Strain induced shape formation in fibred cylindrical tubes

Nardinocchi, Paola; Teresi, Luciano; Varano, Valerio

doi:10.1016/j.jmps.2012.04.010

Cited by 14 publications

(17 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…a special case of a model introduced in [45], where the constant μ > 0 is the shear modulus in the configuration B r in the absence of residual stress, and the final term is consistent with the requirements of the dependence of the energy function on the residual stress highlighted in [9,45]. By substituting equation ( 43) into the constitutive law (38), the Cauchy stress is found to have the form…”

Section: Illustration Of Approach 3: Growth Of a Residually Stressed Materialsmentioning

confidence: 53%

“…Instead, the existing models of anisotropic growth were mainly based on macroscopic anisotropy of material [33,36]. These macroscopic anisotropic models cannot always encode anisotropic growth that is postulated to have different types of regulation in different directions [4,49], although there are some instances where this is examined; see [38] for an example relevant to a specific class of distortions in cylinders where the interplay between inhomogeneities and anisotropy is addressed. One example of the complexity of anisotropy is the helical architecture of fibres where material symmetry alone may not suffice to account for the anisotropy of growth [12,24].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

Huang

Ogden

Penta

2021

J Elast

View full text Add to dashboard Cite

Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the “opening-angle” in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.

show abstract

Section: Illustration Of Approach 3: Growth Of a Residually Stressed Materialsmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

Huang

Ogden

Penta

2021

J Elast

View full text Add to dashboard Cite

show abstract

“…On the contrary, it was found that epicardial PSLs agree with muscle fiber directions, which in the model spiral counterclockwise toward the base. The mechanical interpretation of these results is based on the idea that the driving forces of the LV deformative process are muscle contraction and blood pressure, and the contraction-driven component of the deformation process sets serious compatibility issues (given by surfaces curvature), affecting mainly subendocardium layers due to their higher geometrical stiffness ( (Nardinocchi et al, 2012)). In order to explain this concept it may be useful to imagine the myocardium as divided into two semi-independent layers (endocardium and epicardium), each one moving independently with respect to the other and having uniformly oriented fiber.…”

Section: Medical Example: Left Ventricle Mechanicsmentioning

confidence: 99%

The decomposition of deformation: New metrics to enhance shape analysis in medical imaging.

Varano

Piras

Gabriele

et al. 2018

Medical Image Analysis

View full text Add to dashboard Cite

In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation between two shapes is small, the difference between Centroid Size and m-Volume increment is barely appreciable. In medical imaging applied to soft tissues bodies can undergo very large deformations, involving large changes in size. The cardiac example, analyzed in the present paper, shows changes in m-Volume that can reach the 60%. We show here that standard Geometric Morphometrics tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the space tangent to the shape space in affine and non affine components is enriched to include also the change in size, in order to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in m-Volume rather than change in Centroid Size. This leads to a redefinition of some aspects of the Kendall's size-and-shape space without losing Kendall's original formulation. This new formulation is discussed by means of simulated examples using 2D and 3D platonic shapes as well as a real example from clinical 3D echocardiographic data. We demonstrate that our decomposition based approaches discriminate very effectively healthy subjects from patients affected by Hypertrophic Cardiomyopathy.

show abstract

“…In the following, we will invoke the summation convention, unless otherwise mentioned. Latin indices will be range over (1,2,3) and Greek indices over (1,2).…”

Section: Denote a Generic Point On The Reference Membrane Asmentioning

confidence: 99%

A Design Principle for Actuation of Nematic Glass Sheets

Acharya

2018

J Elast

View full text Add to dashboard Cite

A continuum mechanical framework is developed for determining a) the class of stressfree deformed shapes and corresponding director distributions on the undeformed configuration of a nematic glass membrane that has a prescribed spontaneous stretch field and b) the class of undeformed configurations and corresponding director distributions on it resulting in a stress-free given deformed shape of a nematic glass sheet with a prescribed spontaneous stretch field. The proposed solution rests on an understanding of how the Lagrangian dyad of a deformation of a membrane maps into the Eulerian dyad in three dimensional ambient space. Interesting connections between these practical questions of design and the mathematical theory of isometric embeddings of manifolds, deformations between two prescribed Riemannian manifolds, and the slip-line theory of plasticity are pointed out.

show abstract

Strain induced shape formation in fibred cylindrical tubes

Cited by 14 publications

References 26 publications

Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

The decomposition of deformation: New metrics to enhance shape analysis in medical imaging.

A Design Principle for Actuation of Nematic Glass Sheets

Contact Info

Product

Resources

About