Multiscale aggregating discontinuities method for micro–macro failure of composites

The application of a multiscale method, called the multiscale aggregating discontinuities (MAD) method, to the failure analysis of composites is described. Two distinct features of the MAD method are the use of perforated unit cells, and the extraction of coarse-grained failure information. In the perforated unit cell, all subdomains of the unit cell that are not strictly elliptic are excluded, which enables the decomposition of its stable and unstable material. By means of these concepts, it is possible to compute an equivalent discontinuity at the macroscale, including both the direction and the magnitude of the discontinuity. This equivalent discontinuity is then passed to the macroscale along with the computed stress from the unit cell. The macroscale discontinuity is injected into the macro model by the extended finite element method (XFEM) procedure. In this paper, the method is improved by adding hourglass modes to the unit cell deformations, which better model growing cracks. Several examples comparing the MAD method with direct numerical simulations are presented.     

An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method

Based on embedded atom method (EAM), an embedded atom hyperelastic (EAH) constitutive model is developed. The proposed EAH constitutive model provides a multiscale formalism to determine mesoscale or macroscale material behavior by atomistic information. By combining the EAH with cohesive zone model (CZM), a multiscale embedded atom cohesive finite element model (EA-cohesive FEM) is developed for simulating failure of materials at mesoscale and macroscale, e.g. fracture and crack propagation etc. Based on EAH, the EA-cohesive FEM applies the Cauchy-Born rule to calculate mesoscale or macroscale material response for bulk elements. Within the cohesive zone, a generalized Cauchy-Born rule is applied to find the effective normal and tangential traction-separation cohesive laws of EAH material. Since the EAM is a realistic semi-empirical interatomic potential formalism, the EAH constitutive model and the EA-cohesive FEM are physically meaningful when it is compared with experimental data. The proposed EA-cohesive FEM is validated by comparing the simulation results with the results of large scale molecular dynamics simulation. Simulation result of dynamic crack propagation is presented to demonstrate the capacity of EA-cohesive FEM in capturing the dynamic fracture.     

Multiscale aggregating discontinuities: A method for circumventing loss of material stability

New methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described. These methods, called multiscale aggregating discontinuities, are based on the concept of ‘perforated’ unit cells, which exclude subdomains that are unstable, i.e. exhibit loss of material stability. Using this concept, it is possible to compute an equivalent discontinuity at the coarser scale, including both the direction of the discontinuity and the magnitude of the jump. These variables are then passed to the coarse‐scale model along with the stress in the unit cell. The discontinuity is injected at the coarser scale by the extended finite element method. Analysis of the procedure shows that the method is consistent in power and yields a bulk stress–strain response that is stable. Applications of this procedure to crack growth in heterogeneous materials are given. Copyright © 2007 John Wiley & Sons, Ltd.     

An iterative method for coupling of deformation and failure mechanisms on different length scales

An iterative method for coupling of numerical simulations on two length scales is presented. The computations on the microscale and on the macroscale are linked via a suitable macroscopic constitutive law. The parameters of this material law depend on the deformation history and are obtained from simulations using microstructurally representative volume elements (RVEs) subjected to strain paths derived from the associated material points in the macroscopic structure. Thus, different constitutive parameter sets are assigned to different regions of the macrostructure. The microscopic and macroscopic simulations are performed iteratively and interact mutually via the strain paths and the constitutive parameters, respectively. As an example, the strip tension test for a porous material is modelled using the finite element (FE) method. The coupling procedure, the material law and its numerical implementation are described. The method is shown to allow for a detailed simulation of the deformation mechanisms both on the micro‐ and the macroscale as well as for an assessment of their interactions while keeping the computational efforts reasonably low. Copyright © 2000 John Wiley & Sons, Ltd.     

Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators

This study is concerned with the detailed analysis of fiber-reinforced composite plates with integrated piezoceramic fiber composite actuators. A multiscale framework based on the asymptotic expansion homogenization method is used to couple the microscale and macroscale field variables. The microscale fluctuations in the mechanical displacement and electric potential are related to the macroscale deformation and electric fields through 36 distinct characteristic functions. The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method. The homogenized electroelastic properties of a representative material element are computed using the characteristic functions and the material properties of the fiber and matrix. The three-dimensional macroscopic equilibrium equations for a laminated piezoelectric plate are solved analytically using the Eshelby-Stroh formalism. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. The microscale stresses and electric displacement in the fibers and matrix are computed from the macroscale fields through interscale transfer operators. The multiscale analysis procedure is illustrated using two model problems. In the first model problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/polymer layers is studied. The second model problem concerns a cantilever graphite/polymer substrate with segmented piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.     

