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In this paper, a homogenization method based on peridynamics is proposed, in which the rotation effect of bond is considered and the limitation of Poisson's ratio is overcome. Integral form is used as governing equation instead of differential form in peridynamics, so that it is suitable to conduct homogenization analysis involving defects. Two algorithms, general algorithm and simplified algorithm, are used to homogenize periodic materials in this study. Equivalent material properties are obtained from the displacement gradient tensor. The results are in good agreement with those of other homogenization methods. This method can also be applied to homogenize periodic materials with defects. The defects such as cracks and pores of materials are realized by breaking the bonds between material points. Through this study, a new method for calculating the equivalent properties of materials with defects can be provided. [ABSTRACT FROM AUTHOR]

• Presents a novel computationally-efficient reconstruction of 3D RVE model of second-phase particle-strengthened AA7075-O sheet with real distribution of particles based on FIB-SEM techniques. • Three types of second-phase particles (i.e., irregularly-shaped iron-rich particle Al 3 Fe, elliptically-shaped particle MgZn 2 , and needle-like particle CuAl 2) are determined using SEM-based EDS and EBSD techniques. • Presents a systematic study of the overall elastic-plastic response by developing and applying a hybrid experimental analysis and computational modeling framework. • Good agreement is observed in the comparison of RVE results with that of in-situ SEM tensile tests, indicating that the real 3D microstructure-based RVE models can accurately predict the plastic deformation and interfacial failure evolution in AA7075-O sheet. This paper addresses the challenge of reconstructing randomly distributed second-phase particle-strengthened microstructure of AA7075-O aluminum sheet material for computational analysis. The particle characteristics in 3D space were obtained from focused ion beam and scanning electron microscopy (FIB-SEM) and SEM-based Electron Backscatter Diffraction/Energy Dispersive X-ray Spectrometry (EBSD/EDS) techniques. A theoretical framework for analysis of elastic-plastic deformation of such 3D microstructures is developed. Slip-induced shear band formation, void initiation, growth and linkage at large plastic strains during uniaxial tensile loading were investigated based on reconstructed 3D representative volume element (RVE) models with real-distribution of particles and the results compared with experimental observations. In-situ SEM interrupted tension tests along transverse direction (TD) and rolling direction (RD), employing microscopic-digital image correlation (μ-DIC) technique, were carried out to investigate slip bands, micro-voids formation and obtain microstructural strain maps. The resulting local strain maps were analyzed in relation to the experimentally observed plastic flow localization, failure modes and local stress maps from simulations of RVE models. The influences of particle size, shape, orientation, volume fraction as well as matrix-particle interface properties on local plastic deformation, global stress-strain/strain-hardening curves and interfacial failure mechanisms were studied based on 3D RVE models. When possible, the model results were compared with in-situ tensile test data. In general, good agreement was observed, indicating that the real 3D microstructure-based RVE models can accurately predict the plastic deformation and interfacial failure evolution in AA7075-O aluminum sheet. [ABSTRACT FROM AUTHOR]

The emergence of heterogeneous nanostructured materials (HNMs) offers exciting opportunities to achieve outstanding mechanical properties. Among these materials, gradient nanotwinned (GNT) Cu is a prominent class of HNMs, demonstrating superior strengths by gaining extra strengths compared to non-gradient counterparts. Its layered gradient structure provides a simplified quasi-one-dimensional model system for understanding the extra strengthening effects of structural gradients and resulting plastic strain gradients. This paper presents a comprehensive report for recent experimental and modeling studies on the mechanics of GNT Cu, covering advances in controlled material processing, back stress measurement, deformation field characterization, dislocation microstructure analysis, and strain gradient plasticity modeling. These studies unveil the spatiotemporal evolution of both plastic strain gradients and extra back stresses originating from structural gradients. Direct connections are established between the sample-level extra strength of GNT Cu and the synergistic strengthening effects induced by local nanotwin structures and their gradients. We emphasize the critical role of the size of the representative volume element in assessing the effects of plastic strain gradient and extra back stress. Moreover, lower-order strain gradient plasticity models are validated through experimental characterizations of GNT Cu, paving the way for future investigation into the mechanics of gradient nanostructured metals. Finally, we provide an outlook on research needs for understanding the mechanics of gradient nanostructured metals and, more broadly, HNMs, towards achieving exceptional mechanical properties. [ABSTRACT FROM AUTHOR]

