压电薄板切口尖端前沿力电损伤场分析

基于Yang等建立的三维各向异性压电损伤本构模型,给出了广义平面应力压电损伤问题的本构方程和有限元平衡方程,运用有限元方法分析了张开角和深度对切口前沿力电损伤分布的影响规律。结果表明,张开角对力损伤的影响较小,并且几乎不改变力电损伤的区域尺寸,但是深度对力电损伤的大小和区域尺寸都有很大的影响。     

Bounded shear stress in masonry-like bodies

In the paper, a hyperelastic material with limited tensile and compressive strength is considered. In addition, the maximum value of the tangential component of the stress that can be attained on each plane depends on the intensity of the normal component. Previously formulated for the plane case, the constitutive equation of this material is now extended to three-dimensional bodies, constituting henceforth a generalization of the well-known model of masonry-like materials. The proposed constitutive law has been implemented in the finite element code MADY and has been applied to the study of masonry panels under different load conditions.     

Analysis of an infinite shape memory alloy plate with a circular hole subjected to biaxial tension

This paper presents an exact solution for the stresses in an infinite shape memory alloy plate with a circular hole subjected to biaxial tensile stresses applied at infinity. The solution obtained by assumption of plane stress is based on the two-dimensional version of the Tanaka constitutive law for shape memory materials. The plate is in the austenitic phase, prior to the application of external stresses. However, as a result of tensile loading, stress-induced martensite forms, beginning from the boundary of the hole and extending into the interior, as the load continues to increase. Therefore, in a general case, the plate consists of three annular regions: the inner region of pure martensite, the intermediate region where martensite and austenite coexist, and the outer region of pure austenite. The boundaries between these annular regions can be found as functions of the external stress. Two methods of solution are presented. The first is a closed-form approach based on a replacement of the actual distribution of the martensitic fraction by a piece-wise constant function of the radial coordinate. The second method results in an exact solution obtained by assuming that the ratio between the radial and circumferential stresses in the region where austenite and martensite coexist is governed by the same relationship as that in the encompassing regions of pure austenite and pure martensite.     

基于机器学习软骨细胞的时间依赖性力学行为及本构参数反演

探究软骨细胞机械负载下的力学特性对于理解软骨细胞的正常和病理状态以及骨性关节炎的病因至关重要. 基于软骨细胞有限元计算模型的力学响应与其本构参数之间的高度复杂非线性, 本文提出了分别利用双向深度神经网络TW-Deepnets模型和随机森林RF模型并结合有限元方法来识别软骨细胞本构参数的两种反演方法. 首先, 建立了软骨细胞的无侧限压缩实验有限元模型, 收集MSnHS本构参数空间点与对应的有限元计算模型的压缩反作用力响应数据集. 其次, 结合贝叶斯超参数优化算法搭建了用于软骨细胞本构参数反求的TW-Deepnets模型和RF模型, 对有限元收集的数据进行训练, 并利用单个软骨细胞受到50%压缩程度下的实验数据对软骨细胞的MSnHS本构参数进行了反求. 最后, 通过与实验曲线的对比验证了所提出的反演方法的有效性, 并引入决定系数R2对两种模型的预测准确性进行了对比评估, 检验了模型对各本构参数的预测性能, 分析了MSnHS本构模型中各参数影响软骨细胞力学响应的重要性占比. 结果表明, 本研究提出的本构参数反演方法能够有效获取软骨细胞的本构参数值, 从而准确描述软骨细胞的时间依赖性力学特性, 该方法也可进一步推广到生物细胞在静态或动态负载条件下的复杂参数反演问题.      

Thermoelastic transient response of an infinitely long annular multilayered cylinder

Thermoelastic transient response of multilayered annular cylinders of infinite lengths subjected to known temperature at traction-free inner and outer surfaces are considered. A method based on the Laplace transformation and finite difference method has been developed to analyze the thermoelasticity problem. Using the Laplace transform with respect to time, the general solutions of the governing equation are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions for the temperature and thermal stress distributions in a transient state were obtained. It was found that the temperature distribution, the displacement and the thermal stresses change slightly as time increases. There is no limit of number of annular layers of the cylinder in the presented computational procedures.     

