拉压屈服强度不同材料的厚壁筒的极限分析

对拉压屈服强度不同（简称具有Ｓ－Ｄ效应）的材料的最壁筒进行了极限分析。结果表明，结构的极限承载能力随着材料的压拉比Ｋ的增大而增大。考虑到材料具有不同拉压性能的观点，文中的分析结果具有一般性。所给出的极限荷载公式可供结构工程设计参考     

不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.     

帘线/橡胶复合材料各向异性黏-超弹性本构模型

帘线/橡胶复合材料广泛应用于轮胎等重要工程领域,为了描述其在服役条件下的大变形、非线性、各向异性和高应变率等材料力学行为,基于纤维增强复合材料连续介质力学理论,提出了一种考虑应变率效应的帘线/橡胶复合材料各向异性黏-超弹性本构模型. 该模型中单位体积的应变能被解耦为便于参数识别的基体等容变形能、帘线拉伸变形能、剪切应变能和黏性应变能四部分. 给出了模型参数的确定方法,并通过拟合文献中单轴拉伸、偏轴拉伸实验数据,得到了模型参数. 利用该模型预测了不同加载和变形条件下的力学行为,并将预测结果与实验结果对比分析. 结果表明, 考虑黏性模型和不考虑黏性模型对不同应变率变形条件下的预测结果相差很大,且考虑黏性模型的预测结果与实验结果吻合很好. 因此,与不考虑黏性模型相比,所提出的各向异性黏-超弹性本构模型能更好地表征帘线/橡胶复合材料在大变形、高应变率条件下的力学特性.      

A plasticity and anisotropic damage model for plain concrete

A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.     

Specimen Size and Strain Rate Effects on the Compressive Behavior of Concrete

Three high-performance concrete (HPC) materials with different specimen geometries were characterized using Kolsky compression bar techniques to study the strain rate and specimen size effects on their uniaxial compressive strength. A large-diameter Kolsky bar and recently established annular pulse shaping technique were used to achieve dynamic stress equilibrium and constant strain-rate deformation in the experiments. A complimentary effort was conducted using a 19-mm-diameter Kolsky compression bar to understand the strain rate and specimen size effects on failure strength and dynamic increase factor (DIF) for concrete. It was found that, for all three concrete materials investigated, the failure strength is highly dependent on the specimen geometry, however such a relationship is not apparent for the DIF. The DIF observed in this study shows significantly lower values compared to historical data, which may indicate the importance of well-controlled dynamic testing conditions on the accuracy and validity of experimental results for concrete materials.     

基于D-P准则的压力相关材料结构拓扑优化

基于描述材料力学行为的Drucker-Prager(D-P)屈服准则, 研究了压力相关材料连续体结构拓扑优化设计问题的数学模型和数值算法. 以单元材料人工密度为设计变量, 结合SIMP惩罚模型和多孔微结构局部应力插值模型, 建立了以材料体积最小化为目标、考虑材料D-P屈服条件约束的优化问题数学模型. 利用\varepsilon-松弛方法消除奇异解现象, 采用伴随法有效推导约束函数灵敏度计算公式, 运用基于梯度的连续变量优化算法迭代求解优化问题. 数值算例验证了优化模型的正确性及数值算法的有效性, 并通过与von Mises应力约束优化结果的比较, 说明了材料的压力相关特性会对结构最优拓扑产生重要影响. 该方法设计出的最优拓扑由于充分利用了压力相关材料的抗压能力, 因而更为合理和实际.      

A numerical model for reinforced concrete structures

This paper describes a two-dimensional approach to model fracture of reinforced concrete structures under (increasing) static loading conditions. The first part is dedicated to the concrete material. The concrete is described in compression by a non-local isotropic damage constitutive law. In tension, a fictitious crack/crack band model is proposed. The influence of biaxial stress states is incorporated in the constitutive relations. In the second part a bond model is described. It accounts for different failure mechanisms, a pullout failure and a splitting failure. This approach is applied to prestressed concrete beams with different failure mechanisms. The numerical results are compared to experimental data and show good agreement.     

New evaluations for multiaxial-stress properties of ceramic materials

This paper suggests some new evaluations for multiaxial-stress properties of ceramic materials. These evaluations include some that have been used for other kinds of materials, as well as others which have not been previously employed. In some cases, these methods represent modifications of existing evaluations. The paper is confined to macroscopic behavior based upon bulk laboratory specimens. The influences of volume, stress gradients and localized behavior are not considered here since considerable attention has recently been devoted to these questions. The important problem of fracture strength will not be considered since this property appears to be considerably influenced by localized microscopic behavior. However, new evaluations of remaining mechanical properties for states of combined stresses will be presented. These include elastic and plastic strength, stiffness, ductility, resilience and toughness. Emphasis on combined-stress properties was selected since recent critical reviews indicate the need for for such an evaluation. Part A of this paper outlines new experiments that are needed to evaluate the mechanical properties and to confirm theories proposed in Part B. In Part B of this paper, new macroscopic engineering-type theories for combined-stress behavior are presented for the first time. These theories attempt to predict combined-stress behavior from uniaxial tension and compression (or pure bending and compression) behavior. These theories provide for materials such as ceramics with different properties in tension and compression. A final section of this presentation is devoted to improvements in the evaluations of other mechanical properties of materials as related to high-temperature creep and fatigue properties.     

