Computational method of inverse elastostatics for anisotropic hyperelastic solids

Lu, Jia; Zhou, Xianlian; Raghavan, Madhavan L.

doi:10.1002/nme.1807

Cited by 59 publications

(43 citation statements)

References 23 publications

(44 reference statements)

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“…The proposed algorithm is able to estimate the distribution and the resulting maximum principal stress at physiological loading with satisfactory accuracy. Another computational method for inverse analysis was introduced by Lu et al (2007) and applied to a simple example of a fusiform aneurysm. Rodríguez et al (2009) studied two patient-specific abdominal aortic aneurysm (abbreviated as AAA) geometries at 120 mm Hg in order to determine the wall stresses.…”

Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

Constitutive modelling of arteries

2010

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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.

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Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

Constitutive modelling of arteries

2010

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“…In the previous studies where the mechanical properties are known, a zero-pressure state, which is often used to approximate the zero-stress configuration, can be determined from the loaded configuration (Govindjee and Mihalic 1996;Govindjee and Mihalic 1998;Raghavan et al 2006;De Putter et al 2007;Lu et al 2007a;Lu et al 2007b;Gee et al 2009;Kroon 2010;Vavourakis et al 2011). However, in our problem, both the zero-stress configuration and the mechanical properties are unknown; hence we estimate the zero-stress configuration from the experimental observations.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic behaviour of human gallbladder walls

Hill

Ogden

et al. 2013

Journal of the Mechanical Behavior of Biomedical Materials

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Inverse estimation of biomechanical parameters of soft tissues from non-invasive measurements has clinical significance in patient-specific modelling and disease diagnosis.In this paper, we propose a fully nonlinear approach to estimate the mechanical properties of the human gallbladder wall muscles from in vivo ultrasound images. The iteration method consists of a forward approach, in which the constitutive equation is based on a modified Hozapfel-Gasser-Ogden law initially developed for arteries. Five constitutive parameters describing the two orthogonal families of fibres and the matrix material are determined by comparing the computed displacements with medical images. The optimization process is carried out using the MATLAB toolbox, a Python code, and the ABAQUS solver. The proposed method is validated with published data in artery and subsequently applied to ten human gallbladder samples. Results show that the human gallbladder wall is anisotropic during passive refilling phase, and that the peak stress is 1.6 times greater than that calculated using the linear mechanics. This discrepancy arises because the wall thickness reduces by 1.6 times during the deformation, which is not predicted by conventional linear elasticity. If the change of wall thickness is accounted for, then the linear model can used to predict the gallbladder stress and its correlation with pain. This work provides further understanding of the nonlinear characteristics of human gallbladder.

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“…Later, Govindjee [6] extended the inverse finite element design to hyperelastic orthotropic materials with applications to axi-symmetric problems. More recently, Lu et al [7] and Fachinotti et al [8] developed three-dimensional models for the inverse design of orthotropic hyperelastic solids. Also, inverse finite element was applied to the design of shells [9].…”

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confidence: 99%

Inverse finite element method for large‐displacement beams

Albanesi

Fachinotti

Cardona

2010

Numerical Meth Engineering

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SUMMARYA finite element model for the inverse analysis of large-displacement beams in the elastic range is presented. The model permits determining the initial shape of a beam such that it attains the given design shape under the effect of service loads. This formulation has immediate applications in various fields such as compliant mechanism design where flexible links can be modeled as large-displacement beams. Numerical tests for validation purposes are given, together with two design applications of flexible mechanisms with distributed compliance: a flexible gripper and a flexible S-type clutch.

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Computational method of inverse elastostatics for anisotropic hyperelastic solids

Cited by 59 publications

References 23 publications

Constitutive modelling of arteries

Constitutive modelling of arteries

Anisotropic behaviour of human gallbladder walls

Inverse finite element method for large‐displacement beams

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