Numerical simulation of interface debonding with a combined damage/friction constitutive model

 Experimental studies for pull-out tests in fiber-reinforced composites reveal a softening behaviour due to interface crack growth between fiber and matrix followed by a contact friction behaviour on the cracked area. In this contribution this debonding process is modelled within the framework of interface damage mechanics, where the displacement discontinuities during the progressive decohesion are related to constitutive equations extended by an anisotropic damage model. The contact/friction behaviour after complete separation is described by a friction model analogously to the classical theory of plasticity. The simulation of the load-displacement curve in the pull-out test with the drop-off behaviour is achieved by introducing a Hermite polynomial. The numerical simulations are performed for glas/polystyrol fiber-reinforced composites, thus illustrating the progressive debonding and friction between both constituents and demonstrating a good agreement with experimental data of a pull-out test. Received 18 November 1999     

Nonlinear constitutive model for time-dependent behavior of FRP-concrete interface

The constitutive behavior of the FRP-concrete interface is a prime issue when evaluating the strengthening effects of concrete structures strengthened with externally bonded fiber-reinforced polymer (FRP) sheets or plates. This paper is devoted to developing a new nonlinear viscoelastic model for the study of the long-term behavior of the FRP-concrete interface. The model has the ability to describe the creep of the FRP-concrete adhesive layer and the creep fracture propagation along the FRP-concrete interface. The linear viscoelastic behavior of the FRP-concrete interface is taken into account by using Maxwell’s generalized rheological model through a step-by-step time increment procedure. The nonlinear time-dependent behavior of the adhesive layer is considered through the micro slip criterion model (MSCM), which depends on a displacement failure criterion and the interfacial fracture energy. The proposed model is implemented with a finite element model and it has been calibrated by using the results of time-dependent double-lap shear test specimens. The results demonstrate the reliability of the proposed model and its capability to predict the time-dependent debonding propagation along the FRP-concrete interface. It is also shown that the model can be used to predict a wide range of creep fractures not only under low sustained loading but also under high sustained loading.     

重组竹-混凝土界面粘结-滑移本构模型

为研究胶粘剂连接的重组竹-混凝土界面粘结性能及构建粘结-滑移本构模型,对44个重组竹-混凝土粘结试件进行单剪试验,并考虑了粘结长度、重组竹粘结宽度与厚度、混凝土强度及胶层厚度等因素对粘结性能的影响。研究结果表明：在不同影响因素下,试件破坏模式基本相同,均为混凝土表面发生剥离破坏,粘结界面间裂缝从加载端产生并向自由端发展,破坏过程分为弹性阶段、软化阶段和脱粘平台阶段;界面峰值剪应力随重组竹厚度、混凝土强度、胶层厚度增加而增大,随粘结宽度增加而减小。根据试验粘结-滑移曲线,建立了重组竹-混凝土界面粘结-滑移本构模型,与实验结果进行对比,该模型能较好地反映重组竹-混凝土界面剪应力与滑移量间的关系。     

A fractal model for the static coefficient of friction at the fiber-matrix interface

The physical, geometrical, and mechanical properties at the fiber/matrix interface of a fiber-reinforced composite material have a dominant effect on the overall mechanical behavior of these materials. Specifically, the toughening of these materials is largely attributed to the energy dissipation due to the frictional sliding of fibers at their interface with the matrix material. The micromechanisms involved with interfacial failure and sliding are currently not entirely understood, and the failure threshold is generally predicted using macro-scale friction laws which neglect the micromechanical aspects. The objective of this study is to explore the derivation of a macro-scale static coefficient of friction at the interface of a previously debonded fiber based on the micro-scale properties of the contacting surfaces. Presented results illustrate that the macro-scale static coefficient of friction obtained from the proposed micro-scale model is independent of the normal load and is therefore consistent with the classical Amontons-Coulomb phenomenological laws of friction.     

A hyper-viscoelastic constitutive model for polyurea

This letter presents a new constitutive model for polyurea by superposing the hyperelastic and viscoelastic behaviors of polyurea. The Ogden model is used for the hyperelastic part and its parameters are determined from curve fitting of quasi-static test data. A nonlinear viscoelastic model is employed for describing the viscoelastic behavior and its relaxation time is obtained based on the test data of shear relaxation modulus. A special form of Zapas kernel for the damping function is found to be very effective to capture the viscoelastic behavior of polyurea subjected to wide ranges of strain rate. Both the versatility and accuracy of the model are examined via virtual testing.     

