A new formulation and computation of the triphasic model for mechano-electrochemical mixtures

Hon, Y.C.; Lu, Ming; Xue, Wei; Zhou, Xu

doi:10.1007/s004660050448

Cited by 47 publications

(29 citation statements)

References 10 publications

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“…The total number of boundary constrains is N B (= N B1 + N B2 ), and the total number of constraints is N C (= N B + N G ). Based on the equations above, we can form a matrix for solving the velocity potential at each time step as described in Equation (8). The entries in the matrix can be further formulated as…”

Section: Constraints For Collocationmentioning

confidence: 99%

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Simulation of free‐surface waves in liquid sloshing using a domain‐type meshless method

Chang

2011

Numerical Methods in Fluids

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SUMMARYBased on the idea of avoiding over-fitting in artificial neural-network research using radial basis functions (RBFs), an improved RBF collocation method that reduces the number of RBFs without compromising the accuracy is proposed. This method overcomes the problem of dissatisfying governing equations on boundaries when the conventional RBF collocation method is used in solving partial differential equations. The Poisson and the Laplace equations are chosen to test the proposed method. Based on the method, a three-dimensional numerical model is established to simulate the fully nonlinear free-surface waves of sloshing water in a rectangular tank. Simulations of both two-dimensional and three-dimensional cases are performed. Simulation results from the present model are validated with experimental measurements and other numerical results.

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Section: Constraints For Collocationmentioning

confidence: 99%

“…The RBF collocation methods are very simple and effective. They have been successfully applied in many different areas, including tissue engineering [7,8], heat transfer [9], nonlinear Burgers' equations [10], shallow water equations [11][12][13], Stokes flows [14], electro-magnetic problems [15,16], and finance [17,18].…”

Section: Literature Reviewmentioning

confidence: 99%

Simulation of free‐surface waves in liquid sloshing using a domain‐type meshless method

Chang

2011

Numerical Methods in Fluids

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“…In the following, the governing system of equations for the triphasic theory will briefly be introduced (refer to Lai et al [8], Hon et al [10] or Gu et al [11] for details). The triphasic model for charged and hydrated soft tissues consists of three phases: (1) a solid phase (superscribed by s), (2) a water phase (superscribed by w), and (3) an ion phase composed of anion and cation (superscribed by + and À).…”

Section: Triphasic Theory For Charged and Hydrated Soft Tissuesmentioning

confidence: 99%

“…Recently, Huyghe et al [9] has proposed a quadriphasic model to study the swelling phenomenon in an incompressible porous media. Based on the work of Lai et al [8], Hon et al [10] derived a new set of governing equations from the generalized first law of thermodynamic for an irreversible thermodynamic system. More recently, Gu et al [11] has extended the triphasic model to include multi-electrolytes.…”

Section: Introductionmentioning

confidence: 99%

Numerical algorithm for triphasic model of charged and hydrated soft tissues

Hon

Xue

et al. 2002

Computational Mechanics

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This paper devises an efficient numerical algorithm for solving a two-dimensional triphasic model of charged and hydrated soft tissue by using the radial basis functions. The proposed numerical method is applied directly as a simple meshless collocation algorithm to approximate the solution of the governing system of continuity, momentum, and constitutive equations for the triphasic model. Since there is no requirement on meshing, the method can easily be applied to solve problems under complicated geometry. For verification, numerical simulations of stress, strain, and fluid flow patterns for a plane strain and an axisymmetric mechano-electrochemical coupling model with real synovial joint are given respectively. Classical domain decomposition technique is also combined successfully with the proposed method for solving large scale problems with numerical verification given in solving the axisymmetric case.

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“…Hon et al [3] developed a set of equations for the mixture theory, based on the triphasic system from the [4] used the mechanical equilibrium equation to compute the hydrogel deformation. After computing the concentration of H + ions, the other ionic concentrations were computed by Donnan membrane theory and subsequently the osmotic pressure is computed.…”

Section: Introductionmentioning

confidence: 99%

2D simulation of the deformation of pH-sensitive hydrogel by novel strong-form meshless random differential quadrature method

Mulay

2011

Comput Mech

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The objective of presented work is to simulate the response of 2D hydrogel when subjected to the varying pH of buffer solution and initial fixed-charge concentration inside the hydrogel. The novelty of the work is that this is the first attempt to perform the 2D simulation of pHresponsive hydrogel by novel strong-form meshless method, such as random differential quadrature (RDQ) method. The analytical equations, derived for the hydrogel deformation in the x and y directions, are numerically verified by the square shaped hydrogel disc. The jumps in the distributions of ionic concentrations and electrical potential, across the interface between solution and hydrogel, are effectively captured by the RDQ method. A novel approach is proposed to correctly impose natural boundary conditions for non-uniform boundary. The effects of solution pH and initial fixed-charge concentration on the hydrogel swelling are also successfully investigated.Keywords Random differential quadrature methods · 2D simulation of hydrogel · Meshless method · Differential quadrature method

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A new formulation and computation of the triphasic model for mechano-electrochemical mixtures

Cited by 47 publications

References 10 publications

Simulation of free‐surface waves in liquid sloshing using a domain‐type meshless method

Simulation of free‐surface waves in liquid sloshing using a domain‐type meshless method

Numerical algorithm for triphasic model of charged and hydrated soft tissues

2D simulation of the deformation of pH-sensitive hydrogel by novel strong-form meshless random differential quadrature method

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