Junzhi Cui

A stochastic multiscale method for thermo-mechanical analysis arising from random porous materials with interior surface radiation

Abstract A stochastic multiscale computational method for predicting the thermo-mechanical coupling properties of random porous materials is proposed. Here, the thermal radiation effect at microscale of the material consisting of randomly distributed pores is considered, which has an important impact on the macroscopic temperature and stress fields. A novel unified homogenization procedure, based on two-scale asymptotic expressions, has been established. The higher-order multiscale formulations for solving the dynamic thermo-mechanical coupling problem with the inertia term, coupling term and radiation term are given successively. Then, the statistical prediction algorithm based on the multiscale method is described in detail. Finally, numerical examples for porous materials with varying probability distribution models are calculated by the proposed algorithm, and compared with the data by finite element method with very fine meshes. The comparison shows that the stochastic multiscale computational method developed in this paper is useful for determination of the thermo-mechanical properties of porous materials and demonstrates its potential applications in engineering and technology.

A nonlocal continuum model based on atomistic model at zero temperature

In traditional continuum theories, constitutive relations such as generalized Hookes law and the Fourier law for heat conduction, are representations of macroscopic phenomenons. These theories have severe limitations as the length scale of the structure becomes close to the atomistic dimensions. The failure of the traditional continuum theories at atomistic scale can be attribute to ignoring of the length scale induced by intrinsic non-locality of atomistic interactions. The primary objective of this work is to construct a continuum model strictly based on the atomistic model bypassing any empirical constitutive law and any local homogeneous assumption such as Cauchy-Born rule. The intrinsic non-locality of the atomistic interactions are explicitly built into the model to make the model applicable to cases of strongly nonuniform deformation at the atomistic scales. When the deformation is homogeneous, the model reduces to that derived from Cauchy-Born rule. The present continuum model is expected to work well at atomistic scales. It is also consistent with the traditional continuum as the length scale approach to macro scale.

Statistical Two-Scale Method for Strength Prediction of Composites with Random Distribution and Its Applications

A Statistical two-order and Two-Scale computational Method (STSM) based on two-scale homogenization approach is developed and successfully applied to predicting the strength parameters of random particle reinforced composites. Firstly, the probability distribution model of composites with random distribution of a great number of particles in any e - size statistic screen, as e- size cell, is described. And then, the stochastic two-order and two-scale computational expressions for the strain tensor in the structure, which is made from the composites with random distribution model of e - size cell, are formulated in detail. And the effective expected strength and the minimum strength for the composites with random distribution are expressed, and the computational formulas of them and the algorithm procedure for strength parameter prediction are shown. Finally, some numerical results of its application to the random particle reinforced composites, the concrete with random distribution of a great number of particles in any e- size statistic screen, are demonstrated, and the comparisons with physical experimental data are given. They show that STSM is validated and efficient for predicting the strength of random particle reinforced composites.

Investigations on the deformation behavior of polycrystalline Cu nanowires and some factors affecting the modulus and yield strength

This paper consists of two parts. In the first part, the deformation behavior of polycrystalline Cu nanowires under tension, bending and torsion is studied by using molecular dynamics simulations. The results show that both free surfaces and grain boundaries can control the plastic deformation. In detail, for polycrystalline Cu nanowires under tension, the stress-assisted grain growth caused by atomic diffusion and grain boundary migration is found, which is thought to be the reason for necking. Then under the bending effect, full dislocations and deformation twins of polycrystalline Cu nanowires are found in the grains. Moreover, the twin boundaries act as obstacles to dislocation motion. Finally, full dislocations and fivefold deformation twins are detected in polycrystalline Cu nanowires in the torsional state. These phenomena are in good agreement with the experimental observations of Liao et al (2005 Appl. Phys. Lett. 86 103112). The second part investigates the effects of sample shape and crystallographic structure on the modulus and yield strength under tension, bending and torsion. The results demonstrate that the modulus (in particular the bending and torsion modulus) can be significantly influenced by both the effects; however, remarkable difference in yield strength can merely be caused by different crystallographic structures (here, different crystallographic structures refer to polycrystalline and single-crystalline structures).

