Nonlinear finite element analyses of FRP-reinforced concrete slabs using a new layered composite plate element

A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite layered plate element is constructed based on Mindlin–Reissner plate theory and Timoshenko’s composite beam functions, and transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric nonlinearity and material nonlinearity of the materials, which incorporates tension, compression, tension stiffening and cracking of the concrete, are included in the new model. The developed element and the nonlinear finite element analysis procedures are validated by comparing the computed numerical results of numerical examples with those obtained from experimental investigations and from the commercial finite element analysis package ABAQUS. The element is then employed to investigate the nonlinear structural behavior and the cracking progress of a clamped two-way FRP-reinforced concrete slab. The influences of reinforcement with different materials, ratio and layout in tension or compressive regions on structural behavior of the clamped slabs are investigated by parametric studies.     

Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.     

Microstructure effects on transverse cracking in composite laminae by DEM

A particle discrete element method (DEM) was employed to simulate transverse cracking in laminated fiber reinforced composites. The microstructure of the laminates was modeled by a DEM model using different mechanical constitutive laws and materials parameters for different constituents, i.e. fiber, matrix and fiber/matrix interface. Rectangular, hexagonal and random fiber distributions were simulated to study the effect of fiber distribution on the transverse cracking. The initiation and dynamic propagation of transverse cracking and interfacial debonding were all captured by the DEM simulation, which showed similar patterns to those observed from experiments. The effect of fiber volume fraction was also studied for laminae with randomly distributed fibers. It was found that the distribution and volume fraction of fibers affected not only the transverse cracking path, but also the behavior of matrix plastic deformation and fiber/matrix interface yielding in the material.     

The transverse compression of PPTA fibers Part II Fiber transverse structure

The single fiber transverse compression test (SFTCT) is applied to KEVLAR and TWARON poly (para-phenyleneterephthalamide) fibers, both continuous filament and staple, and of varying denier and heat-treatment, as well as M5 rigid-rod fibers. Resulting force-deflection curves are analyzed by a Hertzian contact model, to give the effective transverse modulus, and estimate the stress state in the fiber at the onset of yield. Confocal microscopy and finite element simulation are used in conjunction with SFTCT to describe the inelastic, transverse deformation of PPTA. The effects of skin-core structure and anisotropy in the fiber cross-section are discussed.     

Response of boron carbide subjected to high-velocity impact

This article presents an evaluation of the response of boron carbide (B₄C) subjected to impact loading under three different conditions. Condition A is produced by plate-impact experiments where the loading condition is uniaxial strain and the stresses and pressures are high. Under plate-impact loading the material fails at the Hugoniot Elastic Limit (HEL) and the failed material undergoes high confining pressures and relatively small inelastic strains. Condition B is produced by projectile impact onto thick targets where the stresses and pressures are dependent on impact velocity, but they are generally lower than those from plate impact. Under thick-target impact/penetration most of the material fails under compression, the inelastic strains are large and the material appears to exhibit more ductility than under condition A. Lastly, condition C is produced by projectile impact and perforation of thin targets where the stresses and pressures are a combination of compression and tension. Under thin-target perforation the material fails in both tension and compression. The Johnson–Holmquist–Beissel (JHB) constitutive model is used to evaluate the material behavior for each of the three conditions, but it is not possible to accurately reproduce the experimental results of the three conditions with a single set of constants. Instead, three different sets of constants are required to accurately model the three impact conditions. These three models/constants are used to provide insight into the complex response of B₄C, and to identify possible mechanisms that are not included in the JHB model.     

An anisotropic discrete fiber model with dissipation for soft biological tissues

Nonlinear three-dimensional constitutive equations are developed for analyzing inelastic effects that cause dissipation in biological tissues. The model combines a structural icosahedral model of six discrete fiber bundles with a phenomenological model of the inelastic distortional deformations of the matrix containing the fibers. The inelastic response of the matrix is characterized by only three material parameters, which can be used to model both rate-independent and rate-dependent response with a smooth elastic-inelastic transition. Also, a robust, strongly objective scheme is discussed, which allows the model to be easily implemented into finite element computer codes. Examples show that the model predictions compare well with experimental data for the nonlinear, anisotropic, inelastic response of a number of tissues. Specifically, the model simulated the biaxial stretching of rabbit skin with an error of 15.7%, stress relaxation of rabbit skin with an error of 17.2%, simple shear of rat septal myocardium with an error of 21.6%, and uniaxial stress in compression of monkey liver with an error of 8.3%.     