Time domain analysis of second-order wave diffraction by an array of vertical cylinders

A time domain method is employed to analyze interactions of water waves and a group or an array of cylinders. The nonlinear free-surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a finite element method (FEM). The mesh required is generated based on a 2-D unstructured grid on a horizontal plane and its extension in the vertical direction. The matrix equation of the FEM is solved through an iteration and the initial solution is obtained from the result at the previous time step. The radiation condition is imposed through a combination of the damping zone method and the Sommerfeld–Orlanski equation. Results for various configurations, including two cylinders, four cylinders, an array of 10 cylinders and two arrays of eight cylinders are provided to show the effect of the interaction and their behaviour near the trapped mode.     

On One Approach to the Solution of Stress Problems for Noncircular Hollow Cylinders

An approach is proposed to solve three-dimensional stress problems for noncircular hollow cylinders. The end conditions are such that the problem can be reduced to a two-dimensional problem. This problem is reduced to a one-dimensional problem by introducing additional functions into the resolvable system of equations. These functions are determined using discrete Fourier series. The one-dimensional problem is solved by a stable numerical method. As an example, the stress state of cylinders with an elliptic cross section is analyzed depending on their thickness and degree of ellipticity.     

THREE-DIMENSIONAL STATIC ANALYSES FOR FGM PLATES WITH MEDIUM COMPONENTS AND DIFFERENT NET STRUCTURES

A new microelement method for the analyses of functionally graded structures was proposed. The key of this method is the maneuverable combination of two kinds of elements. Firstly, the macro elements are divided from the functionally graded material structures by the normal finite elements. In order to reflect the functionally graded distributions of materials and the microconstitutions in each macro-element, the microelement method sets up the dense microelements in every macro-element, and translates nodes to the same as the normal finite elements by the degrees of freedom of all microelemental the compatibility conditions. This microelement method can fully reflect the micro constitutions and different components of materials, and its computational elements are the same as the normal finite elements, so it is an effective numerical method for the analyses of the functionally graded material structures. The three-dimensional analyses of functionally graded plates with medium components and different micro net structures are given by using the microelement method in this paper. The differences of the stress contour in the plane of functionally graded plates with different net microstructures are especially given in this paper.     

岩土的一种强度准则及其变换应力法

基于岩土摩擦性,假设岩土破坏是由其物理空间内特征面上的应力比决定,提出了等效应力比的概念,即物理空间特征面上的剪应力合力与正应力合力的比值.在二维条件下,等效应力比可表示为σ-τ坐标系下与摩尔圆相切的直线扣除截距正切值;在三维条件下,假设在XYZ空间内存在一三维物理空间平面,此三维空间特征平面的等效应力比为影响材料强度特性的决定性因素,基于上述三维空间特征面建立了强度准则并称之为a准则.SMP准则以及广义Mises准则都是a准则的特例,当二维坐标中的截距为零时,则强度准则退化为SMP(spatially mobilized plane)强度准则,而当正切角为零时,则强度准则退化为广义Mises准则.而当截距与外切角均不为零时,则强度准则为介于上述两者之间的一种强度准则,在偏平面上为介于SMP曲边三角形与广义Mises圆形之间的曲边三角形.在子午面上,采用考虑岩土压剪耦合的屈服准则,破坏准则采用幂函数表达式.在偏平面上提出了基于a准则的形状函数,并采用真三维应力状态表示的破坏强度准则表示在三轴压缩路径下以p,q二维应力变量表达的准则公式,推导得到了基于a准则的变换应力公式,可简单地将一般以p,q为基本变量的二维模型转变为三维应力模型.通过强度以及多种应力路径的测试对比,验证了a准则及基于该准则的变换应力公式的合理性.     

