A damage model for collagen fibres with an application to collagenous soft tissues.

We propose a mechanical model to account for progressive damage in collagen fibres within fibrous soft tissues. The model has a similar basis to the pseudoelastic model that describes the Mullins effect in rubber but it also accounts for the effect of cross-links between collagen fibres. We show that the model is able to capture experimental data obtained from rat tail tendon fibres, and the combined effect of damage and collagen cross-links is illustrated for a simple shear test.

Failure properties and microstructure of healthy and aneurysmatic human thoracic aortas subjected to uniaxial extension with a focus on the media.

Current clinical practice for aneurysmatic interventions is often based on the maximum diameter of the vessel and/or on the growth rate, although rupture can occur at any diameter and growth rate, leading to fatality. For 27 medial samples obtained from 12 non-aneurysmatic (control) and 9 aneurysmatic human descending thoracic aortas we examined: the mechanical responses up to rupture using uniaxial extension tests of circumferential and longitudinal specimens; the structure of these tissues using second-harmonic imaging and histology, in particular, the content proportions of collagen, elastic fibers and smooth muscle cells in the media. It was found that the mean failure stresses were higher in the circumferential directions (Control-C 1474kPa; Aneurysmatic-C 1446kPa), than in the longitudinal directions (Aneurysmatic-L 735kPa; Control-L 579kPa).

On fibre dispersion modelling of soft biological tissues: a review.

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions.

Instabilities of soft dielectrics.

The basic modern theory of nonlinear electroelasticity and its use in the formulation of constitutive laws governing the behaviour of dielectric elastomer materials was summarized in a recent review article by Dorfmann & Ogden (Dorfmann & Ogden 2017 Proc. R. Soc.

Coupled agent-based and hyperelastic modelling of the left ventricle post-myocardial infarction.

Understanding the healing and remodelling processes induced by myocardial infarction (MI) of the heart is important, and the mechanical properties of the myocardium post-MI can be indicative for effective treatments aimed at avoiding eventual heart failure. MI remodelling is a multiscale feedback process between the mechanical loading and cellular adaptation. In this paper, we use an agent-based model to describe collagen remodelling by fibroblasts regulated by chemical and mechanical cues after acute MI, and upscale into a finite element 3D left ventricular model.

Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components.

The microstructure of arteries, consisting, in particular, of collagen, elastin, and vascular smooth muscle cells, plays a very significant role in their biomechanical response during a cardiac cycle. In this article, we highlight the microstructure and the contributions of each of its components to the overall mechanical behavior. We also describe the changes of the microstructure that occur as a result of abdominal aortic aneurysms and disease, such as atherosclerosis.

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues.

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles.

Nonlinear electroelasticity: material properties, continuum theory and applications.

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory.

Modelling non-symmetric collagen fibre dispersion in arterial walls.

New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new non-symmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor.

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins.

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks.

Elasticity of biopolymer filaments.

Within the general one-dimensional theory of nonlinear elasticity we analyze the elasticity of biopolymer filaments. The approach adopted is purely mechanical but is reconciled with statistical physics approaches and allows for a proper formulation of boundary-value problems. By specializing the general framework we obtain force-extension relations for inextensible filaments and show how previous work on the biophysics of filaments fits within the framework.

Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta.

This paper provides the first analysis of the three-dimensional state of residual stress and stretch in an artery wall consisting of three layers (intima, media and adventitia), modelled as a circular cylindrical tube. The analysis is based on experimental results on human aortas with non-atherosclerotic intimal thickening documented in a recent paper by Holzapfel et al. (Holzapfel et al.

Constitutive modelling of passive myocardium: a structurally based framework for material characterization.

In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions.

Layer-specific 3D residual deformations of human aortas with non-atherosclerotic intimal thickening.

Data relating to residual deformations in human arteries are scarce. In this paper we investigate three-dimensional residual deformations for intact strips and for their separate layers from human aortas in their passive state. From 11 abdominal aortas with identified anamnesis, 16 pairs of rings and axial strips were harvested, and the rings cut open.

Introducing mesoscopic information into constitutive equations for arterial walls.

We propose a new elastic constitutive law for arterial tissue in which the limiting polymeric chain extensibility of both collagen and elastin fibres is accounted for. The elastic strain-energy function is separated additively into two parts: an isotropic contribution associated with the matrix (incorporating the elastin fibre network) and an anisotropic one associated with the collagen fibres. Information on the limiting extensibility in each case provides some mesoscopic input into the model.

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations.

Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries.

Comparison of a multi-layer structural model for arterial walls with a fung-type model, and issues of material stability.

The goals of this paper are (i) to re-examine the constitutive law for the description of the (passive) highly nonlinear and anisotropic response of healthy elastic arteries introduced recently by the authors, (ii) to show how the mechanical response of a carotid artery under inflation and extension predicted by the structural model compares with that for a three-dimensional form of Fung-type strain-energy function, (iii) to provide a new set of material parameters that can be used in a finite element program, and (iv) to show that the model has certain mathematical features that are important from the point of view of material and numerical stability.

On Rayleigh waves in incompressible orthotropic elastic solids.

In this paper the secular equation for the Rayleigh wave speed in an incompressible orthotropic elastic solid is obtained in a form that does not admit spurious solutions. It is then shown that inequalities on the material constants that ensure positive definiteness of the strain-energy function guarantee existence and uniqueness of the Rayleigh wave speed. Finally, an explicit formula for the Rayleigh wave speed is obtained.