Inverse formulation for geometrically exact stress resultant shells

Zhou, Xianlian; Lu, Jia

doi:10.1002/nme.2215

Cited by 21 publications

(25 citation statements)

References 38 publications

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“…in the definition of E cov αβ , equation (8). From now on, "direct" strains will be replaced with "assumed" strains, and the superimposed tilde that identifies the assumed ones will be obviated in order to simplify the notation.…”

Section: Cure Of Shear Lockingmentioning

confidence: 99%

“…Beyond the field of inverse design, Lu and Zhou [7,8] proposed a singular application of IFEM to the prevention of aneurysms, taking the in vivo image of an aneurysm as the known deformed configuration under a known pressure.…”

Section: Introductionmentioning

confidence: 99%

“…Zhou and Lu [8] introduced IFEM for shells using the stress-resultant approach proposed by Simo et al [10]. Models based in this approach need specialized constitutive equations for the accross-the-thickness membrane and shear stress resultants and stress couple, as described in the pioneering work of Simo and Fox [11].…”

Section: Introductionmentioning

confidence: 99%

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Inverse finite element modeling of shells using the degenerate solid approach

Fachinotti

Albanesi

Valle

2015

Computers & Structures

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The inverse finite element method (IFEM) for degenerated-solid shells is introduced. IFEM allows to determine the undeformed shape of a body (in this case, a shell-like body) such that it attains a desired shape after large elastic deformations. The model is based on the degenerated-solid approach, which enables the use of the standard constitutive laws of Solid Mechanics.A benchmark for validation purposes is first passed. Then, the skills of IFEM for inverse design are demonstrated by means of an application to the design of a micro-valve.

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Section: Cure Of Shear Lockingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inverse finite element modeling of shells using the degenerate solid approach

Fachinotti

Albanesi

Valle

2015

Computers & Structures

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“…The transverse shear force was also assumed to depend linearly on transverse shear strain, with a shear modulus of 5/6μ 1 . Definitions of bending moment, curvature, transverse shear force and transverse shear strain can be found in [21]. Zero displacement conditions were applied at boundary nodes.…”

Section: = F T Fmentioning

confidence: 99%

Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro

et al. 2014

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Continuing advances in mechanobiology reveal more and more that many cell types, especially those responsible for establishing, maintaining, remodelling or repairing extracellular matrix, are extremely sensitive to their local mechanical environment. Indeed, it appears that they fashion the extracellular matrix so as to promote a ‘mechanical homeostasis’. A natural corollary, therefore, is that cells will try to offset complexities in geometry and applied loads with heterogeneous material properties in order to render their local environment mechanobiologically favourable. There is a pressing need, therefore, for hybrid experimental–computational methods in biomechanics that can quantify such heterogeneities. In this paper, we present an approach that combines experimental information on full-field surface geometry and deformations with a membrane-based point-wise inverse method to infer full-field mechanical properties for soft tissues that exhibit nonlinear behaviours under finite deformations. To illustrate the potential utility of this new approach, we present the first quantification of regional mechanical properties of an excised but intact gallbladder, a thin-walled, sac-like organ that plays a fundamental role in normal digestion. The gallbladder was inflated to a maximum local stretch of 120% in eight pressure increments; at each pressure pause, the entire three-dimensional surface was optically extracted, and from which the surface strains were computed. Wall stresses in each state were predicted from the deformed geometry and the applied pressure using an inverse elastostatic method. The elastic properties of the gallbladder tissue were then characterized locally using point-wise stress–strain data. The gallbladder was found to be highly heterogeneous, with drastically different stiffness between the hepatic and the serosal sides. The identified material model was validated through forward finite-element analysis; both the configurations and the local stress–strain patterns were well reproduced.

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“…Lu, 2007 [11] proposed a computational method of inverse elastostatics for anisotropic hyperelastic solids in the context of fibrous hyperelastic solids and provide explicit stress function for soft tissue models. In [12] an inverse method for thin-wall structures modelled as geometrically exact stress resultant shells is presented. Germain, 2010 and 2013 [13][14][15] extended the method originally proposed in [1] to anisotropic hyperelasticity that is based on logarithmic strains.…”

Section: Introductionmentioning

confidence: 99%

On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity

Germain

Landkammer

Steinmann

2014

Advanced Modeling and Simulation in Engineering Sciences

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Background: Inverse form finding methods allow conceiving the design of functional components in less time and at lower costs than with direct experiments. The deformed configuration of the functional component, the applied forces and boundary conditions are given and the undeformed configuration of this component is sought. Methods:In this paper we present a new recursive formulation for solving inverse form finding problems for isotropic elastoplastic materials, based on an inverse mechanical formulation written in the logarithmic strain space. First, the inverse mechanical formulation is applied to the target deformed configuration of the workpiece with the set of internal variables set to zero. Subsequently a direct mechanical formulation is performed on the resulting undeformed configuration, which will capture the path-dependency in elastoplasticity. The so obtained deformed configuration is furthermore compared with the target deformed configuration of the component. If the difference is negligible, the wanted undeformed configuration of the functional component is obtained. Otherwise the computation of the inverse mechanical formulation is started again with the target deformed configuration and the current state of internal variables obtained at the end of the computed direct formulation. This process is continued until convergence is reached. Results: In our three numerical examples in isotropic elastoplasticity, the convergence was reached after five, six and nine iterations, respectively, when the set of internal variables is initialised to zero at the beginning of the computation. It was also found that when the initial set of internal variables is initialised to zero at the beginning of the computation the convergence was reached after less iterations and less computational time than with other values. Different starting values for the set of internal variables have no influence on the obtained undeformed configuration, if convergence can be achieved. Conclusions:With the presented recursive formulation we are able to find an appropriate undeformed configuration for isotropic elastoplastic materials, when only the deformed configuration, the applied forces and boundary conditions are given. An initial homogeneous set of internal variables equal to zero should be considered for such problems.

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Inverse formulation for geometrically exact stress resultant shells

Cited by 21 publications

References 38 publications

Inverse finite element modeling of shells using the degenerate solid approach

Inverse finite element modeling of shells using the degenerate solid approach

Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro

On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity

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