A viscoplastic constitutive model for dynamic fracture

The use of a viscoplastic approach to dynamic fracture prediction is proposed with the aim of producing a model which is applicable to ductile situations. A numerical (finite-element) approach is adopted with specially developed joint elements being used to simulate behaviour within the fracture-process zone. Results are presented for an expanding edge-crack problem. Experimental results are used to calibrate the numerical model by determining the material-specimen parameters under dynamic-fracturing conditions. Detailed results are presented for both LEFM and nonlinear fracture-mechanics approaches.     

土与结构接触面土体软/硬化本构模型及数值实现

将非饱和土广义有效应力原理与三剪强度准则相结合,提出了非饱和土广义有效应力三剪强度准则。将所提准则作为破坏准则,分别采用等量代换法和坐标平移法推导出新的破坏应力比,并将其与非饱和土修正剑桥模型相结合得到了新的屈服函数。相比于原来修正剑桥模型中的破坏应力比为定值,新的屈服函数可以更好地反应土体全应力状态、中间主应力效应和拉压不等效应。在弹塑性理论的框架下,建立了非饱和土的广义有效应力三剪弹塑性本构模型。以江西正常固结非饱和重塑红黏土作为试验研究对象,进行室内土工试验、土水特征曲线试验、压缩回弹试验、非饱和土常规三轴固结排水试验。将该本构模型计算结果与非饱和土三轴固结排水试验结果进行对比验证。结果表明：数值模拟结果与试验结果吻合较好,验证了该本构模型的正确性。在轴向应变较小时,等量代换法和坐标平移法模拟结果比较接近,随着轴向应变增大直至偏应力达到平稳状态的过程中,等量代换法计算结果要大于坐标平移法计算结果,且更接近于试验值。真三轴计算预测结果表明：在固结排水条件下,初始压实度、净围压、基质吸力相同,中间主应力影响系数越大,则剪应力和体应变越大。b值相同的情况下,轴向应变较小时,等量代换法计算结果和坐标平移法计算结果比较接近,随着轴向应变的增大,二者之间的差值也越来越大。

     

A constitutive model for compressible elastomeric solids

A non-linear thermo-elastic constitutive model for the large deformations of isotropic materials is formulated. This model is specialized to account for the physics and thermodynamics of the elastic deformation of rubber-like materials, and based on these molecular considerations a constitutive model for compressible elastomeric solids is proposed. The new constitutive model generalizes the incompressible and isothermal model of Arruda and Boyce (1993) to include the compressibility and thermal expansion of these materials. The model is fit to existing experimental data on vulcanized natural rubbers to determine the material parameters for the rubbers examined. The fit between the simple model and the data is found to be very good for large stretches and moderate volume changes.List of symbols x\s=f(p) Deformation function - p Material point of a body in a reference configuration - x Place occupied by material point p in the current configuration - F(p)\eq(\t6/\t6p) f(p) Deformation gradient - J\s=det F\s>0 Determinant of F - F\s=RU\s=VR Polar decompositions of F - U, V Right and left stretch tensors; positive definite and symmetric - R Rotation tensor; proper orthogonal - U= _1–1 ³ ₁ ² r₁r₁ Spectral representation of U - V= ₁₌₁ ³ _t ² 1_t1₁ Spectral representation of V - _t > 0 Principal stretches - {r_i} Right principal basis - {l_i} Left principal basis - C\s=F ^T F, B\s=FF ^T Right and left Cauchy-Green strain tensors - \gq\s>0 Absolute temperature - \ge Internal energy density/unit reference volume - \gh Entropy density/unit reference volume - \gy\s=\ge\t-\gq\gh Helmholtz free energy/unit reference volume     

A multi-dimensional constitutive model for shape memory alloys

This paper presents a multi-dimensional thermomechanical constitutive model for shape memory alloys (SMAs). This constitutive relation is based upon a combination of both micromechanics and macromechanics. The martensite fraction is introduced as a variable in this model to reflect the martensitic transformation that determines the unique characteristics of shape memory alloys. This constitutive relation can be used to study the complex behavior associated with 2-D and 3-D SMA structures. A simple example using this constitutive model is also presented, which reveals a new and interesting phenomenon of 3-D SMA structures.     

A nonlinear elastic constitutive model for coated fabrics

A nonlinear elastic constitutive model for coated fabrics is developed. The model which accounts for the basic mechanisms of yarn rotation, yarn extension and coating extension is obtained by expressing the equations of equilibrium for a unit cell of the material in terms of effective continuum stresses and strains. A systematic method of determining the model parameters is proposed. Based on the parameters obtained from a single biaxial test, theoretical curves are plotted for various biaxial loading states and compared with experimental results for several commercially available structural fabrics.     