A multiscale framework for the analysis of fracture is developed in order to determine the effective (homogenized) strength and fracture energy of a composite material based on the constituent’s material properties and microstructural arrangement. The method is able to deal with general (mixed-mode) applied strains without a priori knowledge of the orientation of the cracks. Cracks occurring in a microscopic volume element are modeled as sharp interfaces governed by microscale traction-separation relations, including interfaces between material phases to account for possible microscale debonding. Periodic boundary conditions are used in the microscopic volume element, including periodicity that allows cracks to transverse the boundaries of the volume element at arbitrary orientations. A kinematical analysis is presented for the proper interpretation of a periodic microscopic crack as an equivalent macroscopic periodic crack in a single effective orientation. It is shown that the equivalent crack is unaffected by the presence of parallel periodic replicas, hence providing the required information of a single localized macroscopic crack. A strain decomposition in the microscopic volume element is used to separate the contributions from the crack and the surrounding bulk material. Similarly, the (global) Hill–Mandel condition for the volume element is separated into a bulk-averaged condition and a crack-averaged condition. Further, it is shown that, though the global Hill–Mandel condition can be satisfied a priori using periodic boundary conditions, the crack-based condition can be used to actually determine the effective traction of an equivalent macroscopic crack. [ABSTRACT FROM AUTHOR]

This paper describes a newly proposed viscoelastic–viscoplastic constitutive model that is used to characterize the effective mechanical behaviors of fiber-reinforced composites based on micromechanical modeling. A homogenization approach is developed in which the effective stress of the fiber-reinforced composite is decomposed into an elastoplastic component and a viscous component. For the elastoplastic component, a bridge model is adopted to characterize the effective elastoplastic behaviors, while for the viscous component, homogenization theory applied to the time domain is utilized to describe the effective viscous responses. The overall stress for the composite can be obtained by superposing the stress contributions of the two components. The proposed micromechanics-based constitutive model has an explicit form, which contributes to the computational efficiency of the multiscale simulations for the composite structures. Unit cubes with 128 randomly distributed cylindrical fibers of equal size are created as the representative volume element models for numerical validation of the proposed constitutive model. The effects of fiber volume fraction, hardening law, loading condition, and strain rate are considered to comprehensively validate the constitutive model. Experimental results for IM7/8552 carbon fiber–reinforced composite were employed to validate the constitutive model. By comparing the model predictions to the experimental results and numerical observations, the constitutive model was found to provide acceptably good predictions of the viscoelastic–viscoplastic behaviors of the fiber-reinforced composites. [ABSTRACT FROM AUTHOR]

Since polymers play an increasingly important role in both structural and tribological applications, understanding their intrinsic mechanical response is key. Therefore in the last few decades much effort has been devoted into the development of constitutive models that capture the polymers' intrinsic mechanical response quantitatively. An example is the Eindhoven Glassy Polymer model. In practice most polymers are filled, e.g. with hard particles or fibers, with colorants, or with soft particles that serve as impact modifiers. To characterize the influence of type and amount of filler particles on the intrinsic mechanical response, we designed model systems of polycarbonate with different volume fractions of small, order 100 nm sized, either hard or soft particles, and tested them in lubricated uniaxial compression experiments. To reveal the local effects on interparticle level, three-dimensional representative volume elements (RVEs) were constructed. The matrix material is modeled with the EGP model and the fillers with their individual mechanical properties. It is first shown that (only) 32 particles are sufficient to capture the statistical variations in these systems. Comparing the simulated response of the RVEs with the experiments demonstrates that in the small strain regime the stress is under-predicted since the polymer matrix is modeled by using only one single relaxation time. The yield- and the large strain response is captured well for the soft-particle filled systems while, for the hard-particles at increased filler loadings, the predictions are less accurate. This is likely caused by polymer–filler interactions that result in accelerated physical aging of the polymer matrix close to the surfaces. Modifying the S a -parameter, that captures the thermodynamic state of the polymer matrix, allows us to correctly predict the macroscopic response after yield. The simulations reveal that all rate-dependencies of the different filled systems originate from that of the polymer matrix. Finally, an onset is presented to predict local and global failure based on critical events on the microlevel, that are likely to cause the over-prediction in the large-strain response of the hard-particle filled systems. [ABSTRACT FROM AUTHOR]

When spacecraft works, it will suffer different temperature environments, while temperature difference will always introduce changes of shape and size of composite structures. However, some spacecraft parts need high dimensional stability to keep its right function. Till now, the mechanical properties of the composite have been widely studied, however, the thermal properties of composite and optimization of composite considering both thermal and mechanical properties are far from well studied. Composite tubes were optimized to a given coefficient of thermal expansion (CTE), and the stiffness of those tubes was taken into consideration at the same time. Firstly, multi-scale numerical models were developed to calculate the CTE. In micro-scale mode, the CTE of unidirectional fiber reinforced composite was calculated by the fiber CTE through representative volume elements (RVE). In macro-scale, a composite tube model was generated to predict both axial and transverse CTE of the tube based on the CTE computed by RVE. Composite laminates and tubes with given plies were analyzed and tested. Comparison between the predicted results and the experimental one verified the model, which made the foundation for the optimization mode. Secondly, optimization models for composite truss structure were created. The conjugate gradient method was adopted to optimize the plies of composite parts, and the thermal-mechanical optimizing method was developed. Finally, the satellite support truss structure was analyzed by the thermal-mechanical optimizing method. Analyzed results show that this optimized support structure and the whole antenna have an excellent thermal dimensional stability. The thermal-mechanical optimizing method can be used for thermal stability design and analysis of composite support truss structures. [ABSTRACT FROM AUTHOR]