拉压性能不同材料全量型本构关系及厚壁筒的应力分析

将经典全量理论作了推广，考虑了应力状态及塑性体积变形对拉压性能不同材料的塑性行为的影响。应用该本构模型分别计算了厚壁筒在内压和外压作用下的应力分布。给出了径向应力、环向应力和轴向应力沿壁厚的分布图。将本文的计算解与拉压性能相同(不考虑体积变形、强化曲线唯一)的幂函数强化材料的厚壁筒的理论解进行了比较。结果表明，材料的拉压性能不同对厚壁筒的环向应力和轴向应力影响较大。因此，对于拉压性能不同材料，考虑到其对应力状态及塑性体积变形敏感时，是不能将其简化成拉压性能相同、体积不可压缩、强化曲线唯一的理想材料。     

THE VISUAL EXPERIMENTAL TEACHING METHOD FOR MATERIAL FAILURE1)

基于数字图像相关技术,提出材料破坏过程可视化的实验教学方法,并以混凝土材料为例,介绍该方法在劈拉与单轴压缩实验中的应用及其效果。通过监测混凝土劈拉与压缩破坏过程,分析了该材料破坏模式,揭示了混凝土材料劈拉与压缩破坏机理。应用数字图像相关方法获得试件表面应变场分布,验证了材料破坏机理,并提出适用的破坏强度理论。     

Constitutive Relations of Nonlinear Thermoelasticity of Anisotropic Bodies

Quasilinear relations for finite reversible deformation of anisotropic materials are obtained using a thermomechanical approach. Free energy is written as a function of temperature and compatible invariants of the logarithmic strain measure and basis tensors. Nonlinear thermomechanical effects including different types of material behavior in tension and compression and the temperature dependence of the elastic tensor are taken into account.     

Elastic solids with different moduli in tension and compression

A new approach is given to the theory of non-linear elastic materials which have different behaviour in tension and compression. Two applications are made to incompressible non-linear materials using general forms for the strain energy functions. The linear form of the theory is shown to be equivalent to that used by previous writers.     

DESIGN AND PRACTICE OF SCIENCE AND TECHNOLOGY INNOVATION EXPERIMENT PROJECT IN STRUCTURE DESIGN COMPETITION1)

结合土木工程专业大学生结构设计竞赛的特点和学生实践能力培养要求,为了研究结构设计竞赛竹皮构件的受力性能,以竞赛用竹皮和胶水为原料,设计了学生科技创新实验项目,对不同长度、厚度的竹皮构件分别进行抗压、抗拉、抗弯实验和胶水与竹皮的复合强度实验,通过对构件加载进行承载力测试。实验表明厚竹皮的拉、压、弯荷重比性能较好,胶水滴注可以提高竹皮的荷重比,竹皮构件受压非线性特性较为明显。该创新性实验项目紧密结合结构设计竞赛开展,具有极强的实践性和研究性,有利于培养学生的团队协作和创新能力。     

Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.     

Theory of limit equilibrium of bimetallic shells of revolution and circular plates

Bimetallic shells and plates are widely used in technology (see [1, 2]). An investigation into the flexure and stability of thin shells and various types of loading within the limits of elasticity has been carried out in [3]. An investigation into the load-carrying capacity of cylindrical bimetallic shells made of materials which equally resist tension and compression was carried out in [4]. In many cases the materials of the base and plating layers of bimetallic constructions possess substantially different plastic resistance under tension and compression [5]. The given paper is devoted to the investigation of the load-carrying capacity of bimetallic axisymmetric shells which are made of materials that have different resistances to tension and compression; it is also devoted to the assessment of their economy in comparison with homogeneous shells.     

Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

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对具有不同拉压模量的厚壁球壳,采用双剪统一强度理论推导了其扩张问题的应力及位移的 统一解. 分析了不同模量、不同模型控制参数对厚壁球壳扩张时的扩张压力和应力场的影响. 结果表明：厚壁球壳弹性极限压力、应力场、位移场等均随着模量控制参数、模型参数的变 化而变化,在$\alpha<1$的情况下(即$E^ + < E^ - $),可以明显提高球壳的弹 性极限压力$p_e $; 厚壁球壳塑性极限压力与材料的拉压模量无关,与模型参数$\eta $有关,且随$\eta$的增加,先增大后减小. 因此若采用经典的弹性理论和单一的 模型参数对厚壁球壳进行设计计算,会带来较大的误差.