Modeling of fibrous biological tissues with a general invariant that excludes compressed fibers

Dispersed collagen fibers in fibrous soft biological tissues have a significant effect on the overall mechanical behavior of the tissues. Constitutive modeling of the detailed structure obtained by using advanced imaging modalities has been investigated extensively in the last decade. In particular, our group has previously proposed a fiber dispersion model based on a generalized structure tensor. However, the fiber tension–compression switch described in that study is unable to exclude compressed fibers within a dispersion and the model requires modification so as to avoid some unphysical effects. In a recent paper we have proposed a method which avoids such problems, but in this present study we introduce an alternative approach by using a new general invariant that only depends on the fibers under tension so that compressed fibers within a dispersion do not contribute to the strain-energy function. We then provide expressions for the associated Cauchy stress and elasticity tensors in a decoupled form. We have also implemented the proposed model in a finite element analysis program and illustrated the implementation with three representative examples: simple tension and compression, simple shear, and unconfined compression on articular cartilage. We have obtained very good agreement with the analytical solutions that are available for the first two examples. The third example shows the efficacy of the fibrous tissue model in a larger scale simulation. For comparison we also provide results for the three examples with the compressed fibers included, and the results are completely different. If the distribution of collagen fibers is such that it is appropriate to exclude compressed fibers then such a model should be adopted

Use of vulture bone flutes and other products in China

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An exponential constitutive model excluding fibers under compression: application to extension-inflation of a residually stressed carotid artery

Detailed information on the three-dimensional dispersion of collagen fibres within layers of healthy and diseased soft biological tissues has been reported recently. Previously we have proposed a constitutive model for soft fibrous solids based on the angular integration approach which allows the exclusion of any compressed collagen fibre within the dispersion. In addition, a computational implementation of that model in a general purpose finite element program has been investigated and verified with the standard fibre-reinforcing model for fibre contributions. In this study, we develop the proposed fibre dispersion model further using an exponential form of the strain-energy function for the fibre contributions. The finite element implementation of this model with a rotationally symmetrical dispersion of fibres is also presented. This includes explicit expressions for the stress and elasticity tensors. The performance and implementation of the new model are demonstrated by means of a uniaxial extension test, a simple shear test, and an extension–inflation simulation of a residually stressed carotid artery segment. In each example we have obtained good agreement between the finite element solution and the analytical or experimental results

A discrete fibre dispersion method for excluding fibres under compression in the modeling of fibrous tissues

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension–compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost

Computational method for excluding fibers under compression in modeling soft fibrous solids

Soft fibrous solids often consist of a matrix reinforced by fibers that render the material anisotropic. Recently a fiber dispersion model was proposed on the basis of a weighted strain-energy function using an angular integration approach for both planar and three-dimensional fiber dispersions (G.A. Holzapfel and R.W. Ogden: Eur. J. Mech. A/Solids, 49 (2015) 561–569). This model allows the exclusion of fibers under compression. In the present study computational aspects of the model are documented. In particular, we provide expressions for the elasticity tensor and the integration boundary that admits only fibers which are extended. In addition, we give a brief description of the finite element implementation for both 2D and 3D models which make use of the von Mises distribution to describe the dispersion of the fibers. The performance and the finite element implementations of the 2D and 3D fiber dispersion models are illustrated by means of uniaxial extension in the mean fiber direction and more general directions, and simple shear with different mean fiber directions. The finite element results are in perfect agreement with the solutions computed from analytical formulas

Trajectory Optimization for a Cruising Unmanned Aerial Vehicle Attacking a Target at Back Slope While Subjected to a Wind Gradient

