Coupled multi‐scale cohesive modeling of failure in heterogeneous adhesives

A multi‐scale cohesive numerical framework is proposed to simulate the failure of heterogeneous adhesively bonded systems. This multi‐scale scheme is based on Hill's variational principle of energy equivalence between the higher and lower level scales. It provides an easy way to obtain accurate homogenized macroscopic properties while capturing the physics of failure processes at the micro‐scale in sufficient detail. We use an isotropic rate‐dependent damage model to mimic the failure response of the constituents of heterogeneous adhesives. The finite element method is used to solve the equilibrium equation at each scale. A nested iterative scheme inspired by the return mapping algorithm used in computational inelasticity is implemented. We propose a computationally attractive technique to couple the macro‐ and micro‐scales for rate‐dependent constitutive laws. We introduce an adhesive patch test to study the numerical performance, including spatial and temporal convergence of the multi‐scale scheme. We compare the solution of the multi‐scale cohesive scheme with a direct numerical simulation. Finally, we solve mode I and mode II fracture problems to demonstrate failure at the macro‐scale. Copyright © 2010 John Wiley & Sons, Ltd.     

Consistent micro–macro transitions at large objective strains in curvilinear convective coordinates

This paper presents a computational homogenization scheme that is of particular interest for problems formulated in curvilinear coordinates. The main goal of this contribution is to generalize the computational homogenization scheme to a formulation of micro–macro transitions in curvilinear convective coordinates, where different physical spaces are considered at the homogenized macro‐continuum and at the locally attached representative micro‐structures. The deformation and the coordinate system of the micro‐structure are assumed to be coupled with the local deformation and the local coordinate system at a corresponding point of the macro‐continuum. For the consistent formulation of micro–macro transitions, the operations scale‐up and scale‐down are introduced, considering the rotated representation of tensor variables at the different physical reference frames of micro‐ and macro‐structure. The second goal of this paper is to use objective strain measures like the Green–Lagrange strain tensor for the solution of boundary value problems on the micro‐ and macro‐scale by providing the required transformations for the work‐conjugate stress, strain and tangent tensors into variables admissible for the considered micro–macro transitions and satisfying the averaging theorem. Copyright © 2007 John Wiley & Sons, Ltd.     

宏微观双尺度运动裂纹模型面内拉伸下的解析解*

研究裂纹动态扩展中宏微观因素相互作用机制与微观裂尖区的钝化效应。平面拉伸状态下,宏观主裂纹以恒定速度运动。通过一个介观约束应力过渡区,将宏观主裂纹与微观裂尖区相连接,由此建立了一个宏微观双尺度运动裂纹模型。应用弹性动力学与复变函数理论,分别在宏观与微观尺度下对该模型进行解析求解,获得了解析解。通过裂纹张开位移从宏观到微观的连续性条件与宏微观应力场协调条件,将两个不同尺度下的解相耦合,获得了计算宏微观损伤区特征长度的显式表达式。研究表明,运动裂纹的宏观应力场仍具有通常的r&;#61485;1/2的奇异性。由于微观裂尖的钝化,微观应力场奇异性的阶次有所降低,与宏观应力场相比具有弱奇异性。双尺度运动裂纹模型中,可允许裂纹运动速度达到剪切波速,解除了经典运动裂纹理论中裂纹速度不能超过Rayleigh波速的限制。数值结果表明,介观损伤过渡区与裂尖微观损伤区尺寸,及裂纹张开位移等,与裂纹运动速度、材料性质、约束应力比、裂尖钝化角度等因素有关。     