A non-orthogonal constitutive model for characterizing woven composites

Thermoforming of woven fabric reinforced composites usually results in significant in-plane shear deformation in materials, and induces additional anisotropy into the composite. In this paper, a new constitutive model for characterizing the non-orthogonal material behavior under large deformation is proposed. On the basis of stress and strain analysis in the orthogonal and non-orthogonal coordinates and the rigid body rotation matrices, the relationship between the stresses and strains in the global coordinates is obtained. The equivalent material properties are then determined by fitting the numerical load vs. displacement curves to experimental results under biaxial tension and pure shear conditions. This model can be used to efficiently predict material responses under various loading paths for woven composites with different weave architectures. The geometrical non-linearity and the material non-linearity, as well as the complex redistribution and reorientation of the warp and weft yarns during deformation are taken into account. To demonstrate the performance of this model, numerical simulations using a commercial finite element package (ABAQUS/Standard) incorporated with our material model are conducted for various loading cases. Numerical results are in excellent agreement with experimental data.     

A constitutive model for self-reinforced ductile polymer composites

Self-reinforced polymer composites are gaining increasing interest due to their higher ductility compared to traditional glass and carbon fibre composites. Here we consider a class of PET composites comprising woven PET fibres in a PET matrix. While there is a significant literature on the development of these materials and their mechanical properties, little progress has been reported on constitutive models for these composites. Here we report the development of an anisotropic visco-plastic constitutive model for PET composites that captures the measured anisotropy, tension/compression asymmetry and ductility. This model is implemented in a commercial finite element package and shown to capture the measured response of PET composite plates and beams in different orientations to a high degree of accuracy.     

A thermo-viscoelastic constitutive model for compressible amorphous polymers

We propose a compressible thermo-viscoelastic constitutive model at finite deformation for amorphous polymers. Firstly, the compressible hyperelastic deformation energy is extended to include thermal effect. Secondly, in order to describe the viscous property of the materials, internal variables are introduced into the above thermo-hyperelastic constitutive relation. As the Maxwell model is equivalent to the transient network model under certain condition, the rationality of introducing the internal variables for a general deformation mode is proved. The model only contains a few material parameters, just necessary for a complicated thermal-mechanical coupling system. Besides, this model provides an explanation for the deformation energy function from the microscopic mechanism. Based on this model, the influences of the loading rate, compressibility and the thermal expansion coefficient on the coupled thermo-mechanical behavior of polymers are discussed.     

A variational constitutive model for porous metal plasticity

This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.     

A constitutive model for frictional slip on rock interfaces

The shear stress required for frictional slip on rock interfaces is known to depend on the history of the slip velocity. At least one physical model that predicts this behavior also indicates that memory of past normal stresses may persist. A constitutive equation that incorporates memory of both past slip velocities and past normal stresses is proposed, and the appropriate physical property functions are identified. Once measured, these functions allow the computation of the shear stress on a slipping interface for general loading histories.     

A thermomechanical crystal plasticity constitutive model for ultrasonic consolidation

We present a micromechanics-based thermomechanical constitutive model to simulate the ultrasonic consolidation process. Model parameters are calibrated using an inverse modeling approach. A comparison of the simulated response and experimental results for uniaxial tests validate and verify the appropriateness of the proposed model. Moreover, simulation results of polycrystalline aluminum using the identified crystal plasticity based material parameters are compared qualitatively with the electron back scattering diffraction (EBSD) results reported in the literature. The validated constitutive model is then used to simulate the ultrasonic consolidation process at sub-micron scale where an effort is exerted to quantify the underlying micromechanisms involved during the ultrasonic consolidation process.     

A thermodynamically and microscopically motivated constitutive model for piezoceramics

Following the approach in [Smart. Mater. Struct. 9 (1999) 441], a constitutive model based on microscopically motivated internal variables is formulated for piezoceramics under multiaxial electromechanical loadings. The internal variables describe domain switching and reorientation in the material.     

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.     

On the constitutive relation of materials with microstructure using a potential-based cohesive model for interface interaction

Macroscopic constitutive relationship is estimated by considering the microscopic particle/matrix interfacial debonding. For the interfacial debonding, the PPR potential-based cohesive model is utilized. The extended Mori-Tanaka model is employed for micromechanics, while a finite element-based cohesive zone model is used for the computational model. Both models (theoretical and computational) agree well each other in representing the macroscopic constitutive relationship on the basis of the PPR model. The microscopic interfacial cohesive parameters of the PPR model are estimated from macroscopic composite material behavior. In addition, different microscopic debonding processes are observed with respect to different macroscopic constitutive relationships (e.g. hardening, softening, and snap-back).