再生混凝土与钢筋粘结滑移性能的试验研究及力学分析

良好的粘结性能是确保再生混凝土与钢筋能够共同工作的前提条件。通过120个试件的拉拔试验,并结合非平衡态热力学与损伤力学的相关理论分析再生混凝土与钢筋间的粘结滑移性能。提出三段式的粘结滑移本构模型,对比表明该模型对实测粘结滑移曲线具有较好的模拟效果。分析了粘结破坏过程中的能量守恒与能量耗散特性,给出了耗散能与弹性变形能代表值的计算公式,探讨了初始弹性变形能与极限弹性变形能的关系,并基于本构破坏能,对影响粘结性能的因素进行了分析。提出相对损伤变量的概念,定义了界面相对损伤变量,推导出相对损伤滑移方程,分析了界面初始损伤、界面损伤发展阶段以及界面损伤的发展速度。研究结果可为推广应用钢筋再生混凝土结构提供基础研究资料。     

Viscoelastic-damage interface model formulation with friction to simulate the delamination growth in mode II shear

In this paper a formulation of a viscoelastic-damage interface model with friction in mode-II is presented. The cohesive constitutive law contains elastic and damage regimes. It has been assumed that the shear stress in the elastic regime follows the viscoelastic properties of the matrix material. The three element Voigt model has been used for the formulation of relaxation modulus of the material. Damage evolution proceeds according to the bilinear cohesive constitutive law combined with friction stress consideration. Combination of damage and friction is based on the presumption that the damaged area, related to an integration point, can be dismembered into the un-cracked area with the cohesive damage and cracked area with friction. Samples of a one element model have been presented to see the effect of parameters on the cohesive constitutive law. A comparison between the predicted results with available results of end-notched flexure specimens in the literature is also presented to verify the model. Transverse crack tension specimens are also simulated for different applied displacement velocities.     

考虑材料组成特性的混凝土轴拉破坏过程细观数值模拟

为反映骨料、砂浆及其之间的界面过渡区的组合特点和材料性能,基于材料细观非均匀性和有限元方法的混凝土破坏过程细观数值模拟需进行复杂、细致的网格剖分,导致了繁重的前处理工作和可观的计算量。该文对混凝土材料细观单元材质组成的单一化假定进行改进,将内嵌界面过渡区材料的规则化单元视为一种广义复合材料单元,建立了复合型界面损伤模型。采用等效方法确定单元的复合弹性关系,通过有限元法计算单元的局部应力;用细观层次上弹性力学性能的弱化描述单元组成材料的损伤,混凝土材料的破坏过程通过单元各组分的损伤模拟。应用该复合型界面损伤模型研究了混凝土试件的单轴拉伸破坏过程,细观数值模拟结果符合混凝土试件的宏观破坏特征,表明该模型可作为分析混凝土材料破坏过程的一种有效途径。     

Impact of a 3D Woven Textile Composite Thin Panel: Damage and Failure Modeling

An orthotropic elastic resultant shell constitutive model is presented. The constitutive model includes a Tsai-Wu failure criterion to indicate the onset of material failure, and an isotropic scalar damage formulation is incorporated to describe the postfailure material reponse. The model has been implemented in the explicit finite-element code DYNA3D. The model was used to simulate the response of a flat-panel impact test with severe damage. Comparisons with a representative sample from the experimental results, including details of one strain history, are presented. While not addressing the many material complexities of 3D woven textile composites, the resulting engineering tool appears to be useful for assessing the response of thin textile composite structures subjected to damaging impacts.     

Mean field estimates of the response of fiber composites with nonlinear interface

This paper presents a theory of the effective response of composites containing general, nonlinearly separating inclusion–matrix interfaces. The direct method of composite materials theory is utilized to pass from local nonlinear behavior of a solitary inclusion problem to nonlinear aggregate response. Interaction effects at finite volume concentration are captured in the representative solitary problem by employing the Mori–Tanaka mean field estimate. The resulting model falls within the conceptual framework of continuum damage mechanics in that nonlinear effective response depends on internal variables that are governed by local evolution equations. The damage variables turn out to be the expansion coefficients arising in an eigenfunction representation of the displacement jump at a representative inclusion–matrix interface. Interfaces are generally modeled according to a nonlinear force-separation law that allows for both normal and shear decohesion (X-.P. Xu, A. Needleman, Modell. Simul. Mater. Sci. Eng. 1 (1993) 111). Detailed calculations of effective stress–strain response are carried out for the case of transverse shear and plane dilatation of unidirectional fiber composites at various values of concentration and interface constitutive constants. The effects of the various parameters on bifurcation of equilibrium separation in the solitary inclusion problem and on overall composite stability are demonstrated as well.     