The trajectory of a tubular launched cruising unmanned aerial vehicle is optimized using the modified direct collocation method for attacking a target at back slope under a wind gradient. A mathematical model of the cruising unmanned aerial vehicle is established based on its operational and motion features under a wind gradient to optimize the trajectory. The motion characteristics of  “altitude adjustment” and “suicide attack” are taken into full account under the combat circumstance of back slope time key targets. By introducing a discrete time function, the trajectory optimization is converted into a nonlinear programming problem and the SNPOT software is applied to solve for the optimal trajectory of the missile under different wind loads. The simulation results show that, for optimized trajectories, the average attack time decreased by up to 29.1% and the energy consumption is reduced by up to 25.9% under specified wind gradient conditions. A, ωdire, and Wmax have an influence on the flight trajectories of cruising unmanned aerial vehicle. This verifies that the application of modified direct collocation method is reasonable and feasible in an effort to achieve more efficient missile trajectories

Application of the Variational Mode Decomposition for Power Quality Analysis

Harmonics and interharmonics in power systems distort the grid voltage, deteriorate the quality and stability of the power grid. Therefore, rapid and accurate harmonic separation from the grid voltage is crucial to power system. In this article, a variational mode decomposition-based method is proposed to separate harmonics and interharmonics in the grid voltage. The method decomposes the voltage signal into fundamental, harmonic, interharmonic components through the frequency spectrum. An empirical mode decomposition (EMD) and an ensemble empirical mode decomposition (EEMD) can be combined with the independent component analysis (ICA) to analyze the harmonics and intherharmonics. By comparing EMD-ICA, EEMD-ICA methods, the proposed method has several advantages: (1) a higher correlation coefficient of all the components is found; (2) it requires much less time to accomplish signal separation; (3) amplitude, frequency, and phase angle are all retained by this method. The results obtained from both synthetic and real-life signals demonstrate the good performance of the proposed method

Numerical investigation on rock fragmentation under decoupled charge blasting

Blasting using decoupled charge is extensively applied in rock excavation and rock fragmentation. In this study, the rock fragmentation induced by blasting using decoupled charge is investigated by combined finite element modelling and image-processing. After calibrating the numerical model developed in LS-DYNA against the fragment morphology and fragmentation size distribution (FSD) in three air-coupling blasts and three water-coupling blasts, a series of cubic single-hole models are constructed to simulate rock cracking induced by decoupled charge blasting with various decoupling ratios, distinct coupling mediums and different decoupled charge modes. The simulated fracture networks are obtained by blanking the damaged elements whose damage level is over the threshold of crack formation, and the resulting crack patterns are image-processed using ImageJ to identify fragment size. Then, the blast-created FSDs are characterized by a three-parameter generalized extreme value function, and the FSDs with decoupling ratios, coupling mediums and different decoupled charge modes are quantitatively analyzed and compared. The results show that rock fragmentation becomes finer and the FSD range gets narrower with the decrease in decoupling ratio. Meanwhile, smaller fragment sizes and narrower FSD spans are obtained when changing coupling material from air to water and altering radial decoupling to axial decoupling.acceptedVersio

Hybrid Approach for Detecting and Classifying Power Quality Disturbances Based on the Variational Mode Decomposition and Deep Stochastic Configuration Network

This paper proposes a novel, two-stage and hybrid approach based on variational mode decomposition (VMD) and the deep stochastic configuration network (DSCN) for power quality (PQ) disturbances detection and classification in power systems. Firstly, a VMD technique is applied to discriminate between stationary and non-stationary PQ events. Secondly, the key parameters of VMD are determined as per different types of disturbance. Three statistical features (mean, variance, and kurtosis) are extracted from the instantaneous amplitude (IA) of the decomposed modes. The DSCN model is then developed to classify PQ disturbances based on these features. The proposed approach is validated by analytical results and actual measurements. Moreover, it is also compared with existing methods including wavelet network, fuzzy and S-transform (ST), adaptive linear neuron (ADALINE) and feedforward neural network (FFNN). Test results have proved that the proposed method is capable of providing necessary and accurate information for PQ disturbances in order to plan PQ remedy actions accordingly