Hyperelasticity with softening for modeling materials failure

Volokh, K.Y.

doi:10.1016/j.jmps.2007.02.012

Cited by 149 publications

(85 citation statements)

References 39 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also concerning arterial failure, Volokh (2007Volokh ( , 2008) investigated a criterion for failure of arteries during inflation using a two-layer model (media and adventitia) on the basis of a stress-softening function combined with equation (2.29). In addition, Gasser & Holzapfel (2006b) developed a three-dimensional cohesivezone model to analyse dissection in a human artery.…”

Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

Constitutive modelling of arteries

2010

View full text Add to dashboard Cite

This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thickwalled circular cylindrical tube in order to illustrate its extension-inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

show abstract

Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

Constitutive modelling of arteries

2010

View full text Add to dashboard Cite

show abstract

“…[26] Two approaches exist to predict the rupture of a stretchable device. In one approach, the designer assumes a flawless device, calculates the field of deformation using the nonlinear theory of elasticity, and predicts rupture if any material point in the device reaches a critical state of deformation [35][36][37][38][39][40][41][42][43]. In the other approach, the designer identifies a flaw in the device, calculates the energy release rate using the nonlinear theory of elasticity, and predicts rupture if the energy release rate reaches the fracture energy [44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Flaw sensitivity of highly stretchable materials

Chen

Wang

Suo

2017

Extreme Mechanics Letters

196

135

View full text Add to dashboard Cite

Elastomers and gels can often deform multiple times their original length. The stretchability is insensitive to small cuts in the samples, but reduces markedly when the cuts are large. We show that this transition occurs when the depth of cut exceeds a material-specific length, defined by the ratio of the fracture energy measured in the large-cut limit and the work to rupture measured in the small-cut limit. This conclusion generalizes a result in the fracture mechanics of hard materials. For an acrylic elastomer and a polyurethane, we measure the stretch to rupture as a function of the depth of cut, and show that the experimental data agree well with the prediction of the nonlinear elastic fracture mechanics. In a space of material properties we compare many materials (elastomers, gels, ceramics, glassy polymers, biomaterials, and metals), and find that the material-specific length varies from nanometers to centimeters.

show abstract

“…Volokh (2007) [17] pointed out that the traditional hyperelastic model has a defect: as the deformation increases (in terms of right Cauchy-Green deformaton tensor C), the respective deformation energy density ψ e (C) could approach to infinity:…”

Section: Softening Check For Ap-based Hyperelasticitymentioning

confidence: 99%

“…Volokh (2007) [17] named the traditional hyperelasticity as intact hyperelasticity and softening hyperelasticity with upper limit ψ * is defined as:…”

Section: Softening Check For Ap-based Hyperelasticitymentioning

confidence: 99%