Strain-dependent internal parameters in hyperelastic biological materials

Giantesio, Giulia; Musesti, Alessandro

doi:10.1016/j.ijnonlinmec.2017.06.012

Cited by 5 publications

(10 citation statements)

References 20 publications

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“…Instead of employing the active-stress approach for modeling a skeletal muscle's active behavior, an active-strain approach has been used (e.g., Ehret et al, 2011 ; Hernández-Gascón et al, 2013 ; Giantesio and Musesti, 2017 ; Seydewitz et al, 2019 ). For the active-strain approach, one assumes that the deformation gradient tensor F can be multiplicatively split into an active part F a and an elastic contribution F e , i.e.,…”

Section: Methodsmentioning

confidence: 99%

“…e.g., McCulloch et al, 1992 ; Martins et al, 1998 ; Nash and Hunter, 2000 ; Blemker et al, 2005 ; Röhrle et al, 2008 ; Heidlauf et al, 2016 ; Schmid et al, 2019 ), the active-strain approach employs a multiplicative decomposition of the deformation gradient tensor (cf. e.g., Kondaurov and Nikitin, 1987 ; Taber and Perucchio, 2000 ; Nardinocchi and Teresi, 2007 ; Ambrosi et al, 2011a ; Ehret et al, 2011 ; Stålhand et al, 2011 ; Hernández-Gascón et al, 2013 ; Giantesio and Musesti, 2017 ; Seydewitz et al, 2019 ) to incorporate the muscles' active behavior. Any continuum-mechanical formulation, however, is (almost) worthless without appropriate experimental data that characterize the mechanical behavior of the material itself and which is essential for accurately calibrating a specific constitutive model.…”

Section: Introductionmentioning

confidence: 99%

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A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue

2021

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The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue

2021

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“…As far as the passive part is concerned, following again the model given in [4] and [7], we use the exponential strain energy density function (here m is the direction of the muscular fibers). Notice that in the incompressible case I p and K p can be expressed in terms of the usual invariants as…”

Section: A More Complex Energy Related To Skeletal Muscle Tissuementioning

confidence: 99%

“…In this case the mathematical properties of W strain can change considerably and F a does not represent anymore the local distortion of the material that maps the reference configuration to the relaxed one. Moreover, the expression of the stress tensor is much more involved, see [7]: (28)…”

Section: A More Complex Energy Related To Skeletal Muscle Tissuementioning

confidence: 99%

A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials

Giantesio

Musesti

Riccobelli

2018

J Elast

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Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an additive stress Pact in the active stress case and a multiplicative strain Fa in the active strain one. Aim of this paper is the comparison between the two approaches on simple shears.Considering an incompressible and transversely isotropic material, we design constitutive relations for Pact and Fa so that they produce the same results for a uniaxial deformation along the symmetry axis. We then study the two approaches in the case of a simple shear deformation. In a hyperelastic setting, we show that the two approaches produce different stress components along a simple shear, unless some necessary conditions on the strain energy density are fulfilled. However, such conditions are very restrictive and rule out the usual elastic strain energy functionals. Active stress and active strain therefore produce different results in shear, even if they both fit uniaxial data.Our results show that experimental data on the stress-stretch response on uniaxial deformations are not enough to establish which activation approach can capture better the mechanics of active materials. We conclude that other types of deformations, beyond the uniaxial one, should be taken into consideration in the modeling of such materials. Date

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“…One of the novelties of the present paper is to give an active model which is completely hyperelastic, in the sense that the active stress can be computed as the derivative with respect to the deformation gradient of a suitable strain energy function. See also [4] for a detailed discussion on this issue.…”

Section: Introductionmentioning

confidence: 99%

Loss of mass and performance in skeletal muscle tissue: a continuum model

Giantesio

Marzocchi

Musesti

2018

Communications in Applied and Industrial Mathematics

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We present a continuum hyperelastic model which describes the mechanical response of a skeletal muscle tissue when its strength and mass are reduced by aging. Such a reduction is typical of a geriatric syndrome called sarcopenia. The passive behavior of the material is described by a hyperelastic, polyconvex, transversely isotropic strain energy function, and the activation of the muscle is modeled by the so called active strain approach. The loss of ability of activating of an elder muscle is then obtained by lowering of some percentage the active part of the stress, while the loss of mass is modeled through a multiplicative decomposition of the deformation gradient. The obtained stress-strain relations are graphically represented and discussed in order to study some of the effects of sarcopenia.

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Strain-dependent internal parameters in hyperelastic biological materials

Cited by 5 publications

References 20 publications

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue

A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials

Loss of mass and performance in skeletal muscle tissue: a continuum model

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