Constitutive law of healthy gallbladder walls in passive state with damage effect

Biomechanical properties of human gallbladder (GB) wall in passive state can be valuable to diagnosis of GB diseases. In the article, an approach for identifying damage effect in GB walls during uniaxial tensile test was proposed and a strain energy function with the damage effect was devised as a constitutive law phenomenologically. Scalar damage variables were introduced respectively into the matrix and two families of fibres to assess the damage degree in GB walls. The parameters in the constitutive law with the damage effect were determined with a custom MATLAB code based on two sets of existing uniaxial tensile test data on human and porcine GB walls in passive state. It turned out that the uniaxial tensile test data for GB walls could not be fitted properly by using the existing strain energy function without the damage effect, but could be done by means of the proposed strain energy function with the damage effect involved. The stresses and Young moduli developed in two families of fibres were more than thousands higher than the stresses and Young's moduli in the matrix. According to the damage variables estimated, the damage effect occurred in two families of fibres only. Once the damage occurs, the value of the strain energy function will decrease. The proposed constitutive laws are meaningful for finite element analysis on human GB walls.

Determination of a visco-hyperelastic material law based on dynamic tension test data / 生物医学工程学杂志

The objective of this study was to determine the visco-hyperelastic constitutive law of brain tissue under dynamic impacts. A method combined by finite element simulations and optimization algorithm was employed for the determination of material variables. Firstly, finite element simulations of brain tissue dynamic uniaxial tension, with a maximum stretch rate of 1.3 and strain rates of 30 s and 90 s , were developed referring to experimental data. Then, fitting errors between the engineering stress-strain curves predicted by simulations and experimental average curves were assigned as objective functions, and the multi-objective genetic algorithm was employed for the optimation solution. The results demonstrate that the brain tissue finite element models assigned with the novel obtained visco-hyperelastic material law could predict the brain tissue's dynamic mechanical characteristic well at different loading rates. Meanwhile, the novel material law could also be applied in the human head finite element models for the improvement of the biofidelity under dynamic impact loadings.

A new analytical formulation of retention effects on particle diffusion processes

The ultimate purpose of this paper is to present a new analytical formulation to simulate diffusion with retention in a reactive medium under stable thermodynamic conditions. The analysis of diffusion with retention in a continuum medium is developed after the solution of an equivalent problem using a discrete approach. The new law may be interpreted as the reduction of all diffusion processes with retention to a unifying phenomenon that can adequately simulate the retention effect namely a circulatory motion. It is remarkable that the governing equation requires a fourth order differential term as suggested by the discrete approach. The relative fraction of diffusion particles β is introduced as a control parameter in the diffusion-retention law as suggested by the discrete approach. This control parameter is essential to avoid retention isolated from the diffusion process. Two matrices referring to material properties are introduced and related to the real phenomenon through the circulation hypothesis. The governing equation may be highly non-linear even if the material properties are constant, but the retention effect is a function of the concentration level, that is, β is a function of the concentration.

O objetivo último desse trabalho é apresentar uma nova formulação analítica para simular difusão com retenção em um meio reativo sob condições termodinamicamente estáveis. A análise da difusão com retenção em um meio contínuo é desenvolvida a partir da solução de um problema equivalente usando uma abordagem discreta. A nova lei pode ser interpretada como a redução de todos os processos de difusão com retenção a um fenômeno unificador que pode simular adequadamente a retenção. O propósito principal desse trabalho é apresentar uma nova formulação analítica para simular difusão com retenção em meio reativo termodinamicamente estável. A análise da difusão com retenção em um meio contínuo é desenvolvido a partir da solução de um problema equivalente usando uma abordagem discreta. A nova lei pode ser interpretada como a redução de todos os processos com retenção a um fenômeno unificado que pode simular adequadamente o efeito de retenção como um movimento circulatório. É notável que a equação que governa o fenômeno exige a inclusão de um termo diferencial de quarta ordem conforme sugerido pela abordagem discreta. A fração relativa β das partículas difundindo-se no meio é introduzida como um parâmetro de controle no processo de difusão-retenção. Esse parâmetro de controle é essencial para evitar retenção independente do processo de difusão. Duas matrizes contendo parâmetros relativos às propriedades materiais são introduzidas e relacionadas com a hipótese de circulação. A equação que governa o fenômeno pode ser altamente não linear mesmo se as propriedades materiais forem constantes desde que o efeito de retenção seja função da concentração, isto é que β seja função da concentração.