Physically based strain invariant set for materials exhibiting transversely isotropic behavior

Criscione, John C.; Douglas, A. S.; Hunter, William C.

doi:10.1016/s0022-5096(00)00047-8

Cited by 126 publications

(91 citation statements)

References 6 publications

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“…The parameters for shear strains (B 1 and B 2 ) were based on a new strain invariant set for transverse isotropy proposed by Criscione et al 13 The functional forms for W 1 and W 2 adopted for our model are as follows:…”

Section: Constitutive Modelmentioning

confidence: 99%

Three-Dimensional Representation of Complex Muscle Architectures and Geometries

2005

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Abstract-Almost all computer models of the musculoskeletal system represent muscle geometry using a series of line segments. This simplification (i) limits the ability of models to accurately represent the paths of muscles with complex geometry and (ii) assumes that moment arms are equivalent for all fibers within a muscle (or muscle compartment). The goal of this work was to develop and evaluate a new method for creating three-dimensional (3D) finite-element models that represent complex muscle geometry and the variation in moment arms across fibers within a muscle. We created 3D models of the psoas, iliacus, gluteus maximus, and gluteus medius muscles from magnetic resonance (MR) images. Peak fiber moment arms varied substantially among fibers within each muscle (e.g., for the psoas the peak fiber hip flexion moment arms varied from 2 to 3 cm, and for the gluteus maximus the peak fiber hip extension moment arms varied from 1 to 7 cm). Moment arms from the literature were generally within the range of fiber moment arms predicted by the 3D models. The models accurately predicted changes in muscle surface geometry over a 55• range of hip flexion, as compared to changes in shape predicted from MR images (average errors between the model and measured surfaces were between 1.7 and 5.2 mm). This new framework for representing muscle will enhance the accuracy of computer models of the musculoskeletal system.

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Section: Constitutive Modelmentioning

confidence: 99%

Three-Dimensional Representation of Complex Muscle Architectures and Geometries

2005

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“…It is a straightforward matter to extend any, existing, transversely isotropic, integrity basis (e.g., Criscione et al 2001) into an equivalent basis that accounts for splay by applying an appropriate mapping. For example, if the classic integrity basis I I ; I II ; I III ; f I IV ; I V g maps into some other basis b I ; b II ; b III ; b IV ; b V f g by a known mapping, then using I I ; I II ; I III ; I hIVi ; I hVi È É in place of I I ; I II ; I III ; I IV ; I V f gwill produce b hIi ; b hIIi ; n b hIIIi ; b hIVi ; b hVi g for its splay invariants.…”

Section: Elasticitymentioning

confidence: 99%

Invariant formulation for dispersed transverse isotropy in aortic heart valves

Freed

Einstein

Veselý

2005

Biomech Model Mechanobiol

115

100

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Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is derived from a novel closed-form 'splay invariant' that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no reformulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis, demonstrated by modeling a bioprosthetic heart valve.

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“…Criscione et al [2][3][4] have been developing invariants for isotropic and transversely isotropic solids which are physically based and yield nearly orthogonal response. These features help with physical interpretation of the strain measures and with identification of the material response functions.…”

Section: Introductionmentioning

confidence: 99%

Physically Based Invariants for Nonlinear Elastic Orthotropic Solids

Rubin

Jabareen

2007

J Elasticity

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Hydrostatic loading causes an isotropic elastic solid to be in a state of pure dilatation with no distortion relative to its unstressed reference configuration. Similarly, hydrostatic loading causes a general orthotropic solid to be distorted relative to its unstressed reference configuration. This paper introduces physically based invariants for orthotropic nonlinear elastic solids which are measures of distortions that cause deviatoric Cauchy stress. Specifically, these invariants allow for the modeling of the distortion in a hydrostatic state of stress independently of the form of the strain energy function. Consequently, use of these invariants may lead to simpler forms of the strain energy function which adequately model specific orthotropic solids.

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Physically based strain invariant set for materials exhibiting transversely isotropic behavior

Cited by 126 publications

References 6 publications

Three-Dimensional Representation of Complex Muscle Architectures and Geometries

Three-Dimensional Representation of Complex Muscle Architectures and Geometries

Invariant formulation for dispersed transverse isotropy in aortic heart valves

Physically Based Invariants for Nonlinear Elastic Orthotropic Solids

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