A three‐dimensional atomistic‐based process zone model simulation of fragmentation in polycrystalline solids

A three‐dimensional atomistic‐based process zone model (APZM) is used to simulate high‐speed impact induced dynamic fracture process such as fragmentation and spall fracture. This multiscale simulation model combines the Cauchy–Born rule, colloidal crystal process model, and micromechanics homogenization technique to construct constitutive relations in both grains and grain boundary at mesoscale. The proposed APZM has some inherent advantages to describe mechanical behaviors of polycrystalline solids. First, in contrast to macroscale phenomenological constitutive models, the APZM takes into account atomistic binding energy and atomistic lattice structure. In particular, the electron density related embedded atom method (EAM) potential has been adopted to describe interatomistic interactions of metallic polycrystalline solids in bulk elements; second, a mixed type of EAM potential and colloidal crystal depletion potential is constructed to describe heterogeneous microstructure in the process zone; third, the atomistic potential in both bulk material and process zone has the same atomistic origin, and hence, the bulk and process potentials are self‐consistent. The simulation of dynamic fracture process of a cylinder made of aluminum powder metallurgy (P/M) alloy during high‐speed impact/penetration is carried out, and numerical results demonstrate that APZM finite element method has remarkable ability to accurately capture complex three‐dimensional fragmentation formation and damage morphology. Copyright © 2012 John Wiley & Sons, Ltd.     

A Facile Method to Fabricate Anisotropic Hydrogels with Perfectly Aligned Hierarchical Fibrous Structures

Natural structural materials (such as tendons and ligaments) are comprised of multiscale hierarchical architectures, with dimensions ranging from nano‐ to macroscale, which are difficult to mimic synthetically. Here a bioinspired, facile method to fabricate anisotropic hydrogels with perfectly aligned multiscale hierarchical fibrous structures similar to those of tendons and ligaments is reported. The method includes drying a diluted physical hydrogel in air by confining its length direction. During this process, sufficiently high tensile stress is built along the length direction to align the polymer chains and multiscale fibrous structures (from nano‐ to submicro‐ to microscale) are spontaneously formed in the bulk material, which are well‐retained in the reswollen gel. The method is useful for relatively rigid polymers (such as alginate and cellulose), which are susceptible to mechanical signal. By controlling the drying with or without prestretching, the degree of alignment, size of superstructures, and the strength of supramolecular interactions can be tuned, which sensitively influence the strength and toughness of the hydrogels. The mechanical properties are comparable with those of natural ligaments. This study provides a general strategy for designing hydrogels with highly ordered hierarchical structures, which opens routes for the development of many functional biomimetic materials for biomedical applications.     

基于双重网格的混凝土自适应宏细观协同有限元分析方法

混凝土损伤开裂表现出明显的跨尺度特征,其演化过程与细观材料结构直接相关。如何在兼顾效率和精度前提下分析混凝土损伤开裂的跨尺度演化过程一直是比较棘手的问题。在假定处于弹性阶段的混凝土为宏观均匀材料和处于损伤开裂阶段的混凝土为细观非均匀材料的基础上,提出了一种基于双重网格的混凝土自适应宏细观协同有限元分析方法。该方法通过在分析域内布置宏细观双重网格分别建立宏观尺度和细观尺度有限元计算模型,通过宏观尺度至细观尺度的自适应转换在分析过程中动态确定宏细观协同分析的宏观区域和细观区域,通过基于形函数插值的多点位移约束实现宏细观协同有限元模型中的非协调重叠网格连接。算例分析表明,采用该文方法不仅可通过考虑损伤开裂区的细观材料结构保证模拟精度,亦可通过在分析中自适应确定细观尺度分析区域提高模拟效率。     

An adaptive MsFEM for nonperiodic viscoelastic composites

We present a modification of the multiscale finite element method (MsFEM) for modeling of heterogeneous viscoelastic materials and an enhancement of this method by the adaptive generation of both meshes, ie, a macroscale coarse one and a microscale fine one. The fine mesh refinements are performed independently within coarse elements adjusting the microscale discretization to the microstructure, whereas the coarse mesh adaptation optimizes the macroscale approximation. Besides the coupling of the hp‐adaptive finite element method with the MsFEM we propose a modification of the MsFEM to accommodate for the analysis of transient nonlinear problems. We illustrate the efficiency and accuracy of the new approach for a number of benchmark examples, including the modeling of functionally graded material, and demonstrate the potential of our improvement for upscaling nonperiodic and nonlinear composites.     

