两种弹塑性算法的比较

分析了弹塑性一致切线模量算法与径向返回算法，发现一致切线模量算法并不如有关文献报道的那样，比径向返回算法有快得多的收敛速度，两个算例表明了这一点。这使对一致切线模量算法有比较全面的看法。     

疲劳荷载下混凝土梁弯曲损伤指标的探究

混凝土疲劳损伤的计算方法比较复杂,本文经推导及实验验证得出了混凝土的割线模量损伤与塑性应变呈直线关系,同时证明了使用切线模量与割线模量计算得到的损伤是相同的,由此定义了随塑性应变而变化的混凝土弹性模量的疲劳损伤指标为简单的直线方程.将此损伤指标应用于混凝土梁,推导了疲劳荷载下弯曲损伤指标.     

弹塑性板壳结构非线性有限元分析

本文根据塑性流动理论的基本公式，由隐式积分导出了与路径无关的变量更新算法和一致切线模量。采用单元广义应力应变直接离散塑性流动定律，构造了杂交应力单元一致切线刚度矩阵的显式表达式，编制了结构有限元程序ＳＡＦＥ，数值算例表明：本文的计算方法和计算程序是正确可靠的，可用于弹塑性板壳结构的非线性分析，计算结果屈曲临界载荷和极限承载能力。     

牛顿迭代一致性算法及其在板弹塑性有限元分析中的应用

本文简略讨论了有限载荷增量弹塑性有限元分析中传统切线刚度法丧失精度和牛顿迭代平方收敛速度的原因,并提出保持牛顿迭代平方收敛速度、保证一阶精度和无条件稳定性的一致性算法.一致性算法具备以下两个特征:1)采用路径无关计算格式;2)采用一致弹塑性切线模量。根据一致性算法构造出以弯矩和曲率为基本变量的弹塑性板弯曲有限元NIDKQ元。数值结果表明NIDKQ元具有令人满意的精度,同时验证了有限载荷增量下牛顿迭代一致性算法的平方收敛率特性,而传统切线刚度法随着塑性区的扩展将大大降低收敛速度。     

牛顿迭代一致性算法及其在板弹塑性有限元分析中的应用

本文简略讨论了有限载荷增量弹塑性有限元分析中传统切线刚度法丧失精度和牛顿迭代平方收敛速度的原因,并提出保持牛顿迭代平方收敛速度、保证一阶精度和无条件稳定性的一致性算法.一致性算法具备以下两个特征:1)采用路径无关计算格式;2)采用一致弹塑性切线模量。根据一致性算法构造出以弯矩和曲率为基本变量的弹塑性板弯曲有限元NIDKQ元。数值结果表明NIDKQ元具有令人满意的精度,同时验证了有限载荷增量下牛顿迭代一致性算法的平方收敛率特性,而传统切线刚度法随着塑性区的扩展将大大降低收敛速度。     

2.5维自愈合C/SiC复合材料的压缩力学行为

试验研究了2.5维自愈合C/SiC复合材料的压缩力学行为,根据材料的细观结构特点,建立了压缩载荷下的损伤力学模型,得到了经纬向压缩的非线性应力应变关系,预测结果与试验值吻合较好。结果表明,经向和纬向的力学行为不同,纬向的压应力逐渐增大时,切线模量逐渐增大,压缩强度为270.05MPa,而经向压应力逐渐增大时,层间损伤逐渐发生,经纱承受的弯矩越来越大,切线模量逐渐降低,破坏强度为128.66MPa。     

用振动梁方法测量粘弹性材料的复模量和粘弹性参数

本文利用共振梁方法,通过对一点响应、相位滞后和共振频率的测量,可以获得粘弹性材料的复模量以及标准线性固体模型的三个参数,即松弛模量、松弛系数和蠕变系数.实验结果表明,实验原理正确,测试系统可靠而且简单实用.     

基于牛顿-拉夫逊的拉压不同模量问题的数值求解

针对拉压模量不同引起的材料本构非线性,首先,通过引入改进的Heaviside函数将本构方程连续光滑化;然后,基于特征值与特征向量的求导策略,推导有限元求解模型中切线刚度矩阵的列式;最终,提出基于牛顿-拉夫逊迭代格式的拉压不同模量问题的数值求解算法。数值算例验证了本文算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于工程分析中大规模计算问题的求解。     

屈服准则及切线模量修正的弹塑性计算模型

为提高不同应力状态下金属弹塑性行为的模拟精度,采用含应力三轴度修正的von Mises屈服准则,材料弹塑性本构关系在等效应力$\!$-$\!$-$\!$等效应变曲线基础上,提出一个切线模量为主应力函数的理论修正项. 将这两个修正项结合,以子程序形式编程嵌入ABAQUS主程序,以此模拟几种不同形状试样的弹塑性行为,并将其他屈服准则在单一曲线假设下编程与之对比. 模拟结果与真实试验结果对比发现,对于屈服而言,含应力三轴度修正的vonMises屈服准则比其他屈服理论准确;对于弹塑性阶段计算而言,提出的切线模量为主应力函数这一假设比单一曲线假设更加接近真实试验.      