On discontinuous strain fields in incompressible finite elastostatics

Piece-wise homogeneous three-dimensional deformations in incompressible materials in finite elasticity are considered. The emergence of discontinuous strain fields in incompressible materials is studied via singularity theory. Since the simplest singularities, including Maxwell’s sets, are the cusp singularities, cusp conditions for the total energy function of homogeneous deformations for incompressible materials in finite elasticity will be derived, compatible with strain jumping. The proposed method yields simple criteria for the study of discontinuous deformations in three-dimensional problems and for any homogeneous incompressible material. Furthermore the homogeneous stress tensor is also not restricted. Neither fictitious nor simplified constitutive relations are invoked. The theory is implemented in a simple shearing problem.     

An h-adaptive modified element-free Galerkin method

In this work an h-adaptive Modified Element-Free Galerkin (MEFG) method is investigated. The proposed error estimator is based on a recovery by equilibrium of nodal patches where a recovered stress field is obtained by a moving least square approximation. The procedure generates a smooth recovered stress field that is not only more accurate then the approximate solution but also free of spurious oscillations, normally seen in EFG methods at regions with high gradient stresses or discontinuities.The MEFG method combines conventional EFG with extended partition of unity finite element (EPUFE) methods in order to create global shape functions that allow a direct imposition of the essential boundary conditions.The re-meshing of the integration mesh is based on the homogeneous error distribution criterion and upon a given prescribed admissible error. Some examples are presented, considering a plane stress assumption, which shows the performance of the proposed methodology.     

A stable unstructured finite volume method for parallel large-scale viscoelastic fluid flow calculations

A new stable unstructured finite volume method is presented for parallel large-scale simulation of viscoelastic fluid flows. The numerical method is based on the side-centered finite volume method where the velocity vector components are defined at the mid-point of each cell face, while the pressure term and the extra stress tensor are defined at element centroids. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance the pressure–velocity–stress coupling. The log-conformation representation proposed in [R. Fattal, R. Kupferman, Constitutive laws for the matrix–logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281–285] has been implemented in order improve the limiting Weissenberg numbers in the proposed finite volume method. The time stepping algorithm used decouples the calculation of the polymeric stress by solution of a hyperbolic constitutive equation from the evolution of the velocity and pressure fields by solution of a generalized Stokes problem. The resulting algebraic linear systems are solved using the FGMRES(m) Krylov iterative method with the restricted additive Schwarz preconditioner for the extra stress tensor and the geometric non-nested multilevel preconditioner for the Stokes system. The implementation of the preconditioned iterative solvers is based on the PETSc library for improving the efficiency of the parallel code. The present numerical algorithm is validated for the Kovasznay flow, the flow of an Oldroyd-B fluid past a confined circular cylinder in a channel and the three-dimensional flow of an Oldroyd-B fluid around a rigid sphere falling in a cylindrical tube. Parallel large-scale calculations are presented up to 523,094 quadrilateral elements in two-dimension and 1,190,376 hexahedral elements in three-dimension.     

Measurement of Orthogonal Stress Gradients Due to Impact Load on a Transparent Sheet using Digital Gradient Sensing Method

A full-field optical method called Digital Gradient Sensing (DGS) for measuring stress gradients due to an impact load on a planar transparent sheet is presented. The technique is based on the elasto-optic effect exhibited by transparent solids due to an imposed stress field causing angular deflections of light rays quantified using 2D digital image correlation method. The measured angular deflections are proportional to the in-plane gradients of stresses under plane stress conditions. The method is relatively simple to implement and is capable of measuring stress gradients in two orthogonal directions simultaneously. The feasibility of this method to study material failure/damage is demonstrated on transparent planar sheets of PMMA subjected to both quasi-static and dynamic line load acting on an edge. In the latter case, ultra high-speed digital photography is used to perform time-resolved measurements. The quasi-static measurements are successfully compared with those based on the Flamant solution for a line-load acting on a half-space in regions where plane stress conditions prevail. The dynamic measurements, prior to material failure, are also successfully compared with finite element computations. The measured stress gradients near the impact point after damage initiation are also presented and failure behavior is discussed.     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.     

理想正交各向异性弹塑性材料平面应变条件下静止裂纹尖端场

以Hill唯象理论为基础,建立正交各向异性弹塑性材料的本构关系,给出理想正交各向异性弹塑性材料在平面应变条件下混合型静止裂纹尖端的弹塑性场.与J.Pan的解不同,采用自相似假定,可以用解析方法求得不存在应力间断的应力场.对满塑性区条件和应变的奇异性加以讨论,这些为建立断裂准则提供了理论的依据.     