The Molecular Dynamic Finite Element Method (MDFEM)

In order to understand the underlying mechanisms of inelastic material behavior and nonlinear surface interactions, which can be observed on macroscale as damping, softening, fracture, delamination, frictional contact etc., it is necessary to examine the molecular scale. Force fields can be applied to simulate the rearrangement of chemical and physical bonds. However, a simulation of the atomic interactions is very costly so that classical molecular dynamics (MD) is restricted to structures containing a low number of atoms such as carbon nanotubes. The objective of this paper is to show how MD simulations can be integrated into the finite element method (FEM) which is used to simulate engineering structures such as an aircraft panel or a vehicle chassis. A new type of finite element is required for force fields that include multi-body potentials. These elements take into account not only bond stretch but also bending, torsion and inversion without using rotational degrees of freedom. Since natural lengths and angles are implemented as intrinsic material parameters, the developed molecular dynamic finite element method (MDFEM) starts with a conformational analysis. By means of carbon nanotubes and elastomeric material it is demonstrated that this pre-step is needed to find an equilibrium configuration before the structure can be deformed in a succeeding loading step.     

Highly energetic nitrogen species: reliable energetics via the correlation consistent Composite Approach (ccCA)

Gas-phase enthalpies of formation (ΔH(f(g))°) have been determined for 40 nitrogen-containing compounds at 298 K. Three ab initio composite methods have been compared in their abilities to quantitatively determine ΔH(f(g))°; the G3, G3(MP2), and correlation consistent Composite Approach (ccCA) methodologies. The ccCA method resulted in a mean absolute deviation (MAD) of 1.1 kcal mol(-1) when compared to available experimental values. The comparable G3(MP2) method resulted in a MAD of 1.8 kcal mol(-1), while the G3 method resulted in a MAD of 1.2 kcal mol(-1). As a result of their comparable accuracies, the ccCA and G3 methods have been utilized to predict the ΔH(f(g))° of five energetic but highly endothermic tetrazine-containing compounds with potential applications as insensitive high explosives.     

Investigation of fatigue crack closure using multiscale image correlation experiments

Two full-field macroscale methods are introduced for estimating fatigue crack opening levels based on digital image correlation (DIC) displacement measurements near the crack tip. Crack opening levels from these two full-field methods are compared to results from a third (microscale) method that directly measures opening of the crack flanks immediately behind the crack tip using two-point DIC displacement gages. Of the two full-field methods, the first one measures effective stress intensity factors through the displacement field (over a wide region behind and ahead of the crack tip). This method reveals crack opening levels comparable to the limiting values (crack opening levels far from the crack tip) from the third method (microscale). The second full-field method involves a compliance offset measurement based on displacements obtained near the crack tip. This method delivers results comparable to crack tip opening levels from the microscale two-point method. The results of these experiments point to a normalized crack tip opening level of 0.35 for R ∼ 0 loading in grade 2 titanium. This opening level was found at low and intermediate ΔK levels. It is shown that the second full-field macroscale method indicates crack opening levels comparable to surface crack tip opening levels (corresponding to unzipping of the entire crack). This indicates that effective stress intensity factors determined from full-field displacements could be used to predict crack opening levels.     

散状物料转载系统设计DEM仿真方法的研究

颗粒仿真技术可以对散状物料的运动进行观察、机理分析、受力分析、磨损(寿命)估计和系统优化.比较了散状物料转载计算方法,给出了采用DEM方法的建模与模型检验的基本步骤.针对DEM计算方法存在所需计算时间过长的问题,实验比较了降低剪切模量和增大颗粒粒度等方法对DEM计算时间和实验结果的影响,结果表明,在不影响计算结果的前提下可通过降低剪切模量和增大颗粒粒度来缩短DEM仿真计算时间.利用EDEM软件实现了散料转载过程的可视化,比较分析了直线型溜槽、折线型溜槽和曲线型溜槽中物料转载效果.仿真表明：采用变曲率半径效果更好;U型溜槽截面能够减少物料不对中情况的发生.     