An elastic-viscoplastic constitutive model for the hot-forming of aluminum alloys

Under hot-forming conditions characterized by high homologous temperatures and strain-rates, metals usually exhibit rate-dependent inelastic behavior. An elastic-viscoplastic constitutive model is presented here to describe metal behavior during hot-forming. The model uses an isotropic internal variable to represent the resistance offered to plastic deformation by the microstructure. Evolution equations are developed for the inelastic strain and the deformation resistance based on experimental results. A methodology is presented for extracting model parameters from constant true strain-rate compression tests performed at different temperatures. Model parameters are determined for an Al-1Mn alloy and an Al-Mg-Si alloy, and the predictions of the model are shown to be in good agreement with the experimental data.     

Nonlinear constitutive models for FRP composites using artificial neural networks

This paper presents a new approach to generate nonlinear and multi-axial constitutive models for fiber reinforced polymeric (FRP) composites using artificial neural networks (ANNs). The new nonlinear ANN constitutive models are complete and have been integrated with displacement-based FE software for the nonlinear analysis of composite structures. The proposed ANN constitutive models are trained with experimental data obtained from off-axis tension/compression and pure shear (Arcan) tests. The proposed ANN constitutive model is generated for plane–stress states with assumed functional response in some parts of the multi-axial stress space with no experimental data. The ability of the trained ANN models to predict material response is examined directly and through FE analysis of a notched composite plate. The experimental part of this study involved coupon testing of thick-section pultruded FRP E-glass/polyester material. Nonlinear response was pronounced including in the fiber direction due to the relatively low overall fiber volume fraction (FVF). Notched composite plates were also tested to verify the FE, with ANN material models, to predict general non-homogeneous responses at the structural level.     

基于共旋坐标和力插值纤维单元的RC框架结构连续倒塌构造方法

悬链机制会使钢筋混凝土框架结构产生有助于抵抗连续倒塌的附加承载能力,对结构抗连续倒塌能力至关重要。悬链机制处于几何大变形和材料非线性下降段的状态下,需要同时考虑材料非线性和几何非线性,因此对数值分析模型提出了更高的要求。为了解决基于力插值的纤维单元同时处理材料非线性和几何非线性的问题,该文采用基于共旋坐标法,提出了一种基于共旋坐标法的力插值纤维单元。该单元在形成中把变形体和刚体分开,局部坐标系的变形体内采用纤维划分考虑材料非线性,然后加上刚体位移,从局部坐标系到整体坐标系的转换中采用共旋坐标法以考虑几何非线性,给出了二维单元形成原理及非线性求解过程。实例分析结果表明基于共旋坐标法的力插值纤维单元能够较准确的模拟RC框架结构连续倒塌,梁机制阶段主要是材料非线性起控制作用,悬链线机制阶段主要是几何非线性起控制作用。     

针刺C/C-SiC复合材料剪切非线性本构关系

为研究针刺C/C-SiC复合材料的剪切损伤行为,首先,进行了面内剪切加卸载实验,并利用SEM对复合材料的剪切破坏形貌进行了观测;然后,建立了一种塑性与损伤相结合的非线性本构模型描述复合材料的非线性力学行为,以幂函数描述等效塑性应变与等效应力的关系;最后,基于剪切强度的Weibull分布规律提出了一种指数型损伤变量表征剪切刚度的退化,并通过实验数据拟合得到模型中的参数。结果表明:复合材料在卸载后存在明显的残余应变,卸载模量随载荷的增加不断降低,表现出明显的剪切非线性特征;大量无纬布纤维束和纤维单丝拔出,且易在针刺部位发生破坏;由于针刺部位等缺陷的不规律分布,剪切强度存在一定的分散性,符合指数型Weibull统计分布规律;复合材料的剪切非线性主要由基体开裂和纤维/基体界面脱粘等内部损伤引起,从宏观上可以解释为塑性变形和刚度性能折减。所得结论表明本构模型能够很好地表征C/C-SiC复合材料的面内剪切非线性行为。      

