An alternative model for anisotropic elasticity based on fabric tensors

Motivated by the mechanical analysis of multiphase or damaged materials, a general approach relating fabric tensors characterizing microstructure to the fourth rank elasticity tensor is proposed. Using a Fourier expansion in spherical harmonics, the orientation distribution function of a positive, radially symmetric microstructural property is approximated by a scalar and a symmetric, traceless second rank tensor. Following this approximation, a general expression of the elastic free energy potential is derived from representation theorems for anisotropic scalar functions. Based on a homogeneity assumption for the elastic constitutive law with respect to the microstructural property, a particular elasticity model is developed that involves three independent constants beside the fabric tensors. Strict positive definiteness of the corresponding elasticity tensor is ensured under explicit conditions on the independent constants for arbitrary fabric tensors.     

An anisotropic damage model for tensile fatigue

Fatigue damage in materials is considered to be the effect of material degradation, and the dispersion in fatigue life is attributed to variability in microstructure. This paper presents a numerical model to simulate fatigue damage evolution using continuum damage mechanics to characterize material degradation. An explicit microstructure topology representation is achieved using Voronoi tessellations. Unlike conventional models which use a scalar approximation for damage, this model treats the damage variable as an anisotropic tensor. The model is used to simulate tensile fatigue failure in thin steel specimen. The fatigue life estimations from the model compares well with published experimental results. The results predict a high variability in fatigue life that is characteristic of metals and alloys, as compared with the existing isotropic damage models available in the literature. The model was also used to study the influence of material inhomogeneity on fatigue life dispersion.     

A discrete cohesive model for fractal cracks

The fractal crack model described here incorporates the essential features of the fractal view of fracture, the basic concepts of the LEFM model, the concepts contained within the Barenblatt-Dugdale cohesive crack model and the quantized (discrete or finite) fracture mechanics assumptions proposed by Pugno and Ruoff [Pugno N, Ruoff RS. Quantized fracture mechanics. Philos Mag 2004;84(27):2829-45] and extended by Wnuk and Yavari [Wnuk MP, Yavari A. Discrete fractal fracture mechanics. Engng Fract Mech 2008;75(5):1127-42]. The well-known entities such as the stress intensity factor and the Barenblatt cohesion modulus, which is a measure of material toughness, have been re-defined to accommodate the fractal view of fracture.For very small cracks or as the degree of fractality increases, the characteristic length constant, related to the size of the cohesive zone is shown to substantially increase compared to the conventional solutions obtained from the cohesive crack model. In order to understand fracture occurring in real materials, whether brittle or ductile, it seems necessary to account for the enhancement of fracture energy, and therefore of material toughness, due to fractal and discrete nature of crack growth. These two features of any real material appear to be inherent defense mechanisms provided by Nature.     

Multiscale simulation of nanostructures based on spatial secant model: a discrete hyperelastic approach

The main objective of this paper is to present a coarse-grained material model for the simulation of three-dimensional nanostructures. The developed model is motivated by the recent progress in establishing continuum models for nanomaterials and nanostructures. As there are conceptual differences between the continuum field defined in the classical sense and the nanomaterials consisting of discrete, space-filling atoms, existing continuum measures cannot be directly applied for mapping the nanostructures due to the discreteness at small length scale. In view of the fundamental difficulties associated with the direct application of the continuum approach, we introduce a unique discrete deformation measure called spatial secant and have developed a new hyperelastic model based on this measure. We show that the spatial secant-based model is consistently linked to the underlying atomistic model and provides a geometric exact mapping in the discrete sense. In addition, we outline the corresponding computational framework using the finite element and/or meshfree method. The implementation is within the context of finite deformation. Finally we illustrate the application of the model in studying the mechanics of low-dimensional carbon nanostructures such as carbon nanotubes (CNT). By comparing with full-scale molecular mechanics simulations, we show that the proposed coarse-grained model is robust in that it accurately captures the non-linear mechanical responses of the CNT structures.     