Computational homogenization for heat conduction in heterogeneous solids

In this paper, a multi‐scale analysis method for heat transfer in heterogeneous solids is presented. The principles of the method rely on a two‐scale computational homogenization approach which is applied successfully for the stress analysis of multi‐phase solids under purely mechanical loading. The present paper extends this methodology to heat conduction problems. The flexibility of the method permits one to take into account local microstructural heterogeneities and thermal anisotropy, including non‐linearities which might arise at some stage of the thermal loading history. The resulting complex microstructural response is transferred back to the macro level in a consistent manner. A proper macro to micro transition is established in terms of the applied boundary conditions and likewise a micro to macro transition is formulated in the form of consistent averaging relations. Imposition of boundary conditions and extraction of macroscopic quantities are elaborated in detail. A nested finite element solution procedure is outlined, and the effectiveness of the approach is demonstrated by some illustrative example problems. Copyright © 2007 John Wiley & Sons, Ltd.     

A computational homogenization framework for soft elastohydrodynamic lubrication

The interaction between microscopically rough surfaces and hydrodynamic thin film lubrication is investigated under the assumption of finite deformations. Within a coupled micro–macro analysis setting, the influence of roughness onto the macroscopic scale is determined using FE ²-type homogenization techniques to reduce the overall computational cost. Exact to within a separation of scales assumption, a computationally efficient two-phase micromechanical test is proposed to identify the macroscopic interface fluid flux from a lubrication analysis performed on the deformed configuration of a representative surface element. Parameter studies show a strong influence of both roughness and surface deformation on the macroscopic response for isotropic and anisotropic surfacial microstructures.     

A Modeling Approach Across Length Scales for Progressive Failure Analysis of Woven Composites

This paper presents a multiscale modeling approach for the progressive failure analysis of carbon-fiber-reinforced woven composite materials. Hierarchical models of woven composites at three different length scales (micro, meso, and macro) were developed according to their unique geometrical and material characteristics. A novel strategy of two-way information transfer is developed for the multiscale analysis of woven composites. In this strategy, the macroscopic effective material properties are obtained from property homogenizations at micro and meso scales and the stresses at three length scales are computed with stress amplification method from macroscale to microscale. By means of the two-way information transfer, the micro, meso and macro structural characterizations of composites are carried out so that the micromechanisms of damage and their interactions are successfully investigated in a single macro model. In addition, both the nucleation and growth of damages are tracked during the progressive failure analysis. A continuum damage mechanics (CDM) method is used for post-failure modeling. The material stiffness, tensile strength and damage patterns of an open-hole woven composite laminate are predicted with the proposed multiscale method. The predictions are in good agreement with the experimental results.     

Multi-scale computational method for elastic bodies with global and local heterogeneity

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro–macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to the case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is to utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Computational analysis of the thermal conductivity of the carbon–carbon composite materials

Experimental data for carbon–carbon constituent materials are combined with a three-dimensional stationary heat-transfer finite element analysis to compute the average transverse and longitudinal thermal conductivities in carbon–carbon composites. Particular attention is given in elucidating the roles of various micro-structural defects such as de-bonded fiber/matrix interfaces, cracks and voids on thermal conductivity in these materials. In addition, the effect of the fiber precursor material is explored by analyzing PAN-based and pitch-based carbon fibers, both in the same type pitch-based carbon matrix. The finite element analysis is carried out at two distinct length scales: (a) a micro scale comparable with the diameter of carbon fibers and (b) a macro scale comparable with the thickness of carbon–carbon composite structures used in the thermal protection systems for space vehicles. The results obtain at room temperature are quite consistent with their experimental counterparts. At high temperatures, the model predicts that the contributions of gas-phase conduction and radiation within the micro-structural defects can significantly increase the transverse thermal conductivity of the carbon–carbon composites.     

