Woven fabric composite material model with material nonlinearity for nonlinear finite element simulation

The objective of the current investigation is to develop a simple, yet generalized, model which considers the two-dimensional extent of woven fabric, and to have an interface with nonlinear finite element codes. A micromechanical composite material model for woven fabric with nonlinear stress-strain relations is developed and implemented in ABAQUS for nonlinear finite element structural analysis. Within the model a representative volume cell is assumed. Using the iso-stress and iso-strain assumptions the constitutive equations are averaged along the thickness direction. The cell is then divided into many subcells and an averaging is performed again by assuming uniform stress distribution in each subcell to obtain the effective stress–strain relations of the subcell. The stresses and strains within the subcells are combined to yield the effective stresses and strains in the representative cell. Then this information is passed to the finite element code at each material point of the shell element. In this manner structural analysis of woven composites can be performed. Also, at each load increment global stresses and strains are communicated to the representative cell and subsequently distributed to each subcell. Once stresses and strains are associated to a subcell they can be distributed to each constituent of the subcell i.e. fill, warp, and resin. Consequently micro-failure criteria (MFC) can be defined for each constituent of a subcell and the proper stiffness degradation can be modeled if desired. This material model is suitable for implicit and could be modified for explicit finite element codes to deal with problems such as crashworthiness, impact, and failure analysis under static loads.     

Deformation and failure in nanomaterials via a data driven modelling approach

A data driven computational model that accounts for more than two material states has been presented in this work. Presented model can account for multiple state variables, such as stresses,strains, strain rates and failure stress, as compared to previously reported models with two states.Model is used to perform deformation and failure simulations of carbon nanotubes and carbon nanotube/epoxy nanocomposites. The model capability of capturing the strain rate dependent deformation and failure has been demonstrated through predictions against uniaxial test data taken from literature. The predicted results show a good agreement between data set taken from literature and simulations.     

Andrade and critical time-to-failure laws in fiber-matrix composites: Experiments and model

We present creep experiments on fiber composite materials. Recorded strain rates and acoustic emission (AE) rates exhibit both a power-law relaxation in the primary creep regime and a power-law acceleration before global failure. In particular, we observe time-to-failure power-laws in the tertiary regime for acoustic emissions over four decades in time. We also discover correlations between some characteristics of the primary creep (exponent of the power-law and duration) and the time to failure of the samples. This result indicates that the tertiary regime is dependent on the relaxation and damage processes that occur in the primary regime and suggests a method for predicting the time to failure based on the early time recording of the strain rate or AE rate. We consider a simple model of representative elements, interacting via democratic load sharing, with a large heterogeneity of strengths. Each element consists of a non-linear dashpot in parallel with a spring. This model recovers the experimental observations of the strain rate as a function of time.     

Multi-scale modeling of the mechanical response of plain weave composites and cellular solids

Multi-component materials with customized mechanical properties, such as textile composites and sandwich materials (cellular core with metallic or composite skin), show a great prospective for use in aerostructures. Understanding of the mechanical response of these materials is still in progress. In the present paper, the tensile response of plain weave composites as well as the compressive response of cellular solids are investigated using a multi-scale damage model. The model, implemented by means of the FE method, is based on homogenized progressive damage modeling of a representative unit-cell. Four failure modes have been considered in the failure analysis of the tows, while material property degradation was performed using a damage mechanics approach which takes into account strain softening. For the cellular solids, two different types of FE models were considered namely, a beam model and a shell model. Failure analysis and material property degradation of the struts were integrated into a bilinear material model. Simulations show a non-linear tensile response of the plain weave mainly attributed to matrix cracking and shear failures occurring at warp tows and resin-rich areas. For the cellular solid, preliminary elastic analyses show a customizability of the normal stiffness with regard to strut’s dimensions.     

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion for high strain and ballistic applications is presented. A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson–Cook failure criterion. The weakening in the elastic law and in the Johnson–Cook-like constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. Additionally, the mesh size dependency on the prediction of the fracture patterns was studied, showing that was crucial to predict such patterns.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.     

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB).Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior.The goal of this paper is to present a new combined experimental–numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment.Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.     

Materially and geometrically non-linear woven composite micro-mechanical model with failure for finite element simulations

A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine the stiffness degradation for the constituent materials. The developed material model with failure is programmed as user-defined sub-routine in the LS-DYNA finite element code with explicit time integration. The code is used to simulate the failure behavior of woven composite structures. The results of finite element simulations are compared with available test results. The model shows good agreement with the experimental results and good computational efficiency required for finite element simulations of woven composite structures.     