Discrete 3D model as complimentary numerical testing for anisotropic damage

It is proposed to use a discrete particle model as a complimentary “numerical testing machine” to identify the hydrostatic elasticity-damage coupling and the corresponding sensitivity to hydrostatic stresses parameter. Experimental tri-axial tensile testing is difficult to perform on concrete material, and numerical testing proves then its efficiency. The discrete model used for this purpose is based on a Voronoi assembly that naturally takes into account heterogeneity. Tri-tension tests on a cube specimen, based on a damage growth control, are presented. A successful identification of the hydrostatic sensitivity function of a phenomenological anisotropic damage model is obtained.     

非均匀软组织声散射模型的研究概况

本文综述了非均匀软组织声散射模型的研究概况及其在超声组织定征中的应用。将声散射模型进行了系统的分类介绍。并对在建立软组织声散射模型中存在的问题以及研究声散射模型的重要意义进行了分析和讨论。     

强激光对生物组织热作用的一个分析模型

本文在分析生物的传热传质过程的基础上 ,提出了结合实际的生物组织热作用的一个分析模型 :在诸相变边界上物性参数为阶跃函数的多边界 Stefan问题 .进行了一维问题的数值求解 ,它可以确定汽化区的尺寸以及边界的移动速度 ,进而估算出生物组织热损伤区的大小 .并将结果与实验进行了比较 ,来检验模型的合理性 ,得出该模型与实际生物组织热损伤过程相符合的结论     

Mixture probabilistic PCR model for soft sensing of multimode processes

Principal component regression (PCR) has been widely used for soft sensor modeling and quality prediction in last several decades, which is still very popular for both academy researches and industry applications. However, most PCR models are determined by the projection method, which may lack probabilistic interpretation for the process data. In fact, due to the inevitable process noise, most process data are inherently random variables. Several probabilistic PCA methods have already been proposed in the past years. Compared to the deterministic modeling method, the probabilistic model is more appropriate to characterize the behavior of the random variables in the process. This paper first presents a probabilistic derivation of the PCR model (PPCR) and then extends it to the mixture form (MPPCR). For quality prediction of processes with multiple operation modes, a mixture probabilistic soft sensor is developed based on the MPPCR model. Simultaneously, the information of the operation mode can also be located by the proposed soft sensor. To evaluate the performance of the MPPCR model, a numerical example and a benchmark simulation case study of the Tennessee Eastman process are provided. Different methods have been compared with the proposed model, including the global, local, and multi-local PCR models. As a result, the proposed MPPCR model performs the best among these methods.     

随机短纤维增强复合材料弹性模量预测模型

为了研究纤维增强复合材料的力学性能, 借助混合率构造的Reuss-Voigt模型以及三维纤维取向简化模型, 建立了随机短纤维复合材料弹性模量预测模型。利用该模型对玻璃纤维增强尼龙6(PA6)复合材料进行弹性模量预测, 其预测结果与拉伸实验结果误差值小于5%, 表明该预测模型具有较好的准确性。     

A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation

 This paper presents a rate-independent elastoplastic constitutive model for (nearly) incompressible biological fiber-reinforced composite materials. The constitutive framework, based on multisurface plasticity, is suitable for describing the mechanical behavior of biological fiber-reinforced composites in finite elastic and plastic strain domains. A key point of the constitutive model is the use of slip systems, which determine the strongly anisotropic elastic and plastic behavior of biological fiber-reinforced composites. The multiplicative decomposition of the deformation gradient into elastic and plastic parts allows the introduction of an anisotropic Helmholtz free-energy function for determining the anisotropic response. We use the unconditionally stable backward-Euler method to integrate the flow rule and employ the commonly used elastic predictor/plastic corrector concept to update the plastic variables. This choice is expressed as an Eulerian vector update the Newton's type, which leads to a numerically stable and efficient material model. By means of a representative numerical simulations the performance of the proposed constitutive framework is investigated in detail. Received: 12 December 2001 / Accepted: 14 June 2002 Financial support for this research was provided by the Austrian Science Foundation under START-Award Y74-TEC. This support is gratefully acknowledged.     

