Constitutive equations for densification of matrix-coated fibre composites during hot isostatic pressing

This work addresses the development of physically based constitutive equations for the consolidation of fibre-matrix-void systems typically arising in the manufacture of matrix-coated fibre metal matrix composite materials. The analyses consider square array packing of the coated fibres under symmetrical in-plane compressive load and take into account the power-law creep of the matrix. Two models have been developed. The first is based on an energy approach in which assumed velocity fields in the deforming matrix are considered and are expressed in terms of an unknown parameter. In this way, the dependence of the deformation rate on volume fraction of voids and fibres is derived through the use of Hill's minimum principle for velocities. The second model makes use of micro-mechanical finite element modelling in which fibre, matrix and void are modelled explicitly. The micro-mechanical finite element model is developed for validation and comparison. Theoretical predictions are examined. The constitutive equation for consolidation derived from Hill's minimum principle shows good agreement with results obtained from micro-mechanical finite element modelling.     

A micro-mechanical homogenisation model for masonry: Application to shear walls

An improved micro-mechanical model for masonry homogenisation in the non-linear domain, is proposed and validated by comparison with experimental and numerical results available in the literature. Suitably chosen deformation mechanisms, coupled with damage and plasticity models, can simulate the behaviour of a basic periodic cell up to complete degradation and failure. The micro-mechanical model can be implemented in any standard finite element program as a user supplied subroutine defining the mechanical behaviour of an equivalent homogenised material. This work shows that, with the proposed model, it is possible to capture and reproduce the fundamental features of a masonry shear wall up to collapse with a coarse finite element mesh. The main advantage of such homogenisation approach is obviously the possibility to simulate real complex structures while taking into consideration the arrangement of units and mortar, which would otherwise require impractical amount of finite elements and computer resources.     

A thermodynamics based damage mechanics model for particulate composites

A micro-mechanical damage model is proposed to predict the overall viscoplastic behavior and damage evolution in a particle filled polymer matrix composite. Particulate composite consists of polymer matrix, particle fillers, and an interfacial transition interphase around the filler particles. Yet the composite is treated as a two distinct phase material, namely the matrix and the equivalent particle-interface assembly. The CTE mismatch between the matrix and the filler particles is introduced into the model. A damage evolution function based on irreversible thermodynamics is also introduced into the constitutive model to describe the degradation of the composite. The efficient general return-mapping algorithm is exploited to implement the proposed unified damage coupled viscoplastic model into finite element formulation. Furthermore, the model predictions for uniaxial loading conditions are compared with the experimental data.     

Analytical and numerical analysis of frictional damage in quasi brittle materials

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori–Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress–strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.     

Comparison of computational predictions of material failure using nonlocal damage models

In computational analysis of damage failure the strain delocalizations are of great importance in predicting assessment of structure integrity. In this paper we are investigating effects of the intrinsic material length on computational prediction of material failure using both cell model, i.e. the conventional micro-mechanical damage model with the constant–sized finite elements for the damage zones, and nonlocal damage model based on the gradient plasticity. The corresponding experiments performed for an engineering steel are taken as reference for verification. The experimental observation has revealed that reducing the specimen size will arise the specific strength of small notched specimen which cannot be predicted using the cell damage model. The nonlocal damage model based on the strain gradient-dependent constitutive plasticity theory reproduces the experimental records. The material length affects evolution of the material porosity and gives an understandable explanation of the size effect.     

Combination of fracture and damage mechanics for numerical failure analysis

A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J-integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.     

基于能量等效原理的应变局部化分析:Ⅱ.有限元解法

以非局部塑性理论为基础,应用状态空间理论,通过局部和非局部两个状态空间的塑性能量耗散率等效原理,提出了一种求解应变局部化问题的新方法,以得到与网格无关的数值解.针对二维问题的屈服函数和流动法则导出了求解非局部内变量的一般方程,并提出了在有限元环境中求解应变局部化问题的应力更新算法.为了验证所提出的方法,对1个一维拉杆和3个二维平面应变加载试件进行了有限元分析.数值结果表明,塑性应变的分布和载荷-位移曲线都随着网格的变小而稳定地收敛,应变局部化区域的尺寸只与材料内尺度有关,而对有限元网格的大小不敏感.对于一维问题,当有限元网格尺寸减小时,数值解收敛于解析解.对于二维剪切带局部化问题,数值解随着网格尺寸的减小而稳定地向唯一解收敛.当网格尺寸减小时,剪切带的宽度和方向基本上没有变化.而且得到的塑性应变分布和网格变形是平滑的.这说明,所提方法可以克服经典连续介质力学模型导致的网格相关性问题,从而获得具有物理意义的客观解.此模型只需要单元之间的位移插值函数具有C~0连续性,因而容易在现有的有限元程序中实现而无需对程序作大的修改.     

Ignition and detonation of solid explosives: a micromechanical burn model

This paper describes a new computational framework for modeling splid explosives and proof-of-concept calculations. Our goal is to expand predictive model capability through the inclusion of various micro-mechanical burn processes. We propose a model which is complicated enough to represent underlying physics, but simple enough for engineering scale computations. Key components of the model include energy localization, the growth of hot spots, micro-mechanics in/around hot spots, and a phase-averaged mixture equation of state. The nucleation and growth of locally heated regions is treated by a statistical model based on an exponential size distribution. Proof-of-concept calculations are limited to shock loading, but show the capability of simulating Pop-plots, initial temperature effect, detonation waves in 2D, detonation shock confinement test, and multi-dimensional effects in a unified fashion based on micro-physics.