Highly parallel time integration of viscoelastic flows

A highly parallel time integration method is presented for calculating viscoelastic flows with the DEVSS-G/DG finite element discretization. The method is a synthesis of an operator splitting time integration method that decouples the calculation of the polymeric stress by solution of a hyperbolic constitutive equation from the evolution of the velocity and pressure fields by solution of a generalized Stokes problem. Both steps are performed in parallel. The discontinuous finite element discretization of the hyperbolic constitutive equation leads to highly-parallel element-by-element calculation of the stress at each time step. The Stokes-like problem is solved by using the BiCGStab Krylov iterative method implemented with the block complement and additive levels method (BCALM) preconditioner. The solution method is demonstrated for the calculation of two-dimensional (2D) flow of an Oldroyd-B fluid around an isolated cylinder confined between two parallel plates. These calculations use extremely fine finite elements and expose new features of the solution structure.     

A control volume finite difference method for buoyant flow in three-dimensional curvilinear non-orthogonal co-ordinates

This paper presents a control-volume-based finite difference method in non-orthogonal curvilinear coordinates on a local basis in which the vectors and tensors are all based on the general curvilinear coordinates for buoyant flow calculations in arbitrary three-dimensional geometries. The governing equations are transformed from Cartesian co-ordinates into generalized curvilinear co-ordinates. After integrating the set of equations for the control volumes, the finite difference equations are then formulated by a proper treatment of the heat flux and stress tensors and by incorporating the QUICK scheme for the convective terms. The solution procedure then follows the one for three-dimensional Cartesian co-ordinates. Examples are given in problems of natural convection in such three-dimensional enclosures as parallelepiped enclosures and horizontal closed cylinders with differentially heated ends. In the latter case, important applications have been found in crystal growth by means of chemical vapour deposition in a cylindrical ampoule, in which uniform heat fluxes along the two ends are required in order to produce high-quality crystals. Special attention is given to the insertion of baffles in the cylinder to improve the recirculating flow patterns near the two ends.     

Micromorphic approach for finite gradient-elastoplasticity fully coupled with ductile damage: Formulation and computational aspects

It is well established that the use of inelastic constitutive equations accounting for induced softening, leads to pathological space (mesh) and time discretization dependency of the numerical solution of the associated Initial and Boundary Value Problem (IBVP). To avoid this drawback, many less or more approximate solutions have been proposed in the literature in order to regularize the IBVP and to obtain numerical solutions which are, at convergence, much less sensitive to the space and the time discretization. The basic idea behind these regularization techniques is the formulation of nonlocal constitutive equations by introducing some effects of characteristic lengths representing the materials microstructure. In this work, using the framework of generalized nonlocal continua, a thermodynamically-consistent micromorphic formulation using appropriate micromorphic state variables and their first gradients, is proposed in order to extend the classical local constitutive equations by incorporating appropriate characteristic internal lengths. The isotropic damage, the isotropic and the kinematic hardenings are supposed to carry the targeted micromorphic effects. First the theoretical aspects of this fully coupled micromorphic formulation is presented in details and the proposed generalized balance equations as well as the fully coupled micromorphic constitutive equations deduced. The associated numerical aspects in the framework of the classical Galerkin-based FE formulation are briefly discussed in the special case of micromorphic damage. Specifically, the formulation of 2D finite elements with additional degrees of freedom (d.o.f.), the dynamic explicit global resolution scheme as well as the local integration scheme, to compute the stress tensor and the state variables at each integration point of each element, are presented. Application is made to the typical uniaxial tension specimen under plane strain conditions in order to chow the predictive capabilities of the proposed micromorphic model, particularly against its ability to give (at convergence) a mesh independent solution even for high values of the ductile damage (i.e., the macroscopic cracks).     

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength theory (UST) are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua (FLAC/FLAC3D), which includes an associated/non-associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different (SD) materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening behavior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD material structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.