Evaluation of single-phase,discrete, mixture and combined model of discrete and mixture phases in predicting nanofluid heat transfer characteristics for laminar and turbulent flow regimes

It is essential to investigate the appropriate model for simulating nanofluid flow for different flow regimes because, at present, most previous studies do not agree with each other. It was, therefore, the purpose of this study to present a Computational Fluids Dynamics (CFD) investigation of heat transfer coefficients of internal forced convective flow of nanofluids in a circular tube subject to constant wall heat flux boundary conditions. A complete three-dimensional (3D) cylindrical geometry was used. Laminar and turbulent flow regimes were considered. Three two-phase models (mixture model, discrete phase model (DPM) and the combined model of discrete and mixture phases) and the single-phase homogeneous model (SPM) were considered with both constant and variable properties. For the turbulent flow regime, it was found that the DPM with variable properties closely predicted the local heat transfer coefficients with an average deviation of 9%, and the SPM deviated from the DPM model by 2%. It was also found that the mixture and the combined discrete and the mixture phase model gave unrealistic results. For laminar flow, the DPM model with variable properties predicted the heat transfer coefficients with an average deviation of 9%.     

An automated approach for three-dimensional quantification of fibrillar structures in optically cleared soft biological tissues

We present a novel approach allowing for a simple, fast and automated morphological analysis of three-dimensional image stacks (z-stacks) featuring fibrillar structures from optically cleared soft biological tissues. Five non-atherosclerotic tissue samples from human abdominal aortas were used to outline the multi-purpose methodology, applicable to various tissue types. It yields a three-dimensional orientational distribution of relative amplitudes, representing the original collagen fibre morphology, identifies regions of isotropy where no preferred fibre orientations are observed and determines structural parameters throughout anisotropic regions for the analysis and numerical modelling of biomechanical quantities such as stress and strain. Our method combines optical tissue clearing with second-harmonic generation imaging, Fourier-based image analysis and maximum-likelihood estimation for distribution fitting. With a new sample preparation method for arteries, we present, for the first time to our knowledge, a continuous three-dimensional distribution of collagen fibres throughout the entire thickness of the aortic wall, revealing novel structural and organizational insights into the three arterial layers.     

A mixed finite element formulation of triphasic mechano‐electrochemical theory for charged,hydrated biological soft tissues

An equivalent new expression of the triphasic mechano‐electrochemical theory [9] is presented and a mixed finite element formulation is developed using the standard Galerkin weighted residual method. Solid displacement u ^s, modified electrochemical/chemical potentials ϵ^w, ϵ⁺and ϵ⁻ (with dimensions of concentration) for water, cation and anion are chosen as the four primary degrees of freedom (DOFs) and are independently interpolated. The modified Newton–Raphson iterative procedure is employed to handle the non‐linear terms. The resulting first‐order Ordinary Differential Equations (ODEs) with respect to time are solved using the implicit Euler backward scheme which is unconditionally stable. One‐dimensional (1‐D) linear isoparametric element is developed. The final algebraic equations form a non‐symmetric but sparse matrix system. With the current choice of primary DOFs, the formulation has the advantage of small amount of storage, and the jump conditions between elements and across the interface boundary are satisfied automatically. The finite element formulation has been used to investigate a 1‐D triphasic stress relaxation problem in the confined compression configuration and a 1‐D triphasic free swelling problem. The formulation accuracy and convergence for 1‐D cases are examined with independent finite difference methods. The FEM results are in excellent agreement with those obtained from the other methods. Copyright © 1999 John Wiley & Sons, Ltd.     

