率形式Mohr-Coulomb模型严格增量本构研究

从修正的Drucker公设和本构关系的内变量理论出发,对一般形式的含损伤粘塑性屈服模型导出了增量型本构关系的一般形式,并对岩土介质中常用的率形式Mohr-Coulomb模型给出了其本构增量算法的具体形式。所提出的增量本构关系是由增量应变表达增量应力的显式形式,故特别适用于高速冲击等动态力学问题。作为算例,该文以所提出的增量本构关系为基础,开展了岩石平板撞击层裂问题的数值模拟,结果良好。     

SMA长纤维增强弹塑性基体复合材料的力学性能

本文从作者建立的SMA本构模型出发,推导出增量型的SMA本构关系;借助于细观力学的方法,推导出了新的长纤维SMA复合材料的增量型细观本构模型;应用此模型分析了该复合材料的力学性能,得出了一些定量的结论,尤其是计算了复合材料中各相的残余应力的变化,这对智能复合材料的设计提供了很大帮助。     

沥青混合料热粘弹性本构关系试验测定及其力学应用

基于热粘弹性力学理论,就不同的温度条件下沥青混合料的应力松弛特征开展了试验研究,应用热流变简单材料的时温等效原理对试验结果进行了分析和参数拟合,根据试验结果建立了描述沥青混合料粘弹特性的广义Maxwell模型;通过理论推导提出了沥青混合料非定常和非均匀变温条件下增量型热粘弹性本构关系,在此基础上,给出应用本构关系进行沥青路面热粘弹性力学分析的数值实现方法;通过对TSRST试验的模拟,对得到的沥青混合料热粘弹性本构关系及其数值实现方法的合理性进行了验证,并给出一个工程计算实例。     

半固态流变行为模型及应用

半固态成形是21世纪最具潜力的先进制造技术之一.分析了国内外半固态变形行为研究进展,重点阐述了近似单相本构关系模型、两相本构关系模型、宏观-微观耦合本构关系模型的特点及应用,特别是笔者提出的宏观-微观耦合本构关系模型反映了工艺参数和微观组织参数对半固态流变应力的影响.同时,笔者将新型宏观-微观耦合本构关系模型应用于Al-4Cu-Mg合金半固态反挤压过程的有限元数值模拟,获得了工艺参数对应力应变、温度、晶粒尺寸、液相体分数和挤压载荷等的影响规律,数值模拟结果与半固态实验结果基本一致.     

基于双剪统一强度理论应变退化模型的隧道结构稳定性分析

论文基于双剪统一强度准则应变软化模型对圆形隧道稳定性的分析,提出一种简单的数值计算方法来对围岩进行弹塑性分析。该文采用差分法,基于广义形式的双剪应力屈服准则,并采用相关联流动法则,建立本构方程。对于应变软化模型,该文选定塑性应变增量作为软化参数,并且假设强度参数随软化参数成线性函数关系。弹性区的解答引用拉梅解答,而求解塑性区的解答时,将塑性区分成很多微元圆环,并假设每个圆环的径向应力?r沿半径向内均匀递减;其次,建立每个微元圆环的平衡微分方程、本构方程、几何方程及相邻两微元之间的应力增量和应变增量的关系。从弹塑性交界面处的塑性区最外一个圆环开始,求解出每一个微元圆环的解答。并且利用MATLAB进行编程求解出最终的结果:应力场、应变场、径向位移场的数值解。此外还分析讨论了中间主应力影响系数b、软化参数临界值η*对解答的影响,并分析了影响塑性区半径的因素。     

随机刚架结构在平稳随机激励下的动力响应分析

文中研究了随机刚架结构的平稳随机响应问题。考虑结构物理参数的随机性，导出了结构在平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例考察了结构物理参数的随机性对结构动力响应均方值随机性的影响，并获得了若干有意义的结论。     

