biological soft tissue constituents. Experiments have found that moderate strain may stabilize fibrillar collagen to enzymatic degradation. This strain stabilization is crucial for the homeostatic balance during the tissue remodeling process in healthy soft tissue. This article studies a material model applicable to the modeling of collagenous soft tissue. The ground substance properties are taken to be time‐independent, while the mechanical behavior of the fibers is modeled in terms of the Helmholtz free energy of the underlying protofibers along with a survival kernel that accounts for how the fiber density is dependent upon the deformation of the overall material. The examples illustrate the consequences of a compressively induced mechanical disruption to the homeostatic fiber remodeling, and they show the differences in the re‐approach to homeostasis when either the stress or strain remains constant.

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Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

Asghari,

Topol,

Lacalle

et al. 2024

Acta Mech

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In this article, we apply the sensitivity analysis method to capture the influence of various parameters on the inflation pressure, axial force, and the deformation for an inflated and axially stretched cylinder. The material consists of an isotropic ground substance material reinforced with fibers that undergo a continuous and mechano-sensitive remodeling process. The input parameters of the mechanical system are assumed to be distributed according to the uniform probability distribution function. In the sensitivity analysis, we apply the Sobol method to determine how the variations of input parameters affect the inflation as well as the axial force in the cylinder. Special attention is given to the fiber remodeling process associated with a homeostatic balance between the constant fiber creation process and the strain-stabilized fiber dissolution. The results may help to understand the importance of the effect of material parameter changes, for example, due to remodeling processes in the context of diseases or recovering processes, on the overall tissue behavior.

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Bulging of inflated membranes made of fiber reinforced materials with different natural configurations

Cited by 14 publications

References 59 publications

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

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

Modeling of mechanosensitive remodeling processes in collagen fibers

Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

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