基于反向耦合模原理光栅的薄膜模型研究

提出了将Round方法与薄膜理论相结合的多层薄膜模型,将光纤光栅看成一多层薄膜体系,每层薄膜用界面传输矩阵和膜层传输矩阵表示,将每层的传输矩阵相乘后得到光栅的总传输矩阵,用它分析了基于反向耦合模原理的各光纤光栅。数值计算结果表明,该模型计算方法简单,而且和耦合模理论吻合得很好,可以用此模型来分析光纤光栅的各种参数对光栅的影响。     

纤维增强复合材料黏弹性行为的预测模型

根据标准线性固体模型构造了一种预测纤维增强复合材料黏弹性行为的模型, 推导出该模型的本构方程与松弛模量和蠕变柔量表达式, 该模型经有限元仿真验证具有较高的精度。利用该模型研究了纤维几何特性对蠕变柔量和松弛模量的影响。结果表明, 复合材料蠕变柔量与纤维比长度呈线性关系, 而当纤维比半径增大到临界值后, 其变化对材料的松弛模量和蠕变柔量影响减小, 该临界值随纤维弹性模量的增大而减小; 当纤维模量与基体模量相差较大时, 复合材料的增强系数和减柔系数几乎不受时间变化的影响。      

An exact solution for an anisotropic plate with an elliptic hole under arbitrary remote uniform moments

The problem of an anisotropic plate containing an elliptic hole subjected to remote bending or twisting moments is considered. In contrast with the previous works on the problem, the requirement that the deflection be a single-valued function is satisfied by introducing a correction constant. An exact solution for general anisotropic materials under arbitrary uniform loading conditions is derived. Explicit expressions for the deflection and moments on the edge of an elliptic hole in an orthotropic plate subjected to bending or twisting moments are obtained. The moment intensity factors as the elliptic hole degenerates into a crack are given.     

An elastic mechanics model and computation method for geotechnical material

岩土材料内摩擦性质是岩土的基本力学性质之一,无论岩土处于何种受力状态,都应考虑岩土体的内摩擦力。然而,至今只有岩土极限分析与塑性力学中考虑岩土体的内摩擦力,而在弹性理论与能量理论等诸方面均未体现。认为岩土体无论是处于塑性状态还是弹性状态,都存在着内摩擦力,为此建立岩土材料弹性力学的摩擦体力学单元。基于土体试验提出黏聚力先发挥,摩擦力随变形逐渐发挥,并假设摩擦因数与应变成正比,由此确定摩擦力的计算,最后仿效线弹性力学计算方法,但此时摩擦体的剪切模量G已非常数,从而形成摩擦体的非线性弹性力学计算方法。算例表明,按该方法计算出的弹性地基上的位移和剪应力小于传统方法计算出的位移和应力值,这比较符合实际情况,表明采用摩擦体力学单元对岩土材料是合适的。     

An invariant-based anisotropic material model for short fiber-reinforced thermoplastics: Coupled thermo-plastic formulation

This paper presents the development of a new fully-coupled thermo-mechanical invariant-based elasto-plastic constitutive model for short fiber reinforced composites (SFRPs). The invariant-based character of the current formulation under quasi-static multiaxial loading conditions allows the incorporation of the anisotropic (transversely isotropic) response of these materials, which results from the employed injection molding process for their production. From the modeling point of view, the thermo-mechanical nonlinear behavior of these materials is performed through the definition of a thermal-dependent anisotropic yield surface and a non-associative plastic potential function. This novel coupled formulation is accordingly derived and implemented into the FE code FEAP by means of the user capability UEL, i.e. the constitutive model is integrated within an user-defined element. The performance of the model is first assessed using a set of benchmark computations, and subsequently validated with available experimental data, showing the potential applicability of the proposed formulation.     

Adaptation of the virtual fields method for the identification of biphasic hyperelastic model parameters in soft biological tissues with osmotic swelling

Biphasic hyperelastic models have become popular for soft hydrated tissues, and there is a pressing need for appropriate identification methods using full-field measurement techniques such as digital volume correlation. This paper proposes to address this need with the virtual fields method (VFM). The main asset of the proposed approach is that it avoids the repeated resolution of complex nonlinear finite element models. By choosing special virtual fields, the VFM approach can extract hyperelastic parameters of the solid part of the biphasic medium without resorting to identifying the model parameters driving the osmotic effects in the interstitial fluid. The proposed approach is verified and validated through three different examples: the first and second using simulated data and then the third using experimental data obtained from porcine descending thoracic aortas samples in osmotically active solution.