Second-order two-scale computational method for damped dynamic thermo-mechanical problems of quasi-periodic composite materials

Abstract In this paper, a novel second-order two-scale (SOTS) analysis method and related numerical algorithm are developed for damped dynamic thermo-mechanical problems of quasi-periodic composite materials. The formal SOTS solutions for these problems are constructed by the multiscale asymptotic analysis. Then we theoretically explain the importance of the SOTS solutions by the error analysis in the pointwise sense. Furthermore, the convergence result with an explicit rate for the SOTS solutions is obtained in the integral sense. In addition, a SOTS numerical algorithm is proposed to solve these problems effectively. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on asymptotic homogenization method. Then, the error analysis in the pointwise sense is given to illustrate the importance of developing SOTS solutions. Furthermore, the error estimates for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

High-order three-scale computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales

Abstract This study develops a novel high-order three-scale (HOTS) computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales. The heterogeneities of the composites are taken into account by periodic distributions of unit cells on the mesoscale and microscale. Firstly, the multiscale asymptotic analysis for these multiscale problems is given detailedly. Based on the above-mentioned analysis, the new unified micro-meso-macro HOTS approximate solutions are successfully constructed for these multiscale problems. Two classes of auxiliary cell functions are established on the mesoscale and microscale. Then, the error analyses for the conventional two-scale solutions, low-order three-scale (LOTS) solutions and HOTS solutions are obtained in the pointwise sense, which illustrate the necessity of developing HOTS solutions for simulating the heat conduction behaviors of composite structures with multiple periodic configurations. Furthermore, the corresponding HOTS numerical algorithm based on finite element method (FEM) is brought forward in details. Finally, some numerical examples are presented to verify the feasibility and validity of our HOTS computational method. In this paper, a unified three-scale computational framework is established for heat conduction problems of axisymmetric composite structures with multiple spatial scales.

The hole-filling method and multiscale algorithm for the heat transfer performance of periodic porous materials

In this paper, we consider the transient heat transfer problem with rapidly oscillating coefficients in periodic porous materials. The hole-filling method through filling all holes with a very compliant material is investigated, and as the thermal conductivity parameters of the weak phase go to zero, the proof of the limiting process is derived in detail. Then, the multiscale analysis and computations based on the hole-filling method for the associated multiphase problem in a domain without holes are proposed. Finally, some numerical results are given, which show a good agreement and verify the feasibility of the hole-filling method. A multiscale analysis and computation based on hole-filling method is proposed.Transient heat transfer problem of periodic porous materials is considered.Proof of the limiting process as the parameters of the weak phase go to zero is derived.Some numerical results are given in detail to validate the multiscale method developed.

Deformation mechanisms of Cu nanowires with planar defects

Molecular dynamics simulations are used to investigate the mechanical behavior of Cu nanowires (NWs) with planar defects such as grain boundaries (GBs), twin boundaries (TBs), stacking faults (SFs), etc. To investigate how the planar defects affect the deformation and fracture mechanisms of naowires, three types of nanowires are considered in this paper: (1) polycrystalline Cu nanowire; (2) single-crystalline Cu nanowire with twin boundaries; and (3) single-crystalline Cu nanowire with stacking faults. Because of the large fraction of atoms at grain boundaries, the energy of grain boundaries is higher than that of the grains. Thus, grain boundaries are proved to be the preferred sites for dislocations to nucleate. Moreover, necking and fracture prefer to occur at the grain boundary interface owing to the weakness of grain boundaries. For Cu nanowires in the presence of twin boundaries, it is found that twin boundaries can strength nanowires due to the restriction of the movement of dislocations. The pile up of dislocations on twin boundaries makes them rough, inducing high energy in twin boundaries. Hence, twin boundaries can emit dislocations, and necking initiates at twin boundaries. In the case of Cu nanowires with stacking faults, all pre-existing stacking faults in the nanowires are observed to disappear during deformation, giving rise to a fracture process resembling the samples without stacking fault.