Fractal model for virgin compression of pure clays

The well-known linear relation between the void ratio and the logarithm of pressure for the one-dimensional consolidation has widely incorporated into elastoplastic constitute equation of soils, however, it is not at all straight line for more compressible clays and has several physically unaccepted properties. The compression of clays is explained by fractal theory, and is seen as a balance between the vertical pressure and repulsive force between clay plates. The distance between clay plates depends on the structure formation of the clay flocculation and clay surface. The structure formation of the clay flocculation and clay surface can be modeled by fractal approach. A new formulation of one-dimensional virgin compression of pure clays, expressed by the linear function of ln ν–ln p or ln e–ln p, is proposed based on the fractal model for clay structure. The linear function of ln ν–ln p is suitable to express the virgin compression of the extremely high plasticity clays up to the high pressure of 5000 kPa. For low plasticity clays, the virgin compression satisfies with the linear relationship of ln e–ln p at the pressure higher than 100 kPa. These too are show to be in satisfactory agreement with experimental data. The gradient of the plots of ln ν–ln p and ln e–ln p is related to the fractal dimensions of clay structure, the fundamental material parameters for the first time.     

Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics.Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening,isotropic hardening and dam- age.Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria,such as the volume dilatancy under the compression,strain-rate sen- sitivity,stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures.Moreover,we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.     

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation

The present work focuses on the development of a physically-based model for large deformation stress-strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic-viscoplastic model of [Boyce et al., 1988] and [Boyce et al., 2000]. The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic-viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core-hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress-strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.     

混凝土剪切断裂能与分形维数关系的研究

混凝土断裂试件断口蕴涵着丰富的力学信息，而传统的欧几里得几何难以对复杂的断口形貌进行描述，本文引入分形几何理论对断口形貌进行研究，结合宏观的断裂参量进行数值分析，从而找到了混凝土断裂微观现象与宏观力学量联系的桥梁，本文分析了混凝土四点剪切加载试件的断裂性能，计算了断裂韧度、断裂能等相关参数，并通过扫描电子显微镜对断口形貌观测，运用分形理论计算了此类断口的分形维数，分析了Ⅱ型断裂断裂能和分形维数之间的关系。     

混凝土的弹塑性损伤双面本构模型

针对混凝土材料拉压应变空间下损伤机制的不同,结合连续损伤力学和塑性理论建立了一个全新的本构模型。该模型中损伤和塑性变形的演变由应变空间的同一个非弹性曲面来控制,但对拉压应变空间中非弹性曲面的演变分别采用了随动强化法则和各向同性演化规律。计算结果表明,该模型能较好地描述混凝土材料在单轴及多轴单调加载和低周反复荷载下的典型非线性特征。     

混凝土的一种标量损伤弹塑性本构模型

荷载作用下材料性能的劣化是混凝土结构的微观损伤机理,其宏观表现为结构刚度的折减和承载力的降低。论文推导了基于不可逆热力学过程的弹塑性标量损伤本构,给出时间离散的屈服准则。采用基于向后Euler法的应力更新算法——两步图形返回的最近点投影法,推导了满足迭代结果收敛假设的塑性参数及算法刚度张量,给出了空间梁单元本构积分算法的Jacobi矩阵。将模型用于混凝土简支梁的承载力试验模拟,与计算数据对比表明了模型和算法的合理性和有效性。     

混凝土冻融损伤本构模型研究

基于各向同性连续损伤力学理论,以损伤条件下的弹性模量和泊松比为变量,基于Ottosen理论模型建立了混凝土冻融损伤破坏准则,并以Ottosen本构理论模型为基础,利用建立的冻融损伤破坏准则构建了混凝土冻融损伤本构模型,并编制了本构模型有限元程序,经过试验验证模型计算结果较为准确,为有限元计算和冻融作用后混凝土结构模拟应...     

