The Stable Finite Element Method for Minimization Problems

Liu, B.; Huang, Yu Sang

doi:10.1166/jctn.2008.2560

Cited by 8 publications

(5 citation statements)

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“…The energy minimization problem is solved using an incremental FE method. 35 The incremental FE method seeks to minimize the energy function so as to determine the stable energy state and corresponding device shape. The degradation rate is computed from a function that relates the properties of biodegradable materials with strain energy.…”

Section: Related Workmentioning

confidence: 99%

Modeling and simulation of material degradation in biodegradable wound closure devices

et al. 2014

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Biodegradable materials have been used as wound closure materials. It is important for these materials to enhance wound healing when the wound is vulnerable, and maintain wound closure until the wound is heal. This article studies the degradation process of bioresorbable magnesium micro-clips for wound closure in voice/laryngeal microsurgery. A novel computational approach is proposed to model degradation of the biodegradable micro-clips. The degradation process that considers both material and geometry of the device as well as its deployment is modeled as an energy minimization problem that is iteratively solved using active contour and incremental finite element methods. Strain energy of the micro-clip during degradation is calculated with the stretching and bending functions in the active contour formulation. The degradation rate is computed from strain energy using a transformation formulation. By relating strain energy to material degradation, the degradation rates and geometries of the micro-clip during degradation can be represented using a simulated degradation map. Computer simulation of the degradation of the micro-clip presented in the study is validated by in vivo and in vitro experiments.

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Section: Related Workmentioning

confidence: 99%

Modeling and simulation of material degradation in biodegradable wound closure devices

et al. 2014

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“…The average nominal strain along x‐direction is denoted by

\overset{ϵ}{true}

. The finite deformation Timoshenko beam element is used to establish the adaptive element in the mapping space, and the postbuckling algorithm developed by Liu et al is adopted.…”

Section: Postbuckling Of An Infinite Beam On Elastic Substratementioning

confidence: 99%

Adaptive periodical representative volume element for simulating periodical postbuckling behavior

Qiu

Wang

et al. 2014

Numerical Meth Engineering

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SUMMARYFinite element method (FEM) with fixed representative volume element (RVE) encounters some difficulties in simulating the periodical postbuckling behaviors of infinite long beam or infinite large film on soft substrate under compression, because the wavelength and pattern of buckling are not known before simulation and will change with the increase of compression strain. In this paper, an adaptive periodical RVE is constructed in a mapping space to avoid remeshing in the real space, and the mapping coefficients, that is, the dimension and shape of RVE in real space, are treated as variables in average energy density minimization to obtain correct postbuckling configurations. The validness and efficiency of the proposed algorithm have been demonstrated by our numerical examples.

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“…6(a), 6(¿)), and 6(c) is the value of the residual intemal moment in bond angles. The atomistic simulation is performed by the atomic-scale finite element method [28][29][30]. If there is no residual internal moment, as a standard Morse potential function assumed, unrealistically dramatic wrinkles shown in Fig.…”

Section: (B)mentioning

confidence: 99%

Mechanics Interpretation on the Bending Stiffness and Wrinkled Pattern of Graphene

Wang

Liu

et al. 2013

Journal of Applied Mechanics

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In this paper we attempt to answer two questions on graphene from a mechanic's viewpoint: why does this one-atom-thick monolayer have finite bending stiffness to ensure its stability? and what is its wrinkle mechanism? As for the first question, it is found that the repulsive residual internal moment in the bond angle can lead to a nonzero bending stiffness, which makes the graphene fiat. Together with long-range attraction among atoms, such as van der Waals forces, a graphene prefers to have a self-buckling wrinkled configuration with many waves.

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The Stable Finite Element Method for Minimization Problems

Cited by 8 publications

References 0 publications

Modeling and simulation of material degradation in biodegradable wound closure devices

Modeling and simulation of material degradation in biodegradable wound closure devices

Adaptive periodical representative volume element for simulating periodical postbuckling behavior

Mechanics Interpretation on the Bending Stiffness and Wrinkled Pattern of Graphene

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