Evaluation of interfacial strength in CF/epoxies using FEM and in-situ experiments

A combined experimental and numerical study has been carried out in order to study the mechanism of initial failure in transversely loaded CF/epoxy composites. Two composites with a high and a low temperature-curing matrix were investigated. Three point bending experiments on macroscopic composite specimen with special laminate lay-ups were carried out in a scanning electron microscope (SEM). The in-situ experiments allow observing the onset of microscopic composite failure under transverse loading and measurement of the macroscopic applied load at onset of failure. The experimental results show that interfacial failure was the dominating failure mechanism for both materials. For the same carbon fiber with the same treatment the interfacial failure was adhesive (weak interface) or cohesive (strong interface), depending on the matrix system. The interfacial stresses at initiation of failure were determined successfully by a non-linear micro/macro FE-analysis and compared with experimental results obtained from micro composite test. The results show that the interfacial normal strength (INS) governs failure under transverse loads.     

Two‐scale diffusion–deformation coupling model for material deterioration involving micro‐crack propagation

In this paper, we introduce a two‐scale diffusion–deformation coupled model that represents the aging material deterioration of two‐phase materials involving micro‐crack propagations. The mathematical homogenization method is applied to relate the micro‐ and macroscopic field variables, and a weak coupling solution method is employed to solve the two‐way coupling phenomena between the diffusion of scalar fields and the deformation of quasi‐brittle solids. The macroscopic mechanical behavior represented by the derived two‐scale two‐way coupled model reveals material nonlinearity due to micro‐scale cracking induced by the scalar‐field‐induced deformation, which can be simulated by the finite cover method. After verifying the fundamental validity of the proposed model and the analysis method, we perform a simple numerical example to demonstrate their ability to predict aging material deterioration. Copyright © 2010 John Wiley & Sons, Ltd.     

Two‐scale computational modelling of water flow in unsaturated soils containing irregular‐shaped inclusions

The focus of this paper is two‐dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two‐scale Richards’ equation‐based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro‐scale as a two‐dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro‐scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two‐scale model in a completely coupled manner. Numerical simulations are presented for a two‐dimensional infiltration problem. Copyright © 2014 John Wiley & Sons, Ltd.     

An adaptive multi‐scale approach to the modelling of masonry structures

We present an adaptive multi‐scale approach for predicting the mechanical behaviour of masonry structures modelled as dynamic frictional multi‐body contact problems. In this approach, the iterative splitting of the contact problem into normal contact and frictional contact is combined with a semismooth Newton/primal‐dual active‐set procedure to calculate deformations and openings in the model structures. This algorithm is then coupled with a novel adaptive multi‐scale technique involving a macroscopic scale, which is the size of the masonry structure, and a mesoscopic scale, which is the size of the constituents (bricks, stone‐blocks), to predict appearance of dislocations and stress distribution in large‐scale masonry structures. Comparisons of the numerical results with data from experimental tests and from practical observations illustrate the predictive capability of the multi‐scale algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical modeling of orthotropic diffusivities in a fiber reinforced composite with discontinuities using homogenization

Thermo-oxidative aging in polymer matrix composites (PMC) is usually simulated using diffusion–reaction models in which temperature, oxygen concentration and weight loss effects are considered at the “smeared” macro-scale. Consequently, homogenization techniques are necessary to determine the effective diffusivity of the composite lamina based on diffusivities of the fiber and the polymer matrix phases. This paper describes a simple analytical methodology based on one-dimensional steady-state flow continuity consideration to determine the homogenized diffusivity in the direction transverse and longitudinal to the fibers, including physical discontinuities such as fiber/matrix debonding due to oxidative shrinkage. Computations of effective homogenized diffusivities as a function of fiber volume fraction are presented, and the effect of discontinuities on homogenized diffusivities is quantified. Comparisons with FEA results are also presented.     