基于牛顿-拉夫逊的拉压不同模量问题的数值求解

针对拉压模量不同引起的材料本构非线性,首先,通过引入改进的Heaviside函数将本构方程连续光滑化;然后,基于特征值与特征向量的求导策略,推导有限元求解模型中切线刚度矩阵的列式;最终,提出基于牛顿-拉夫逊迭代格式的拉压不同模量问题的数值求解算法。数值算例验证了本文算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于工程分析中大规模计算问题的求解。     

A generalized approach to formulate the consistent tangent stiffness in plasticity with application to the GLD porous material model

It has been shown that the use of the consistent tangent moduli is crucial for preserving the quadratic convergence rate of the global Newton iterations in the solution of the incremental problem. In this paper, we present a general method to formulate the consistent tangent stiffness for plasticity. The robustness and efficiency of the proposed approach are examined by applying it to the isotropic material with J₂ flow plasticity and comparing the performance and the analysis results with the original implementation in the commercial finite element program ABAQUS. The proposed approach is then applied to an anisotropic porous plasticity model, the Gologanu–Leblond–Devaux model. Performance comparison between the consistent tangent stiffness and the conventional continuum tangent stiffness demonstrates significant improvement in convergence characteristics of the overall Newton iterations caused by using the consistent tangent matrix.     

Processing and characterization of biodegradable polymer nanocomposites: detection of dispersion state

Nanobiocomposites of poly(lactic acid) (PLA) with 3–5 wt% organically modified montmorillonite (OMMT) were prepared by melt compounding in two different mixers, miniature twin-screw extruder and internal batch mixer, leading to different degrees of dispersion. The progress of dispersion was characterized by melt rheology coupled with light attenuation. Processed PLA/OMMT samples showed percolating networks in the melt, detected by a step increase in low-frequency elastic moduli. The melt elasticity of nanocomposites increased, while the light attenuation coefficient and the loss tangent decreased progressively with mixing energy and reached saturation that can be attributed to the maximum level of clay dispersion achieved in the present experimental conditions. Results showed that a combination of low-frequency loss tangent and light attenuation coefficient provides a potentially sensitive method for the characterization of the degree of clay dispersion. The direct correlation between light attenuation coefficient and loss tangent follows linear dependence and may open an approach for the rapid inline analysis of the degree of dispersion in melt-processed nanocomposites.     

Closed-form solution for horizontal and vertical shiftings of viscoelastic material functions in frequency domain

The closed-form shifting (CFS) algorithm is a simple mathematical methodology which determines the unique solution in the process of constructing master curves at selected reference temperature and pressure conditions. In a previous paper, the CFS algorithm has been fully described for monotonically increasing or monotonically decreasing functions only. This paper presents detailed steps of the generalized CFS methodology for non-monotonic functions, like the loss tangent. Performing shifting on the loss tangent, which does not require vertical shifting, is particularly important for materials which require vertical adjustment of dynamic viscoelastic functions, i.e., loss and storage moduli. Thus, based on horizontal shifting of the loss tangent, the CFS-based procedure of consecutive horizontal-vertical superposition for the storage modulus is proposed and analyzed. The analysis is done on the example of two synthetically generated non-monotonic tan delta segments and corresponding storage modulus segments in respect to different experimental parameters. It has been shown that the error brought by the shifting method into non-monotonic loss tangent and storage modulus master curves is twice smaller than the corresponding experimental noise level.     

Computational micro-to-macro transitions of discretized microstructures undergoing small strains

Summary  The paper investigates algorithms for the computation of homogenized stresses and overall tangent moduli of microstructures undergoing small strains. Typically, these microstructures define representative volumes of nonlinear heterogeneous materials such as inelastic composites, polycrystalline aggregates or particle assemblies. We consider a priori given discretized microstructures, without focusing on details of specific discretization techniques in space and time. The key contribution of the paper is the construction of a family of algorithms and matrix representations of the overall properties of discretized microstructures. It is shown that the overall stresses and tangent moduli of a typical microstructure may exclusively be defined in terms of discrete forces and stiffness properties on the boundary. We focus on deformation-driven microstructures, where the overall macroscopic deformation is controlled. In this context, three classical types of boundary conditions are investigated: (i) linear displacements, (ii) constant tractions and (iii) periodic displacements and antiperiodic tractions. Incorporated by the Lagrangian multiplier method, these constraints generate three classes of algorithms for the computation of equilibrium states and the overall properties of microstructures. The proposed algorithms and matrix representations of the overall properties are formally independent of the interior spatial structure and the local constitutive response of the microstructure and are therefore applicable to a broad class of model problems. We demonstrate their performance for some representative model problems including elastic–plastic deformations of composite materials. Received 29 May 2001; accepted for publication 2 January 2002     

