A variational homogenization approach applied to the multiscale analysis of the viscoelastic behavior of tendon fascicles

Carniel, Thiago André; Fancello, Eduardo Alberto

doi:10.1007/s00161-018-0714-y

Cited by 10 publications

(13 citation statements)

References 65 publications

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“…In order to consider fibers stiffer than the matrix, the material parameters assume the following values: μ = 12.50 MPa, κ = 50.00 MPa, k = 970.17 MPa, and α = 2.83. These values represent a common order of magnitude found in tendon fibers, i.e., between collagen fibrils and the surrounding matrices [5].…”

Section: The Constitutive Modelmentioning

confidence: 80%

“…The first one intends to mimic the wavy fibrous microstructures found in some types of scaffolds [20,22,32]. The second one is bioinspired by the helical arrangement of collagen fibers observed within tendon fascicles [5,18].…”

Section: Verification Of the Homogenization Proceduresmentioning

confidence: 99%

“…The numerical specimen shown in Fig. 2a, b is bioinspired by the microstructure of tendon fascicles [5]. In this case, helical fibers have crimp length of 99.3 μm and diameter of 4.6 μm, and they are distributed parallel to one another (see Fig.…”

Section: Verification Case 2: Helical Fibersmentioning

confidence: 99%

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A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

et al. 2020

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Most of the classical computational homogenization techniques at finite strains comprise strain-driven homogenization approaches, in the sense that all the components of the macroscopic deformation gradient F are known as the input data to the homogenization procedure, being the macroscopic stress tensor computed afterwards. On the other hand, a macroscopic uniaxial stress state renders to a multiscale boundary condition driven by the knowledge of both macroscopic conditions, i.e., stress and strain. In this regard, this manuscript presents a computational homogenization approach for the analyses of such mechanical conditions. Aiming further numerical investigations of soft tissues and tissue engineering scaffolds, materials whose microstructures are composed of wavy arrangements of fibers, are investigated. The proposed numerical approach is grounded within a variational framework based on representative volume elements (RVEs) and formulated at finite strains. Tensile tests performed on numerical specimens larger than the RVEs are proposed as reference solutions. The numerical results point out that the present homogenization approach is able to predict not only the macroscopic (homogenized) quantities but also the microscopic kinematic fields investigated. One of the major contributions of the present work is the possibility to investigate how the changes of the macroscopic volume depend on the strain distribution at the microscale under macroscopic uniaxial stress states, since this behavior is intrinsically related to the microstructural material response.

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Section: The Constitutive Modelmentioning

confidence: 80%

Section: Verification Of the Homogenization Proceduresmentioning

confidence: 99%

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A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

et al. 2020

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“…However, the precise magnitude, frequency, and duration of stimulation required for normal tendon homeostasis remain unknown. In addition, despite numerous in vivo , in vitro , and ex vivo studies on tendon mechanical properties and the development of prediction models ( Galloway et al, 2013 ; Fang and Lake, 2016 ; Herod et al, 2016 ; Thorpe and Screen, 2016 ; Thompson et al, 2017 ; Chen et al, 2018 ; Carniel and Fancello, 2019 ; Theodossiou and Schiele, 2019 ), the precise in vivo loading levels required to induce tendon repair are yet unspecified. In this regard, further understanding of the in vivo loading of tendons is vital to understand the mechanobiological stimuli required to induce anabolic or reduce catabolic activity ( Lavagnino et al, 2015 ).…”

Section: Optimization Of Type I Collagen-based Scaffolds For the Development Of Specific Tissue Substitutesmentioning

confidence: 99%

Mimicking the Hierarchical Organization of Natural Collagen: Toward the Development of Ideal Scaffolding Material for Tissue Regeneration

Salvatore

Gallo

Natali

et al. 2021

Front. Bioeng. Biotechnol.

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Biological materials found in living organisms, many of which are proteins, feature a complex hierarchical organization. Type I collagen, a fibrous structural protein ubiquitous in the mammalian body, provides a striking example of such a hierarchical material, with peculiar architectural features ranging from the amino acid sequence at the nanoscale (primary structure) up to the assembly of fibrils (quaternary structure) and fibers, with lengths of the order of microns. Collagen plays a dominant role in maintaining the biological and structural integrity of various tissues and organs, such as bone, skin, tendons, blood vessels, and cartilage. Thus, “artificial” collagen-based fibrous assemblies, endowed with appropriate structural properties, represent ideal substrates for the development of devices for tissue engineering applications. In recent years, with the ultimate goal of developing three-dimensional scaffolds with optimal bioactivity able to promote both regeneration and functional recovery of a damaged tissue, numerous studies focused on the capability to finely modulate the scaffold architecture at the microscale and the nanoscale in order to closely mimic the hierarchical features of the extracellular matrix and, in particular, the natural patterning of collagen. All of these studies clearly show that the accurate characterization of the collagen structure at the submolecular and supramolecular levels is pivotal to the understanding of the relationships between the nanostructural/microstructural properties of the fabricated scaffold and its macroscopic performance. Several studies also demonstrate that the selected processing, including any crosslinking and/or sterilization treatments, can strongly affect the architecture of collagen at various length scales. The aim of this review is to highlight the most recent findings on the development of collagen-based scaffolds with optimized properties for tissue engineering. The optimization of the scaffolds is particularly related to the modulation of the collagen architecture, which, in turn, impacts on the achieved bioactivity.

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“…proposed to obtain the equivalent properties of a microstructure such as the Surface average approach, volume average approach, force-based approach, Asymptotic Homogenization, among others. This process is widely used in different fields as piezoelectric actuators [156][157][158][159][160][161][162][163], biomedical applications [164][165][166], determine thermal and mechanical properties [167][168][169][170], and composite material in general.…”

Section: Homogenizationmentioning

confidence: 99%

An Effective Compatibility Scheme in Multiscale Topology Optimization of Structures

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A variational homogenization approach applied to the multiscale analysis of the viscoelastic behavior of tendon fascicles

Cited by 10 publications

References 65 publications

A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

Mimicking the Hierarchical Organization of Natural Collagen: Toward the Development of Ideal Scaffolding Material for Tissue Regeneration

An Effective Compatibility Scheme in Multiscale Topology Optimization of Structures

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