An unsymmetric constitutive equation for anisotropic viscoelastic fluid

A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid–liquid crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie–Ericksen theory is described by the first Rivlin–Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion–extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extrudate of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a series of new anisotropic non-Newtonian fluid problems can be addressed. The project supported by the National Natural Science Foundation of China (10372100, 19832050) (Key project). The English text was polished by Yunming Chen.     

基于能量守恒理论的带肋钢筋-混凝土粘结滑移本构关系研究

针对钢筋-混凝土粘结滑移的劈裂破坏模式,将整个破坏过程分为未开裂的弹性阶段和带裂缝阶段。弹性阶段采用弹性厚壁圆筒模型,带裂缝阶段采用考虑混凝土软化特性的厚壁圆筒模型。基于这两种模型,研究了粘结滑移劈裂破坏过程的能量变化规律,推导出了两种模型的能量计算公式。利用能量守恒定律建立了钢筋-混凝土粘结滑移本构关系的微分方程,并通过数值积分方法得到了粘结滑移本构模型。该本构模型能够体现混凝土与钢筋材料参数和几何参数的影响,对不同形状的粘结滑移关系曲线具有较好的适应性。最后,将得到的本构关系与文献的试验结果进行对比,并分析了各参数的变化规律。     

围压状态下的混凝土本构模型

利用已有不同围压下的混凝土三向压缩试验, 分析研究不同围压条件对混凝土强度和应力-应变关系的影响。试验表明, 把混凝土简单视为脆性材料的观点并不符合实际情况, 塑性特征也是混凝土材料主要力学特征。由热力学定律出发, 本文提出了多次方形式的屈服函数和与围压状态相关联的损伤标准化函数, 提出了考虑围压状态的混凝土本构模型。试验结果与数值计算比较表明, 该本构关系可以很好地描述混凝土在不同围压状态下的力学损伤发展和脆-塑性转换力学特征, 也可以描述拉伸作用下的应力-应变关系, 具有一定的普遍意义。     

盐腐蚀后混凝土的动态本构模型

为探究混凝土受盐腐蚀后的动态力学响应,配置了粉煤灰质量分数为15%的普通硅酸盐水泥混凝土,将其置于质量分数均为15%的NaCl和Na₂SO₄溶液中浸泡腐蚀60 d后,利用?100 mm分离式霍普金森压杆实验装置,测试其受腐蚀后的动态力学性能,并结合宏观唯象损伤统计理论和Weibull分布思想,建立了混凝土受盐腐蚀后的动态统计损伤本构模型。结果表明:受盐腐蚀后,混凝土试件的动态抗压强度均有不同程度的下降,且NaCl溶液腐蚀试件的降幅大于Na₂SO₄溶液腐蚀试件;模型曲线与实验曲线的拟合度较高,能够较准确地描述混凝土在冲击荷载作用下的动态力学响应规律。     

混凝土损伤本构模型下梁承载力研究

为解决混凝土非线性特性难以描述的难题,通过MTS815.02岩石电液伺服系统,对圆柱体混凝土试件施加定围压比为0.2的围压,得出C25、C35、C45混凝土在＂理想无损伤＂状态下的应力-应变曲线;用Ramberg-Osgood公式描述其应力-应变关系,引入损伤变量演化方程,进而得出混凝土一维受压损伤本构模型。通过与实验数据的对比证明了模型的有效性和准确性;详细地分析了无初始损伤条件下配筋梁受弯破坏时的损伤演化过程;计算C25、C35、C45钢筋混凝土梁的受弯承载力。分析结果显示：随着混凝土强度由C25提高到C45,按此模型计算与按规范公式计算所得梁承载力的差异由1.9%升高至2.84%;下降段损伤累积量占总体损伤度的比例由46.26%升高至86.04%。研究表明,本文的分段曲线损伤模型可以较好地模拟梁混凝土的非线性受压过程,并能够给出损伤程度的预测。     