Meso-Scale Progressive Damage Behavior Characterization of Triaxial Braided Composites under Quasi-Static Tensile Load

Based on continuum damage mechanics (CDM), a sophisticated 3D meso-scale finite element (FE) model is proposed to characterize the progressive damage behavior of 2D Triaxial Braided Composites (2DTBC) with 60° braiding angle under quasi-static tensile load. The modified Von Mises strength criterion and 3D Hashin failure criterion are used to predict the damage initiation of the pure matrix and fiber tows. A combining interface damage and friction constitutive model is applied to predict the interface damage behavior. Murakami-Ohno stiffness degradation scheme is employed to predict the damage evolution process of each constituent. Coupling with the ordinary and translational symmetry boundary conditions, the tensile elastic response including tensile strength and failure strain of 2DTBC are in good agreement with the available experiment data. The numerical results show that the main failure modes of the composites under axial tensile load are pure matrix cracking, fiber and matrix tension failure in bias fiber tows, matrix tension failure in axial fiber tows and interface debonding; the main failure modes of the composites subjected to transverse tensile load are free-edge effect, matrix tension failure in bias fiber tows and interface debonding.     

Effect of Constitutive Parameters on Cavity Formation and Growth in a Class of Incompressible Transversely Isotropic Nonlinearly Elastic Solid Spheres

Cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres are described as a bifurcation problem, for which the strain energy density is expressed as a nonlinear function of the invariants of the right Cauchy-Green deformation tensor. A bifurcation equation that describes cavity formation and growth is obtained. Some interesting qualitative properties of the bifurcation equation are presented. In particular, cavitated bifurcation is examined for a solid sphere composed of an incompressible anisotropic Gent-Thomas material model with a transversely isotropy about the radial direction. The effect of constitutive parameters on cavity formation and growth is then carried out. It is proved that a cavity forms in the interior of the sphere earlier or later than that in the isotropic Gent-Thomas sphere as the anisotropic parameter takes certain values. The condition for the bifurcation to the left or to the right of the cavity solution is proposed. The stability and the catastrophe of the equilibrium solutions are discussed by using the minimal potential energy principle. Whereas, in contrast to other isotropic nonlinear elastic spheres, cavitated bifurcation in the isotropic Gent-Thomas sphere is quite different, it is proved that the cavity solution can bifurcate locally to the left. The growth of a pre-existing micro-void in the sphere is examined, which interprets the physical implications of the preceding bifurcation problem.     

基于能量的弹塑性损伤实用本构模型

建立一个实用的弹塑性损伤本构模型。在有效应力空间采用经验公式计算塑性变形,能将模型塑性部分与损伤部分解耦,降低模型的数值处理复杂性,同时大大简化模型塑性应变的计算。结合不可逆热力学理论,基于损伤能量释放率建立损伤准则,损伤能量释放率由修正后的弹性Helmholtz自由能导出,模型中将弹性Helmholtz自由能分解为应力球量部分和应力偏量部分,将其应力球量部分产生的损伤取为零,同时根据应力状态引入折减系数对其应力偏量部分进行修正,使得模型能较为准确的模拟混凝土材料在双轴加载下的本构行为。将应力张量谱分解为正、负两部分以分别定义材料受拉、受压损伤演化,并采用受拉损伤变量、受压损伤变量分别模拟混凝土材料在拉、压加载下的本构特性。引入一个加权损伤变量使得模型能较准确的反映混凝土材料的“拉-压软化效应”。最后该文给出初步试验验证,证明了该文模型的有效性。     

3D constitutive model of anisotropic damage for unidirectional ply based on physical failure mechanisms