A statistical model of microcracking of concrete under uniaxial compression

At increasing external load, numerous microcracks propagate in discrete and successive stages within a body of concrete material according to the hierarchy of their tensile fracture strengths. Each microcrack propagation is conditional upon the statistical encounter of its associated fracture criterion. This paper shows the development of a statistical model for the progressive microcrack growth process within a body of concrete material at monotonic uniaxial loading in compression to ultimate failure. This model is formulated by using the Weibull's statistical theory of the strength of materials. The body of heterogeneous concrete material is simulated as a continuum comprising a large population of microscopic “weakest-link” isoenergy elements, each of which contains a unit-volume of representative micro-structural material which is linearly elastic, homogeneous and isotropic. The statistical modelling is derived from the stochastic evaluation of the tensile micro-fracture probabilities of these isoenergy elements at increasing global uniaxial compressive strains.     

Dynamic limit analysis formulation for impact simulation of structural members

This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain hardening, strain-rate hardening and thermal softening. The time dependent term in the governing equation is integrated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-rate hardening and thermal softening as well as strain hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstrates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.     

多相孔隙介质的本构描述

在混合物理论的框架内,提出了一个处理和和非饱和的多相孔隙介质（工程材料）变形和强度本构建模的新方法,并给出了相应的具体描述,该方法将多相工程材料看成由两个层次的３种混合物模型组成,即第一层次的“固相”和“液相”混合物模型和第二层次的由“固相”和“液相”组成的混合物模型,用该模型来模拟要研究的多相工程材料,这里定义的“固相”和“液相”实际上也是由各自组分组成的混合物,用以反映“固相”介质和“液相”介     

Estimation of material properties of nanocomposite structures

A method for the numerical modelling of mechanical behaviour of nanocomposite materials reinforced with the carbon nanotubes, based on computational homogenization as a multi-scale method, is presented. Since the carbon nanotube inside of the representative volume element (RVE) is modelled as a space frame structure, theoretical background and a proper way of modelling of carbon nanotubes is given. Novelty in this paper is an incorporation of interactions, based on the weak van der Waals forces and modelled by nonlinear rod elements, into a multiscale model as described below. An algorithm is developed for analysis of those interactions. Since the problem of modelling nanocomposite structures is a three-dimensional multi-scale problem, one part of this work is dedicated to multi-scale modelling methods, especially to the first order computational homogenization. Computational homogenization and representative volume element are the basis of the presented numerical model of the nanocomposites. Nano scale model is based on beam and non-linear rod finite elements. For the purpose of the software verification, examples, i.e. models of the nanocomposite material are presented. Obtained results are compared with the results given by the other authors.     

具有恒定冲击载荷的梯度泡沫金属材料设计

多胞材料可通过大变形大量地吸收冲击能量，引入密度梯度可进一步提高其耐撞性。梯度多胞材料的宏观力学响应对材料密度分布极为敏感，不同类型的细观构型的影响也极为不同。已有的研究工作主要局限在对给定的密度梯度分析其动态响应，较少对耐撞性设计方法进行研究。本文针对梯度闭孔泡沫金属材料，基于非线性塑性冲击波模型发展了耐撞性反向设计方法，以维持冲击物受载恒定为目标，运用级数法获得了简化模型和渐近解。利用变胞元尺寸法构建了连续梯度变化的三维Voronoi细观有限元模型，并利用ABAQUS/Explicit有限元软件对理论设计进行数值验证。结果表明，反向设计理论简化模型的渐近解对于梯度闭孔泡沫金属材料的耐撞性设计是有效的，所提出的耐撞性设计方法在控制冲击吸能过程和冲击物受载方面具有指导意义。     

On the problem of interfacial damage in fibre-reinforced composites under variable loads

In this paper, the theoretical background for the failure analysis of fibre-reinforced composites under variable repeated loads in the framework of direct methods is presented. It is based on a local shakedown analysis in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite.     

A multi-mechanism model for cutting simulations combining visco-plastic asymmetry and phase transformation

We develop a multi-mechanism model for strainrate- and temperature-dependent asymmetric plastic material behavior accompanied by phase transformations, which are important phenomena in steel production processes. To this end the well-known Johnson–Cook model is extended by the concept of weighting functions, and it is combined with a model of transformation-induced plasticity (TRIP) based on Leblond’s approach. The bulk model is formulated within a thermodynamic framework at large strains, and it will be specialized and applied to cutting processes in steel production. In this prototype situation we have: Transformation of the martensitic initial state into austenite, then retransformation of martensite. For incorporation of visco-plastic asymmetry two variations of the classical Johnson–Cook model are presented: In “Model A” we introduce a rate dependent flow factor with a rate independent yield function. In “Model B” we introduce a rate independent flow factor with a rate dependent yield function. In the examples parameters are identified for the material DIN 100Cr6, and we illustrate the characteristic effects of our multimechanism model, such as strain softening due to temperature, rate dependence and temperature dependence as well as the SD-effect. A finite-element simulation illustrates the different mechanisms for a cutting process.     