考虑微观界面的2D编织SiC/SiC复合材料宏-细-微多尺度渐进损伤失效分析

该文将微观界面组分纳入宏-细-微三个尺度的多尺度渐进损伤失效分析中.对细、微观单胞模型施加周期性边界条件获取放大因子并采用k-means聚类方法进行缩聚;通过缩聚的放大因子求解宏观模型对应的细、微观组分应力并进行损伤失效判定;计算宏观模型退化后的弹性参数用于后续计算;针对2D编织SiC/SiC复合材料开展了渐近损伤失效...     

An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture

This paper describes an adaptive numerical framework for cohesive fracture models based on a spacetime discontinuous Galerkin (SDG) method for elastodynamics with elementwise momentum balance. Discontinuous basis functions and jump conditions written with respect to target traction values simplify the implementation of cohesive traction–separation laws in the SDG framework; no special cohesive elements or other algorithmic devices are required. We use unstructured spacetime grids in a h‐adaptive implementation to adjust simultaneously the spatial and temporal resolutions. Two independent error indicators drive the adaptive refinement. One is a dissipation‐based indicator that controls the accuracy of the solution in the bulk material; the second ensures the accuracy of the discrete rendering of the cohesive law. Applications of the SDG cohesive model to elastodynamic fracture demonstrate the effectiveness of the proposed method and reveal a new solution feature: an unexpected quasi‐singular structure in the velocity response. Numerical examples demonstrate the use of adaptive analysis methods in resolving this structure, as well as its importance in reliable predictions of fracture kinetics. Copyright © 2009 John Wiley & Sons, Ltd.     

Goal-oriented adaptivity based on a model hierarchy of mean-field and full-field homogenization methods in linear elasticity

Homogenization methods are drawing increasing attention for simulation of heterogeneous materials like composites. For balancing the accuracy and the numerical efficiency of such strategies, we deal with both model and discretization errors of the finite element method (FEM) on a macroscale. Within a framework of goal-oriented adaptivity, we consider linear elastic heterogeneous materials, for which first-order homogenization schemes apply. A novel model hierarchy is proposed based on mean-field and full-field homogenization methods. For the former, we consider several well-established schemes like Mori-Tanaka or self-consistent as basic models, and for the latter, as superior models, unit cell problems are solved via the FEM under an a priori chosen boundary condition. For a further stage of the model hierarchy, we consider hierarchical unit cells within the frame of the FEM toward an adaptive selection of the unit cell size. By means of several numerical examples, we illustrate the effectiveness of the proposed adaptive approach.     

Multiscale finite element modeling of failure process of composite laminates

A multiscale nonlinear finite element modeling technique is developed in this paper to predict the progressive failure process for composite laminates. A micromechanical elastic–plastic bridging constitutive model, which considers the nonlinear material properties of the constituent fiber and matrix materials and their interaction and the damage and failure in fibrous composites at the fiber and matrix level, is proposed to represent the material behavior of fiber-reinforced composite laminates. The micromechanics constitutive model is employed in the macroscale finite element analysis of structural behavior especially progressive failure process of the fiber-reinforced composites based on a 4-node 24-DOF shear-locking free rectangular composite plate element.     

Various methods to the thermistor problem with a bulk electrical conductivity

In this paper, Explicit Finite Difference (EFD), Galerkin Finite Element (GFE) and Heat‐Balance Integral (HBI) methods are applied to the one‐dimensional thermistor problem with a bulk electrical conductivity to obtain its steady‐state solutions. It is shown that EFD, GFE and HBI solutions exhibit the correct physical characteristic of the problem, and they are in very good agreement with the exact solution. The only marked difference is time to attain steady states. Copyright © 1999 John Wiley & Sons, Ltd.     

A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading

There is increasing demand for analytical methods that estimate the fatigue life of engineering components and structures with a high degree of accuracy. The fatigue life is determined by the stress–strain sequences at the critical locations. Therefore, these sequences have be calculated with sufficient accuracy for arbitrary nonproportional cyclic loading. Based on the experience with a variety of material models following macroscale continuum mechanics approaches, an improved set of constitutive equations is proposed. The stress–strain behaviour of a commercial structural steel has been investigated experimentally. Firstly, the results of this experimental study serve to identify the material parameters comprised in the model. Secondly, the predicted stress–strain paths are compared to their experimentally determined counterparts as well as to paths predicted by other models. The overall accuracy of the proposed model is quite satisfying, especially as far as calculated amplitudes are concerned.