Abstract: The mechanical behavior of TiO2 nanoparticle-reinforced resin-based dental composites was characterized in this work using a three-dimensional nanoscale representative volume element. The impacts of nanoparticle volume fraction, aspect ratio, stiffness and interphase zone between the resin matrix and nanoparticle on the bulk properties of the composite were characterized. Results clearly demonstrated the mechanical advantage of nanocomposites in comparison to microfiber reinforced composites. The bulk response of the nanocomposite could be further enhanced with the increased nanoparticle volume fraction, or aspect ratio, while the influence of nanoparticle stiffness was minimal. The effective Young’s modulus and yield strength of the composite was also significantly affected by the interphase stiffness. Results obtained in this work could provide insights for the optimization of nanoparticle-reinforced dental composites. [Copyright &y& Elsevier]

Abstract: A novel computational model is presented using the eigenstrain formulation of the boundary integral equations for modeling the particle-reinforced composites. The model and the solution procedure are both resulted intimately from the concepts of the equivalent inclusion of Eshelby with eigenstrains to be determined in an iterative way for each inhomogeneity embedded in the matrix. The eigenstrains of inhomogeneity are determined with the aid of the Eshelby tensors, which can be readily obtained beforehand through either analytical or numerical means. The solution scale of the inhomogeneity problem with the present model is greatly reduced since the unknowns appear only on the boundary of the solution domain. The overall elastic properties are solved using the newly developed boundary point method for particle-reinforced inhomogeneous materials over a representative volume element with the present model. The effects of a variety of factors related to inhomogeneities on the overall properties of composites as well as on the convergence behaviors of the algorithm are studied numerically including the properties and shapes and orientations and distributions and the total number of particles, showing the validity and the effectiveness of the proposed computational model. [Copyright &y& Elsevier]

Abstract: The overall mechanical response as well as strain and stress field statistics of an heterogeneous material made of two randomly distributed, linear elastic phases, are investigated numerically. The Boolean model of spheres is used to generate microstructures consisting of either porous or rigid inclusions, at any volume fraction of the phases. Stress and strain field integral ranges, or equivalently the representative volume element, are computed and linked to features of the field statistics, and to the microstructure geometry. [Copyright &y& Elsevier]

Abstract: Piezoelectric 3–3 composites are often prepared from unpoled PZT ceramics and polymer matrices. During the poling process the PZT cannot deform freely due to the clamping by the surrounding polymer, which after poling results in the occurrence of residual mechanical stress in the composite. Based on the multi-linear constitutive model of ferroelectric and ferroelastic piezoceramics, a nonlinear finite element analysis was performed within the representative volume element to model the poling behavior of this kind of composites, in which appropriate periodic boundary conditions were prescribed for the displacements and the electric field of the composites. Considering the fact from experimental data that changes of the remanent strain induced by the switching process are volume preserving, we introduced different criteria in evaluating the maximum and minimum values of the ferroelastic strain S f. A numerical simulation was then conducted to investigate the effects of different poling voltages and volume fractions of the PZT ceramic on the distribution of residual mechanical stress in the PZT of composites. The results show that if V f <18% a portion of the compressive mechanical stress in the poling direction on the PZT ceramic may cause a mechanical depolarization of the PZT ceramic. [Copyright &y& Elsevier]

The concept of representative volume element (RVE) plays a key role in correlating the properties of microscopically heterogeneous materials with those of their macroscopically homogenized ones. However, up to now little quantitative knowledge is available about RVE scales or sizes of various engineering materials, which have been becoming a necessity due to the rapid development of, for instance, microelectromechanical systems. A new and convenient definition of the minimum RVE size is introduced. Then more than 500 kinds of cubic polycrystalline material in the planar stress state are numerically tested. The major finding from these numerical experiments is that the RVE size for the effective shear modulus (as well as the Young''s modulus) depends roughly linearly upon the anisotropy degree of the single crystal, while the effective area modulus does not. For the latter observation a theoretical proof is also given. With a maximum relative error 5%, all the materials tested (with one exception) have a minimal RVE size of 20 or less times as large as the grain size. [Copyright &y& Elsevier]