Effective pressure-sensitive elastoplastic behavior of particle-reinforced composites and porous media under isotropic loading

The composite under investigation consists of an elastoplastic matrix reinforced by elastic particles or weakened by pores. The material forming the matrix is pressure-sensitive. The Drucker–Prager yield criterion and a one-parameter non-associated flow rule are employed to formulate the yield behavior of the matrix. The objective of this work is to estimate the effective elastoplastic behavior of the composite under isotropic tensile and compressive loadings. To achieve this objective, the composite sphere assemblage model of Hashin [Z. Hashin, The elastic moduli of heterogeneous materials, ASME J. Appl. Mech. 29 (1962) 143–150] is used. Exact solutions are thus derived as estimations for the effective secant and tangent bulk moduli of the composite. The effects of the loading modes and phase properties on the effective elastoplastic behavior of the composite are analytically and numerically evaluated.     

A damage model for concrete beams in compression

A usual class of phenomenological “1 − d” damage models is revisited: starting from experimental observations showing that the Young’s and tangent moduli evolve linearly during a compression test on concrete, an appropriate expression for the damage threshold is obtained, which differs from the usual ones. The linear variation of the moduli with respect to the strain variation allows to simplify the incremental equilibrium equations and to improve the accuracy of the simulation.     

一类铁电模型的参变量变分原理及其应用

将参变量变分原理引入铁电问题。对一类借用了经典弹塑性理论中的概念和方法的多轴铁电模型建立基于Helmholtz自由能的参变量变分原理,可以有效处理传统变分原理中由非关联流动法则或屈服面不考虑材料系数变化所引起的切线模量非对称困难。相应于参变量变分原理,引入参数二次规划算法,可获得具有可靠数值稳定性的一套铁电算法。将该算法应用于一个具体的铁电模型,数值计算结果表明本文方法的有效性。     

Tangent Second-Order Estimates for the Large-Strain, Macroscopic Response of Particle-Reinforced Elastomers

An approximate homogenization method is proposed and used to obtain estimates for the effective constitutive behavior and associated microstructure evolution in hyperelastic composites undergoing finite-strain deformations. The method is a modified version of the “tangent second-order” procedure (Ponte Castañeda and Tiberio in J. Mech. Phys. Solids 48:1389, 2000), and can be used to provide estimates for the nonlinear elastic composites in terms of corresponding estimates for suitably chosen “linear comparison composites”. The method makes use of the “tangent” moduli of the phases, evaluated at suitable averages of the deformation gradient, and yields a constitutive relation accounting for the evolution of characteristic features of the underlying microstructure in the composites, when subjected to large deformations. Satisfaction of the exact, macroscopic incompressibility constraint is ensured by means of an energy decoupling approximation splitting the elastic energy into a purely “distortional” component, together with a “dilatational” component. The method is applied to elastomers containing random distributions of aligned, rigid, ellipsoidal inclusions, and explicit analytical estimates are obtained for the special case of spherical inclusions distributed isotropically in an incompressible neo-Hookean matrix. In addition, the method is also applied to two-dimensional composites with random distributions of aligned, elliptical fibers, and the results are compared with corresponding results of earlier homogenization estimates and finite element simulations.     

Measuring Poisson's ratios in wood

Poisson's ratios and Young's moduli were measured for five sugar pine (Pinus lambertiana Douglas) boards in a plane delineated by the grain direction and a tangent to the growth increments. One test specimen per board was loaded in a direction parallel to the grain; a second one was loaded perpendicular to the grain in the tangential direction. Test results from four of the five boards fulfilled theoretical expectations with a maximum deviation of ±8 percent for the quotients of Poisson's ratios divided by Young's moduli. Linear relationships were found to exist between the rate of stress parallel to the load, the rate of strain parallel to the load, and the rate of strain perpendicular to the load. With increasing magnitudes of strain rate, values for Poisson's ratios and Young's moduli approached limit values. It was speculated that at least some of the elastic constants are time dependent. However, the term in the equations which describes that property had large errors.