A 3D anisotropic continuum damage model is developed for the computational analysis of the elastic–brittle behaviour of fibre-reinforced composite. The damage model is based on a set of phenomenological failure criteria for fibre-reinforced composite, which can distinguish the matrix and fibre failure under tensile and compressive loading. The homogenized continuum theory is adopted for the anisotropic elastic damage constitutive model. The damage modes occurring in the longitudinal and transverse directions of a ply are represented by a damage vector. The elastic damage model is implemented in a computational finite element framework, which is capable of predicting initial failure, subsequent progressive damage up to final collapse. Crack band model and viscous regularization are applied to depress the convergence difficulties associated with strain softening behaviours. To verify the accuracy of the damage model, numerical analyses of open-hole laminates with different lay-up configurations under tension and compression were performed. The numerical predictions were compared with the experimental results, and satisfactory agreement was obtained.     

复合材料DCB试件裂纹扩展理论分析

在弹性地基梁模型基础上,通过挠度与相对位移关系引入了双线性cohesive本构关系,并通过界面损伤因子统一描述界面损伤状态,在裂纹尖端考虑了损伤黏聚区存在,分别获得了各段通解。采用连续性边界条件求解积分常数,并以裂纹长度以及黏聚区范围为变量求解获得了载荷-位移曲线,从而获得了双悬臂梁（DCB）试件裂纹扩展过程。通过与已有理论模型结果对比,验证了本文理论分析的正确性,而文中理论考虑了弹性段后非线性的存在,且可同时考察3个cohesive参数的影响。通过研究界面参数变化对载荷-位移曲线的影响,从而对准确模拟界面时cohesive参数的选取提供一定的依据,并分析了界面参数与黏聚区长度的关系。     

Delamination study of through-thickness reinforced composite laminates via two-phase interface model

A technique to enhance the strength of the composite laminates in the thickness direction consists in inserting through-thickness reinforcement, by which the potential delamination crack faces are bridged in order to increase the interlaminar fracture strength. In this paper, the composite delamination is analyzed in the context of non-linear fracture mechanics making use of the interface concept. The presence of the reinforcement fibres provides an anisotropic elastic and post-elastic mechanical response, which herein is described by an original two-phase interface model. The two phases, namely the adhesive joint (or matrix of the composite) and the reinforcement, are characterized by their own constitutive laws and coupled at the equilibrium level.     

Combining interface damage and friction in a cohesive‐zone model

A new method to combine interface damage and friction in a cohesive‐zone model is proposed. Starting from the mesomechanical assumption, typically made in a damage‐mechanics approach, whereby a representative elementary area of the interface can be additively decomposed into an undamaged and a fully damaged part, the main idea consists of assuming that friction occurs only on the fully damaged part. The gradual increase of the friction effect is then a natural outcome of the gradual increase of the interface damage from the initial undamaged state to the complete decohesion. Suitable kinematic and static hypotheses are made in order to develop the interface model whereas no special assumptions are required on the damage evolution equations and on the friction law. Here, the Crisfield's interface model is used for the damage evolution and a simple Coulomb friction relationship is adopted. Numerical and analytical results for two types of constitutive problem show the effectiveness of the model to capture all the main features of the combined effect of interface damage and friction. A finite‐step interface law has then been derived and implemented in a finite‐element code via interface elements. The results of the simulations made for a fibre push‐out test and a masonry wall loaded in compression and shear are then presented and compared with available experimental results. They show the effectiveness of the proposed model to predict the failure mechanisms and the overall structural response for the analysed problems. Copyright © 2006 John Wiley & Sons, Ltd.     

Assessment of bonding stresses between FRP sheets and masonry pillars during delamination tests

Under the simplifying assumption of perfect adhesion, motivated by the wide adoption of highly resistant glues, delamination of FRP-reinforced masonry pillars turns out to be governed exclusively by the non-linear behavior of the quasi-brittle, heterogeneous support. However, at the structural level, the macroscopic delamination response can be described effectively by concentrating all the sources of dissipation and non-linearity at the masonry-FRP interface, and assuming the support to behave as a linear-elastic body. In this paper, a detailed and critical comparison between two different fully three-dimensional finite element models is developed: (i) a model in which only masonry (i.e. brick and mortar independently) is damageable whilst the FRP reinforcement adheres perfectly to the support (namely, exclusively bulk damage is accounted for), and an alternative model (ii) in which a cohesive, zero thickness interface between the FRP and the support is considered (i.e. interface damage), whilst masonry behaves as a heterogeneous linear elastic material. The overall response during delamination and local stress distributions at the interface are critically investigated, varying the FRP reinforcement width.     