结构性软黏土的修正剑桥模型

天然软黏土普遍受到土结构性的影响,如何在土体本构模型中反映这一影响显得非常重要。该文从修正剑桥模型出发,引入结构屈服应力参数表征受土结构性影响的天然土初始屈服面的形状;引入各向异性参数描述天然土体初始各向异性引起的屈服面旋转。基于土结构性突变屈服破坏机理,屈服前结构性软黏土呈现弹性的力学性质,屈服后土结构性的影响完全丧失,采用同修正剑桥模型一致的硬化规律和流动法则。根据一致性连续条件,推导增量型的应力-应变关系,建立适用于结构性软黏土的弹塑性本构模型。选取国外已有的天然沉积Bothkennar软黏土,对比典型应力路径下的试验实测结果与模型计算结果,显示了该文模型模拟结构性软黏土受力变形特性的优越性。     

板壳非线性分析的新理论新方法

提出了板壳非线性分析的新理论新方法。首先建立了下列几个新的本构关系:塑性应变向量增量与总应变向量增量的新关系,热塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系,粘塑性应变向量增量与总应变向量增量的新关系,热粘塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系。这些关系分别称为弹塑性应变增量理论、热弹塑性应变增量理论、弹粘塑性应变增量理论及热弹粘塑性应变增量理论,避开了屈服曲面、加载曲面、流动法则及复杂的非线性应力应变关系。其次建立了非线性样条无网格法,这种方法是以新的本构关系、几何非线性理论、变分原理、广义变分原理、加权残数法及样条离散化为基础建立的,避免了经典本构关系及有限元法带来的巨大困难及缺陷,不仅计算简便,而且精度高,收敛速度很快。建立了板壳非线性分析的统一格式,对板壳的几何非线性分析、材料非线性分析及双重非线性分析都适用。     

二维非线性单原子正方晶格色散摄动分析

声子晶体的色散关系决定弹性波在其中的传播方式。从二维无限周期结构的波动方程出发,提出了一种分析非线性离散型声子晶体的色散关系的一阶近似摄动法。通过引入Bloch理论与小参数摄动展开法,得到了一阶近似的色散关系与频散曲线,以分析不同方向上的阻抗配置与非线性系数对频散及群速度的影响。以二维单原子正方晶格为例,得到了其一阶频散曲线。色散结果显示带隙及传播方向与波幅相关。最后模拟了晶格对点谐波激励的响应,以验证摄动分析有效性。     

平稳随机激励下线性随机桁架结构动力响应分析

考虑桁架结构的物理参数、几何尺寸的随机性，利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法，从结构平稳随机响应在频域上的表达式出发，导出了随机桁架结构在平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例考察了结构物理参数和几何尺寸的随机性对结构位移响应均方值和应力响应均方值随机变量随机性的影响，并获得了一些有意义的结论。     

柔性材料对爆炸载荷的缓冲效应研究

建立了柔性材料桙钢复合壳体在爆炸载荷作用下应力波传播问题的完备方程组;使用有限元方法完成 了对复合壳体在爆炸载荷作用下应力波传播规律的系列数值模拟,并着重讨论了不同炸药层和柔性材料层厚度 对柔性材料与钢交界面载荷的影响。     

Modelling damage accumulation in filled polymers

A variant of the non-linear endochronic viscoelasticity theory is developed wherein the reduced-time function depends on a damage parameter, equivalent strains or stresses, as well as on some functions enabling one to distinguish between loading and unloading processes. Some combinations of the first and second invariants of strain and stress tensors are used as the equivalent strains or stresses.
The existence of flaws is taken into account by the introduction of special equivalent stresses which are dependent on principal tensile stresses and the characteristics of the material.
As a criterion of damage equivalence in non-linear viscoelastic materials, the condition of a specific dissipation equality is introduced. Experiments for the determination of material functions entering the constitutive equations are outlined.
The proposed variant of the theory has made it possible to realistically explain the results of creep and constant loading rate tensile tests and creep tests to rupture under conditions of two-step loading sequences acting on filled polymeric materials.     