Propagation of material and surface profile uncertainties on MEMS micro‐resonators using a stochastic second‐order computational multi‐scale approach

This paper aims at accounting for the uncertainties because of material structure and surface topology of micro‐beams in a stochastic multi‐scale model. For micro‐resonators made of anisotropic polycrystalline materials, micro‐scale uncertainties exist because of the grain size, grain orientation, and the surface profile. First, micro‐scale realizations of stochastic volume elements are obtained based on experimental measurements. To account for the surface roughness, the stochastic volume elements are defined as a volume element having the same thickness as the microelectromechanical system (MEMS), with a view to the use of a plate model at the structural scale. The uncertainties are then propagated up to an intermediate scale, the meso‐scale, through a second‐order homogenization procedure. From the meso‐scale plate‐resultant material property realizations, a spatially correlated random field of the in‐plane, out‐of‐plane, and cross‐resultant material tensors can be characterized. Owing to this characterized random field, realizations of MEMS‐scale problems can be defined on a plate finite element model. Samples of the macro‐scale quantity of interest can then be computed by relying on a Monte Carlo simulation procedure. As a case study, the resonance frequency of MEMS micro‐beams is investigated for different uncertainty cases, such as grain‐preferred orientations and surface roughness effects. Copyright © 2016 John Wiley & Sons, Ltd.     

FE Macro/Micro Models for Contact Temperature Prediction at Steel/Composite Interfaces

Finite element (FE) contact and thermal macro/micro models have been developed to study the real thermal behavior of a fiber/matrix microstructure under sliding motion of a steel asperity. At first the contact parameters were evaluated using an approximate contact technique, followed by a transient thermal FE evaluation. The latter considers the heat partition between the steel asperity and the real fiber/matrix microenvironment of a normally oriented carbon fiber/polyether ether ketone composite. The temperature results obtained were compared with those representing a macroscopic approach.     

Micro/macro-mechanical approach of first ply failure in CFRP

A combined experimental and numerical study has been carried out in order to predict initial failure in transversely loaded carbon fibre/epoxy composites. Three-point bending experiments on macroscopic composite specimens with special laminate lay-ups were carried out in a scanning electron microscope (SEM). The in-situ experiments allow observing the onset of microscopic composite failure under transverse loading and measurement of the global applied load at onset of failure. The experimental results show that interfacial failure was the dominating failure mechanism. The interfacial stresses at initiation of failure were determined successfully by a non-linear micro/macro FE-Analysis and compared with experimental results obtained from 3-point bending tests of standard composite specimens. The results show that the interfacial normal strength (INS) governs the failure process.     

Study on Fracture Behaviour of a Polymer‐Bonded Explosive Simulant Subjected to Uniaxial Compression Using Digital Image Correlation Method

Abstract: Quasi‐static uniaxial compression experiments were conducted on a polymer‐bonded explosive (PBX) simulant. At macro‐scale, the deformation and fracture process of samples were recorded using a charge‐coupled‐device camera. Microscopic examination was conducted to in situ observe the deformation and fracture processes of samples using SEM equipped with a loading stage. Microscopic damage modes, including interfacial debonding and particle fracture, were observed. The digital image correlation (DIC) technique was used to calculate the recorded images, and the macro‐ and micro‐scale displacement and strain fields were determined. Crack initiation, crack propagation, fracture behaviour and failure mechanism of samples were studied. The effects of aspect ratios on fracture behaviour and failure mechanism of PBX simulant were analysed.     

复合材料多尺度分析方法与典型元件拉伸损伤模拟

复合材料具有多尺度特性,多尺度模拟方法能够考虑细观损伤、演变对宏观材料性能和力学行为的影响,是复合材料响应分析的一种重要方法和手段。基于多尺度渐进展开理论,对复合材料弹性问题控制方程进行尺度分解,推导了细观尺度与宏观尺度的控制方程,建立了复合材料宏观和细观尺度响应之间的关联。基于协同多尺度计算策略,利用通用有限元软件的用户子程序与脚本二次开发,在宏观模型计算中实时调用细观模型进行多尺度渐进损伤模拟,实现了宏观和细观尺度的信息传递与反馈。建立的复合材料多尺度数值模拟方法可以快速集成细观损伤模型以及宏观唯象强度理论,具有良好的通用性。碳/碳复合材料拉伸模拟算例结果与试验结果吻合较好。