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Relations between a micro-mechanical model and a damage model for ductile failure in shear

Gurson type constitutive models that account for void growth to coalescence are not able to describe ductile fracture in simple shear, where there is no hydrostatic tension in the material. But recent micro-mechanical studies have shown that in shear the voids are flattened out to micro-cracks, which rotate and elongate until interaction with neighbouring micro-cracks gives coalescence. Thus, the failure mechanism is very different from that under tensile loading. Also, the Gurson model has recently been extended to describe failure in shear, by adding a damage term to the expression for the growth of the void volume fraction, and it has been shown that this extended model can represent experimental observations. Here, numerical studies are carried out to compare predictions of the shear-extended Gurson model with the shear failures predicted by the micro-mechanical cell model. Both models show a strong dependence on the level of hydrostatic tension. Even though the reason for this pressure dependence is different in the two models, as the shear-extended Gurson model does not describe voids flattening out and the associated failure mechanism by micro-cracks interacting with neighbouring micro-cracks, it is shown that the trends of the predictions are in good agreement.     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。     

A coupled micro-mechanical based model for saturated soils

It is generally accepted that the apparent behavior of geo-materials is the representation of the average micro-mechanical behavior of its constituents. Constitutive models that do not incorporate these micro-mechanical features in calibrating the material parameters cannot address various material localization features in large strain problems such as shear bands and slope failures, etc. In the absence of such micro-mechanical features the calibration of such models may be incorrect.A rigorous formulation that incorporates these micro-mechanical based mechanisms into the general behavior of the saturated soils is presented here. The plastic rotation of particles, the interaction of particles, the rate dependency, the damage, and the coupling of particles with pore fluid pressure are incorporated through the plastic spin, the gradient theory, the visco-plasticity, the damage theory, and the coupled theory of mixtures, respectively. The link between the micro-mechanical mechanisms and the macro-mechanical behavior is made through the use of RVE (representative volume element). As a result, a full formulation for the micro-mechanics implemented continuum plasticity for saturated soils is presented here.     

Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks

In the framework of rate-independent systems, a family of elastic-plastic-damage models is proposed through a variational formulation. Since the goal is to account for softening behaviors until the total failure, the dissipated energy contains a gradient damage term in order to limit localization effects. The resulting model owns a great flexibility in the possible coupled responses, depending on the constitutive parameters. Moreover, considering the one-dimensional quasi-static problem of a bar under simple traction and constructing solutions with localization of damage, it turns out that in general a cohesive crack appears at the center of the damage zone before the rupture. The associated cohesive law is obtained in a closed form in terms of the parameters of the model.     

Upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads

A micro-mechanics-based model is proposed to investigate the rate-dependent constitutive relation for crack-weakened rock masses subjected to dynamic compressive loads. The present micro-mechanical model reveals that the nucleation, growth and coalescence of sliding cracks dominate the failure and macroscopic properties of crack-weakened rock masses subjected to dynamic compressive loads. The interactions among multiple parallel sliding cracks in crack-weakened rock masses subjected to dynamic compressive loads are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the stress–strain relation. Based on the micro-mechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the rate-relation for rock masses containing multiple rows of echelon cracks subjected to dynamic compressive loads. The factors that affect the rate-dependent properties of crack-weakened rock masses have been analyzed. The strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, is employed in the analysis. The rate-dependent constitutive relation of crack-weakened rock masses is derived from micro-mechanical framework and the asymptotic analysis. The closed-form explicit expression for the rate-dependent constitutive relation of rock masses containing echelon cracks subjected to dynamic compressive loads is obtained. Finally, the present model is used to analyze the complete stress–strain relation and strength for jointed rock masses at shiplock slope of the Three Gorges Dam.     

基于微态方法的耦合韧性损伤的弹塑性本构模型

基于广义连续介质力学提出了一个热力学一致性的耦合微态韧性损伤的弹塑性本构模型。该模型遵循Forest的微态方法,在有限变形中提出引入额外的微态损伤因子及其一阶梯度以考虑材料的内部特征尺度。通过广义虚功原理得到了微态损伤的补充控制方程,对亥姆霍兹自由能进行扩展,得到了新的包含微态损伤变量的损伤能量释放率,在微态损伤的正则化作用下,采用隐式迭代更新局部损伤和应力等状态变量。基于Galerkin加权余量法,推导了以传统位移和微态损伤为基本未知量的有限元列式。利用该数值模型,对DP1000材料的单向拉伸实验和十字形零件的冲压实验进行了应变局部化与材料断裂的有限元分析。结果表明,该微态弹塑性损伤模型可以得到一致的有限元模拟响应曲线并收敛到实验曲线,从而避免发生网格依赖性问题。     

Analysis of structural behavior during collision event accounting for bow and side structure interaction

The main goal of this study was to investigate the effects of selected ship collision parameter values on the characteristics of the absorbed energy in several ship collision scenarios.Non-linear simulations were performed using a finite element method(FEM)to obtain virtual experiment data.In the present research,the size of the side damage from a collision phenomenon were measured and used to verify the numerical configuration together with the calculation results using an empirical equation.Parameters in the external dynamics of a ship collision such as the location of the contact point and velocity of the striking ship were taken into consideration.The internal energy and deformation size on the side structure were discussed further in a comparative study.The effects of the selected parameters on several structural behaviors,namely energy,force,and damage extent were also observed and evaluated in this section.Stiffener on side hull was found to contribute significantly into resistance capability of the target ship against penetration of the striking bow.Remarkable force during penetration was observed to occur when inner shell was crushed as certain velocity was applied in the striking bow.