Bifurcations in the mechanics of hypoelastic composite materials

This paper analyses the modification of a hypoelastic material behavior at the small variations of the material parameters, using elements of the bifurcation theory. The considered material is obtained by the combination of two granular hypoelastic materials, which have the memory of the initial stress state, and their stress work depends on stress history. Its constitutive equation is deduced by means of the constitutive equations of the component materials. In consequence, mechanical properties of those two materials are interpenetrated, generating, for the new material, domains of stability, as well as surfaces in stress space, surfaces on which the strain–stress system is not invertible. It results that it is necessary to choose correctly the component materials, their share and the process of forming the new material, so that the imposed solicitation by the operation conditions should be accessible to a composite material. When we are modelling, the choice of the component materials means the choice of their constitutive equations—the share of the component materials will fix the stability domain of the composite material—the forming process chosen correctly will determine that the initial stress state (from which the loading path will start) should be in the stability domain of the material.     

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Dry granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasi-static, large deformation. This system is studied in the presence of contact adhesion, using the discrete element method (DEM). Several continuum fields like the density, the deformation gradient and the stress tensor are computed locally and are analyzed with the goal to formulate objective constitutive relations for the flow behavior of cohesive powders. From a single simulation only, by applying time- and (local) space-averaging, and focusing on the regions of the system that experienced considerable deformations, the critical-state yield stress (termination locus) can be obtained. It is close to linear, for non-cohesive granular materials, and nonlinear with peculiar pressure dependence, for adhesive powders—due to the nonlinear dependence of the contact adhesion on the confining forces. The contact model is simplified and possibly will need refinements and additional effects in order to resemble realistic powders. However, the promising method of how to obtain a critical-state yield stress from a single numerical test of one material is generally applicable and waits for calibration and validation.     

A density-dependent endochronic plasticity for powder compaction processes

This paper is concerned with the numerical modeling of powder cold compaction process using a density-dependent endochronic plasticity model. Endochronic plasticity theory is developed based on a large strain plasticity to describe the nonlinear behavior of powder material. The elastic response is stated in terms of hypoelastic model and endochronic plasticity constitutive equations are stated in unrotated frame of reference. A trivially incrementally objective integration scheme for rate constitutive equations is established. Algorithmic modulus consistent with numerical integration algorithm of constitutive equations is extracted. It is shown how the endochronic plasticity describes the behavior of powder material from the initial stage of compaction to final stage, in which material behaves as solid metals. It is also shown that some commonly used plasticity models for powder material can be derived as special cases of the proposed endochronic theory. Finally, the numerical schemes are examined for efficiency in the modeling of a plain bush, a rotational-flanged and a shaped tablet powder compaction component.     

Achieving pervasive fracture and fragmentation in three-dimensions: an unstructuring-based approach

There are few methods capable of capturing the full spectrum of pervasive fracture behavior in three-dimensions. Throughout pervasive fracture simulations, many cracks initiate, propagate, branch and coalesce simultaneously. Because of the cohesive element method framework, this behavior can be captured in a regularized manner. However, since the cohesive element method is only able to propagate cracks along element facets, a poorly designed discretization of the problem domain may introduce artifacts into the simulated results. To reduce the influence of the discretization, geometrically and constitutively unstructured means can be used. In this paper, we present and investigate the use of three-dimensional nodal perturbation to introduce geometric randomness into a finite element mesh. We also discuss the use of statistical methods for introducing randomness in heterogeneous constitutive relations. The geometrically unstructured method of nodal perturbation is then combined with a random heterogeneous constitutive relation in three numerical examples. The examples are chosen in order to represent some of the significant influencing factors on pervasive fracture and fragmentation; including surface features, loading conditions, and material gradation. Finally, some concluding remarks and potential extensions are discussed.     