有限变形下材料的弹塑性损伤行为及结构响应分析

该文基于一种弹塑性损伤本构模型,分析了材料在有限变形下的力学行为及结构力学响应。将模型建立的本构方程进行线性化处理,嵌入到有限元计算软件ABAQUS的子程序中,实现模型在结构计算中的应用。针对铝合金材料(6061-T6),建立了两种不同的结构模型进行数值模拟。模拟结果与实验结果对比表明,模型能较好地描述材料的变形过程及结构的力学行为。最后基于模型的理论基础,分析了材料在超出弹性范围时的复杂变形行为。     

Constitutive equation for a class of non-simple elastic materials

Summary Initial yield is the upper limit of the purely elastic deformation behaviour of an elasticplastic solid. Thus the choice of the constitutive equation describing the purely elastic deformation behaviour determines the initial yield function. The constitutive equation of a simple elastic material is only compatible with von Mises yield criterion, a conclusion which applies also to the classical infinitesimal theory. A more general form of constitutive equation for an elastic material is formulated by way of the concept of a stress loading function, the proposed constitutive equation being quadratic in the stress. The two loading coefficients associated with the stress loading function are assumed to be deriveable from a generalised isotropic yield criterion which is now assumed to hold over the entire range of deformation, and in this context is referred to as the stress intensity function. The proposed constitutive equation has the same representation in terms of the left Cauchy-Green deformation tensor as that for a simple elastic material. Using the Cayley-Hamilton theorem, this representation is rearranged and expressed in terms of a measure of finite strain which is defined to be one quarter of the difference between the left Cauchy-Green deformation tensor and its inverse. In this way the strain properties of the proposed constitutive equation are formulated by way of the concept of a strain response function. The three response coefficients associated with the strain response function are assumed to be deriveable from a generalised, isotropic, strain intensity function. The predictions of the proposed constitutive equation are considered in the context of the combined stressing of a thin sheet of incompressible material. In this way, it is shown that the proposed constitutive equation is not limited in the same way as the constitutive equation of a simple elastic material.     

Load transfer in a composite containing a broken fiber with imperfect bonding

The effect of interface behavior on the local deformation field is studied by analyzing a composite consisting of a broken fiber imperfectly bonded to its surronding matrix. The fiber-matrix interface is modelled by constitutive relations that specify the value of the shear stress in terms of the relative displacements of the fiber and the matrix along the interface. Two different forms of constitutive relations are considered, one corresponding to an elastic interface model, another to a plastic interface model with possible debonding at sufficiently large interface displacement. The latter model is used to study the process of interface crack growth and fiber pull out. Analytic and numerical solutions are presented for the both models.     

Minimum bond length and size effects in FRP-substrate bonded joints

The load transfer mechanism between the fibre-reinforced polymer (FRP) materials and the substrate plays a crucial role in the overall response of retrofitted structural members. The FRP-support material interface can be studied by using pull tests in which a reinforcement plate is bonded to a prism and subjected to a tensile force. The experimental results obtained regard the assembly (FRP strip-support block), then a central problem is how to carry out the interface constitutive laws and the related parameters. The principal objective of the present paper is to contrive a procedure which, for a fixed interface constitutive law, permits to derive the interface mechanical parameters from the pull tests experimental data. This procedure has its basis on the size effect phenomena which the experimental tests evidence. Furthermore, the size effect laws show that the effective or minimum bond length coincides with the internal length of the interface and permits to distinguish small and large specimens in the sense of fracture mechanics.     

Damage-dependent viscoelastic constitutive relations for glass-fiber woven/polyester composite plate

A damage-dependent viscoelastic constitutive model for a glass-fiber woven/polyester composite plate is presented in this paper. The constitutive relations were derived within the framework of thermodynamics and continuum damage mechanics from some results of the necessary material tests. The elastic moduli and the damage variable of the material are assumed to be anisotropic. In this theoretical model, both the damage- and the time-dependent properties are phenomenological reflections on the macroscopic deformation process.     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。