A plasticity model for pressure-dependent anisotropic cellular solids

The initial and subsequent yield surfaces for an anisotropic and pressure-dependent 2D stochastic cellular material, which represents solid foams, are investigated under biaxial loading using finite element analysis. Scalar measures of stress and strain, namely characteristic stress and characteristic strain, are used to describe the constitutive response of cellular material along various stress paths. The coupling between loading path and strain hardening is then investigated in characteristic stress–strain domain. The nature of the flow rule that best describes the plastic flow of cellular solid is also investigated. An incremental plasticity framework is proposed to describe the pressure-dependent plastic flow of 2D stochastic cellular solids. The proposed plasticity framework adopts the anisotropic and pressure-dependent yield function recently introduced by Alkhader and Vural [Alkhader M., Vural M., 2009a. An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations. J. Mech. Phys. Solids 57(5), 871–890]. It has been shown that the proposed yield function can be simply calibrated using elastic constants and flow stresses under uniaixal loading. Comparison of stress fields predicted by continuum plasticity model to the ones obtained from FE analysis shows good agreement for the range of loading paths and strains investigated.     

Experimental Study and Fractal Analysis of Heterogeneity in Naturally Fractured Rocks

Capillary pressure curves of six low porosity and low permeability core samples from The Geysers geothermal field were measured using the mercury-intrusion approach to characterize the heterogeneity of rock. One high permeability Berea sandstone core sample was analyzed similarly, for comparison. The maximum pressure of mercury intruded into the rock was about 200 MPa to reach the extremely small pores. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of the Berea sandstone. It was found that the frequently used capillary pressure models could not be used to represent the data from The Geysers rock samples. This might be because of the fractures in the rock. To this end, a fractal technique was proposed to model the features of the capillary pressure curves and to characterize the difference in heterogeneity between The Geysers rock and Berea sandstone. The results demonstrated that the rock from The Geysers geothermal field was fractal over a scaling range of about five orders of magnitude. The values of the fractal dimension of all the core samples (six from The Geysers and one Berea sandstone) calculated using the proposed approach were in the range from 2 to 3. The results showed that The Geysers rock with a high density of fractures had a greater fractal dimension than Berea sandstone which is almost without fractures. This shows that The Geysers rock has greater heterogeneity, as expected.     

First-order gradient damage theory

Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.     

An analytical soluion of wave forces on large square cylinder

Wave forces on large square cylinder are determined by using the conformal transformation method. It is found that only for square cylinder, the governing equation is still the Helmholtz equation after the conformal transformation. An analytical solution of wave forces on square cylinder is presented by using the solution of wave forces on a circular cylinder.     

宏微观渐进展开损伤本构模型及其在碳纤维增强复合材料中的应用

基体开裂、纤维拔出、界面剥离等是碳纤维增强复合材料常出现的局部各向异性损伤现象,这些损伤逐渐扩展,削弱了材料的强度和刚度,影响材料的承载能力.对此利用宏微观摄动理论对位移进行双范围渐进展开,在微观位移中引入损伤应变,通过计算损伤应变集中因子,得到了含损伤的均质化损伤弹性常数(宏观有效刚度矩阵),用平均法和混合法检验了无...     

On a finite-strain viscoplastic law coupled with anisotropic damage: theoretical formulations and numerical applications

Based on a dissipation inequality at finite strains and the effective stress concept, a Chaboche-type infinitesimal viscoplastic theory is extended to finite-strain cases coupled with anisotropic damage. The anisotropic damage is described by a rank-two symmetric tensor. The constitutive law is formulated in the corotational material coordinate system. Thus, the evolution equations of all internal variables can be expressed in terms of their material time derivatives. The numerical algorithm for implementing the material model in a finite element programme is also formulated, and several numerical examples are shown. Comparing the numerical simulations with experimental observations indicates that the present material model can describe well the primary, secondary and tertiary creep. It can also predict the anisotropic damage modes observed in experiments correctly.     

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.