A spherical discrete element model: calibration procedure and incremental response

When using spherical elements within the Discrete Element Method, computational costs can be kept low even for large numbers of elements. However, this oversimplification of the granular geometry has drawbacks when quantitatively assessing the model even for frictional geomaterials. To overcome this limitation, the local constitutive law must at least take into account the transfer of a moment between elements. This moment, which is added to normal and shear local interaction forces, increases the number of local parameters. Moreover, when local plastic thresholds are considered, the calibration of the model becomes tricky. With such a set of local parameters, a calibration procedure is proposed, which attempts to define the respective role of each parameter in the macroscopic behavior. A series of numerical simulations of triaxial compression tests has been performed to check the capability of this model to get good quantitative results and the incremental behavior of the numerical medium is studied by performing a series of axisymmetric stress probes with varying directions. The corresponding strain responses are measured. From different initial stress states, the results indicate that the incremental response is well described by elastoplasticity with a single mechanism, and a non-associative flow rule.     

Design optimization of non-linear structures with rate-dependent and rate-independent constitutive models

A design optimization process for non-linear structures with history-dependent materials modelled using the endochronic constitutive theory is described. This constitutive model does not use the concept of a yield surface and describes plastic, viscoplastic and viscoelastic behaviour with one set of equations. Therefore, development of the yield surface is not traced in numerical calculations, simplifying the implementation of response and sensitivity analyses. The total Lagrangian formulation incorporating both geometric and material non-linear effects is used. Shape, non-shape and material design parameters are treated simultaneously using the control volume concept, and static and dynamic problems are treated. A simple structure is optimized for several cases of static and impact loading conditions to demonstrate the procedure. Plastic and viscoplastic material behaviour as well as shape and non-shape design parameters are treated in the example problems.     

A cyclic multiaxial model for concrete

A rate-independent plasticity constitutive model is proposed, for the stress-strain and strength behavior of plain concrete, under complex multiaxial stress-paths, including stress reversals. The only material parameters required by the model are the uniaxial cylinder strength f _cand the strain at the peak of the monotonic stress-strain curve, ₀ . The model is based on a bounding surface in stress space, which is the outermost surface that can be reached by the stress point. When the size of the bounding surface decreases with increasing maximum compressive principal strain _max on the material, strength degradation during cyclic loading as well as the falling post-failure branch of the stress-strain curves, can be modeled. The distance from the current stress point to the bounding surface, determines the values of the main parameters of the inelastic stress-strain relations, i.e. of the plastic shear modulus H ^P, and the shear-compaction/dilatancy factor Strains are almost completely inelastic from the beginning of deformation. The inelastic portion of the incremental strain is computed by superposition of 1) the deviatoric strain increment, which occurs in the direction of the deviatoric stress and is proportional to the octahedral shear stress increment and inversely proportional to the plastic shear modulus 2) the volumetric strain increment, which consists of a portion which is proportional to the hydrostatic stress increment, and another which equals the product of the octahedral shear strain increment and the shear compaction/dilatancy factor Stress reversals are defined separately for the hydrostatic and the deviatoric component of the stress tensor, and the parameters of the inelastic stress-strain relations are given as different functions of the stress and strain history, for virgin loading, unloading, reloading, or for the post-failure falling branch.The incremental stress-strain law is set in the form of incremental compliance and rigidity matrices, and implemented into a nonlinear dynamic finite element code.     

Incremental forms of Schapery’s model: convergence and inversion to simulate strain controlled ramps

Schapery’s nonlinear viscoelastic model is written in incremental form, and three different approximations of nonlinearity functions in the time increment are systematically analysed with respect to the convergence rate. It is shown that secant slope is the best approximation of the time shift factor, leading to significantly higher convergence rate. This incremental form of the viscoelastic model, Zapas’ model for viscoplasticity, supplemented with terms accounting for damage effect is used to predict inelastic behaviour of material in stress controlled tests. Then the incremental formulation is inverted to simulate stress development in ramps where strain is the input parameter. A comparison with tests shows good ability of the model in inverted form to predict stress–strain response as long as the applied strain is increasing. However, in strain controlled ramps with unloading, the inverted model shows unrealistic hysteresis loops. This is believed to be a proof of the theoretically known incompatibility of the stress and strain controlled formulations for nonlinear materials. It also shows limitations of material models identified in stress controlled tests for use in strain controlled tests.