A simple meso-macro model based on SQP for the non-linear analysis of masonry double curvature structures

A 3D model for the evaluation of the non-linear behavior of masonry double curvature structures is presented. In the model, the heterogeneous assemblage of blocks is substituted with a macroscopically equivalent homogeneous non-linear material. At the meso-scale, a curved running bond representative element of volume (REV) constituted by a central block interconnected with its six neighbors is discretized through of a few six-noded rigid wedge elements and rectangular interfaces. Non linearity is concentrated exclusively on joints reduced to interface, exhibiting a frictional behavior with limited tensile and compressive strength with softening. The macroscopic homogenous masonry behavior is then evaluated on the REV imposing separately increasing internal actions (in-plane membrane actions, meridian and parallel bending, torsion and out-of-plane shear). This simplified approach allows to estimate heuristically the macroscopic stress–strain behavior of masonry at the meso-scale. The non-linear behavior so obtained is then implemented at a structural level in a novel FE non-linear code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and non-linear interfaces, exhibiting deterioration of the mechanical properties.Several numerical examples are analyzed, consisting of two different typologies of masonry arches (a parabolic vault and an arch in a so-called “skew” disposition), a ribbed cross vault, a hemispherical dome and a cloister vault. To fully assess numerical results, additional non-linear FE analyses are presented. In particular, a simplified model is proposed, which relies in performing at a structural level a preliminary limit analysis – which allows to identify the failure mechanism – and subsequently in modeling masonry through elastic elements and non-linear interfaces placed only in correspondence or near the failure mechanism provided by limit analysis. Simulations performed through an equivalent macroscopic material with orthotropic behavior and possible softening are also presented, along with existing experimental evidences (where available), in order to have a full insight into the capabilities and limitations of the approach proposed.     

仿生波纹夹层结构耐撞性分析及优化

为提高薄壁夹层结构耐撞性,以虾螯为仿生原型,设计梯度分布的仿生波纹形夹层结构,包括单层、双层和三层波纹结构。以初始峰值载荷F_p、比吸能E_s为耐撞性指标,利用有限元法分析了单元高宽比γ（γ₁、γ₂和γ₃分别为单元第1层、第2层和第3层的高宽比）对波纹夹层结构耐撞性的影响,采用多目标粒子群优化方法得到了夹层结构最优参数。结果表明,单层波纹结构耐撞性随单元高宽比γ的增大逐渐变差,双层波纹结构下层结构单元高宽比γ对耐撞性的影响大于上层结构单元高宽比γ对耐撞性的影响,较小的γ值有利于提高三层波纹结构的比吸能。结构优化结果表明:单层结构最优尺寸γ₁为0.8;双层结构最优尺寸为γ₁ = 0.5和γ₂ = 1.2;三层结构最优组合为γ₁ = 0.6,γ₂ = 0.6和γ₃ = 0.9。上述结果可为薄壁夹层结构轻量化设计提供新思路。     

Local elastodynamic stresses in the unit cell of a woven fabric composite

Summary A theoretical study of the local elastodynamic stresses of woven fabric composites under dynamic loadings is presented in this article. The analysis focuses on the unit cell of an orthogonal woven fabric composite, which is composed of two sets of mutually orthogonal yarns of either the same fiber (nonhybrid fabric) or different fibers (hybrid fabric) in a matrix material. Using the mosaic model for simplifying woven fabric composites and a shear lag approach to account for the inter-yarn deformation, a one-dimensional analysis has been developed to predict the local elastodynamic and elastostatic behavior. The initial and boundary value problems are formulated and then solved using Laplace transforms. Closed form solutions of the dynamic displacements and stresses in each yarn and the bond shearing stresses at the interfaces between adjacent yarns are obtained in the time domain for any type of in-plane impact loadings. When time tends to infinity, the dynamic solutions approach to their corresponding static solutions, which are also developed in this article. Solutions of certain special cases are identical to those reported in the literature. Lastly, the dynamic stresses and bond shearing stresses of plain weave composites subjected to step uniform impacts are presented and discussed as an example of the general analytical model. Received 3 May 1999; accepted for publication 22 September 1999