Static Response of Geometrically Nonlinear Laminated Composite Plates Having Uncertain Material Properties

The effect of uncertainty in material properties on the transverse bending of laminated composite plate is investigated. The transverse shear and large rotations have been included in the system equation in the framework of higher order shear deformation theory. The analysis uses Green–Lagrange nonlinear strain displacement equations to model geometric nonlinearity. The stochastic finite element analysis is performed using a direct iteration approach to handle deterministic geometric nonlinearity and perturbation approach to handle the randomness in the material properties. Mean and variance of the transverse deflection have been obtained by employing a C⁰ isoparametric nonlinear finite element model.     

Large inelastic strain analysis by multilayer shell elements

Summary The objective of this contribution is to model large inelastic strains of ductile metals, to couple this material model with a multilayer shell kinematics and finally to achieve a finite element formulation applicable in general form to shell analysis. Elasto-plastic constitutive law is formulated by using the multiplicative decomposition of the deformation gradient and Neo-Hookean model for elastic strains assuming an overall isotropic material behavior. These 3D-material model is then enforced directly into a multilayer shell kinematics which provides a very accurate consideration of local effects, particularly stresses across the thickness. Finite element formulation is accomplished by means of the enhanced strain concept. Thus the well known deficiencies due to incompressible deformations and the inclusion of transverse strains are avoided. Several examples are given to demonstrate the performance of the algorithms developed concerning various aspects.     

A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension

A computational model based on the finite element method is presented for the estimation of strength of a fiber-reinforced lamina subjected to a combination of the transverse compression and axial tension. A complex damage mechanism including fiber breakage, fiber/matrix debonding and matrix plastic deformation is reproduced in the proposed model by using appropriate constitutive equations. The numerical simulation of mechanical response of the unidirectional lamina under biaxial loading is used to obtained the failure locus. Subsequently, the model is verified against an analytical solution and experimental data. It was found that the numerical calculations agree better with experimental results than analytical predictions.     

单向纤维增强聚合物复合材料压缩渐进破坏单向纤维增强聚合物复合材料压缩渐进破坏

复合材料结构在承压时破坏如何演化,是其强度破坏分析的基础和核心任务。本文提出了基于连续介质损伤力学（CDM）的单向纤维增强聚合物复合材料压缩破坏渐进损伤分析（PDA）模型。建模中考虑了材料非线性行为、失效判断及损伤演化中材料性能退化等基本问题,分别对应于拉压不对称弹塑性本构关系、Puck准则、LaRC05准则及考虑破坏面方向的刚度退化方法。该模型通过用户材料子程序接口VUMAT引入到有限元软件ABAQUS中实现了有限元求解。对文献中提供的纵向、横向及偏轴压缩案例进行了数值计算并与试验数据对比。数值分析结果与试验数据吻合较好,证明了该方法的合理性和有效性,对开展多向层合板压缩破坏分析富有参考价值。      

Modeling the inelastic deformation and fracture of polymer composites – Part I: Plasticity model

A new transversely-isotropic elastic–plastic constitutive model for unidirectional fiber reinforced polymers (FRP) is presented. The model is able to represent the fully nonlinear mechanical behavior under multi-axial loading conditions and under triaxial stress states prior to the onset of cracking. Since associated flow rules often give a wrong prediction of plastic Poisson coefficients, a non-associated flow rule is introduced to provide realistic predictions of the volumetric plastic strains. This paper focusses on the simulation of triaxiality dependent plasticity based nonlinearities of FRP until failure occurs. The onset and propagation of failure is predicted by a new smeared crack model presented in an accompanying paper (Camanho et al., 2012). In order to demonstrate the capabilities of the new material model, a yield surface parameter identification for IM7-8552 carbon epoxy is presented and simulations of quasi-static transverse and off-axis compression tests and of uniaxial compression tests superimposed with various values of hydrostatic pressure are shown as a model verification.     

A nonlinear fractional viscoelastic material model for polymers

In this contribution a test scheme based on tensile tests at different velocities, relaxation experiments and deformation controlled loading and unloading processes with intermediate relaxations has been used to experimentally characterize the nonlinear, inelastic material behavior. Based on the experimental observations a small strain nonlinear fractional viscoelastic material model is derived. In order to use the model within a finite element analysis, the constitutive equations have been generalized for the multiaxial case. The experimental test scheme and the fractional viscoelastic material model are subsequently applied to characterize and compute the mechanical behavior of the thermoplastic Polypropylene. After the identification of the material parameters several uniaxial and multiaxial simulations have been carried out and compared with experimental results.     

Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites

Damage constitutive models based on micromechanical formulation and a combination of micromechanical and macromechanical damage criterions are presented to predict progressive damage in aligned and random fiber-reinforced composites. Progressive interfacial fiber debonding models are considered in accordance with a statistical function to describe the varying probability of fiber debonding. Based on an effective elastoplastic constitutive damage model for aligned fiber-reinforced composites, micromechanical damage constitutive models for two- and three-dimensional (2D and 3D) random fiber-reinforced composites are developed. The constitutive relations and overall yield function for aligned fiber orientations are averaged over all orientations to obtain the constitutive relations and overall yield function of 2D and 3D, random fiber-reinforced composites. Finally, the present damage models are implemented numerically and compared with experimental data to show the progressive damage behavior of random fiber-reinforced composites. Furthermore, the damage models will be implemented into a finite element program to illustrate the dynamic inelastic behavior and progressive crushing in composite structures under impact loading.     

复合材料层合板非线性热屈曲分析

本文基于高阶变形理论和修正型Hahn-Tsai非线性本构模型,提出一种复合材料层合板非线性热屈曲分析方法.针对四边简支反对称角铺设复合材料层合板,导出了非线性热屈曲临界温度封闭解.数值结果表明:材料非线性能显著降低层合板临界温度.      

Constitutive relations for cracked metal matrix composites

A method is given for the prediction of the overall stress-strain response of elastoplastic solids containing a doubly periodic rectangular array of cracks. The behavior of the undamaged inelastic material is represented by constitutive laws for metal matrix composites based on a micromechanics analysis. The effect of cracking is incorporated by adopting a second order expansion of the displacement vector, in conjunction with the equations of equilibrium and displacement and traction continuity conditions. Due to the nonlinearity and path dependence of deformation, the stresses need to be represented by a higher order expansion than the second. The method is implemented to predict the overall stress-strain response of a cracked isotropic inelastic material, as well as cracked unidirectional and laminated metal matrix composites.     

Damage Dependent Constitutive Behavior and Energy Release Rate for a Cohesive Zone in a Thermoviscoelastic Solid

In this paper a cohesive zone is introduced ahead of a crack tip in order to avoid the singularity at the crack tip. By applying thermodynamics to the cohesive zone and the surrounding body, a fracture criterion will be established so that the inelastic energy dissipation both in the cohesive zone and the surrounding bulk material can be distinguished from the energy released by fracture, and the propagation of crack can be predicted. In addition, the cohesive zone constitutive equation is constructed utilizing the Helmholtz free energy in the form of a single hereditary integral for a nonlinear viscoelastic material. The resulting constitutive model for the cohesive zone contains an internal state variable which represents the damage state within the cohesive zone. When the cohesive zone opening displacement is known, the energy release rate is thus history dependent, which is expressed in terms of the damage state, the length of separation in the cohesive zone and the geometric configuration of the cohesive zone opening displacement. Example results contained herein demonstrate this effect. This revised version was published online in July 2006 with corrections to the Cover Date.