Size effect of lattice material and minimum weight design

The size effects of microstructure of lattice materials on structural analysis and minimum weight design are studied with extented multiscale finite element method（EMsFEM） in the paper. With the same volume of base material and configuration, the structural displacement and maximum axial stress of micro-rod of lattice structures with different sizes of microstructure are analyzed and compared.It is pointed out that different from the traditional mathematical homogenization method, EMsFEM is suitable for analyzing the structures which is constituted with lattice materials and composed of quantities of finite-sized micro-rods.The minimum weight design of structures composed of lattice material is studied with downscaling calculation of EMsFEM under stress constraints of micro-rods. The optimal design results show that the weight of the structure increases with the decrease of the size of basic sub-unit cells. The paper presents a new approach for analysis and optimization of lattice materials in complex engineering constructions.     

Two-dimensional lattice gases for regular binary mixtures

This paper reports on the development of two-dimensional lattice gas models for regular binary mixtures. In particular, results are reproduced concerning equilibrium solutions and an expression for the diffusion coefficient. In our model, a volume force is incorporated, and the system of macroscopic evolution equations resembles the Boussinesq approximation in convection theory. As an example, a lattice gas Rayleigh-Bénard system is considered. We conclude with a few remarks on implementation and optimisation of the program using a SIMD parallel computer.     

Multiscale simulation of material removal processes at the nanoscale

A dynamic multiscale simulation method has been used to study the nanoscale material removal processes for single crystals. The model simultaneously captures the atomistic mechanisms during material removal from the free surface and the long-range mobility of dislocations and their interactions without the computational cost of full atomistic simulations. The method also permits the simulation of system sizes that are approaching experimentally accessibly systems, albeit in 2D. Simulations are performed on single crystal aluminum to study the atomistic details of material removal, chip formation, surface evolution, and generation and propagation of dislocations for a wide range of tool speeds (20-800 m/s) at room temperature. The results from these simulations demonstrate the power of the developed method in capturing both long-range dislocation plasticity and short-range atomistic phenomena during tool advance. In addition, we have investigated the effect of the scratching depth during the material removal process. Fluctuations of scratching tangential force are related to dislocation generation events during the material removal process. A transition from dislocation generation and glides at lower tool speeds to localized amorphization at high tool speeds is found to give rise to an optimal tool speed for low cutting forces.     

Multiscale constitutive modeling and numerical simulation of fabric material

A multiscale model for a fabric material is introduced. The model is based on the assumption that on the macroscale the fabric behaves as a continuum membrane, while on the microscale the properties of the microstructure are accounted for by a constitutive law derived by modeling a pair of overlapping crimped yarns as extensible elasticae. A two-scale finite element method is devised to solve selected boundary-value problems.     

On beams made of a phase-transforming material

This paper presents a theory for the mechanics of beams made of single crystals of shape memory alloys. The behavior of such beams can be quite unexpected and complicated due to the presence and propagation of phase boundaries. It is shown that the usual laws of mechanics do not fully determine the propagation of phase boundaries and that there is a need for additional constitutive information in the form of a kinetic relation. A simple experiment to measure this kinetic relation is proposed. Finally, a strategy to use such beams for propulsion at small scales is presented.     

Multiscale simulation of flow and heat transfer of nanofluid with lattice Boltzmann method

Based on the lattice Boltzmann (LB) approach, a novel hybrid method has been proposed for getting insight into the microscale characteristics of the multicomponent flow of nanofluid. In this method, the whole computational domain is divided into two regions in which different-sized meshes are involved for simulation (fine mesh and coarse mesh). The multicomponent LB method is adopted in the fine mesh region, and the single-component LB approach is applied to the coarse mesh region where the nanofluid is treated as a mixed single-component fluid. The conservation principles of mass, momentum and energy are used to derive a hybrid scheme across the different scaled regions. Numerical simulation is carried out for the Couette flow and convective heat transfer in a parallel plate channel to validate the hybrid method. The computational results indicate that by means of the present method, not only the microscopic characteristics of the nanofluid flow can be simulated, but also the computational efficiency can be remarkably improved compared with the pure multicomponent LB method.     

Elastic behaviour of a regular lattice for meso-scale modelling of solids

A modelling strategy is proposed to link the meso-scale mechanical response of a solid material to the macroscopic material behaviour. The model is based on a regular lattice of truncated octahedral cells, with sites at the cell centres linked by two sets of bonds. The relationship between the macroscopic elastic behaviour of the model and the elastic properties of the bonds is studied numerically. The results demonstrate that, in contrast to previously proposed lattice arrangements, any elastic properties of metallic or cementitious materials can be obtained by appropriate selection of the axial and the shear stiffness of the bonds. Discussion of the modelling approach includes the potential of the site-bond model to simulate the evolution of damage driven not only by mechanical deformation but also by processes that involve the interaction of different mechanisms.     

Buckling of a column made of functionally graded material

Buckling of a column made of functionally graded material is investigated. The functional grading is performed in the longitudinal direction. The following problem is addressed: determine the variation of the elastic modulus with the axial coordinate such that the buckling load exceeds the preselected value. In this study, only polynomial variation of the buckling mode is considered and only the case of cantilever column is treated.     

Effective elastic moduli of triangular lattice material with defects

This paper presents an attempt to extend homogenization analysis for the effective elastic moduli of triangular lattice materials with microstructural defects. The proposed homogenization method adopts a process based on homogeneous strain boundary conditions, the micro-scale constitutive law and the micro-to-macro static operator to establish the relationship between the macroscopic properties of a given lattice material to its micro-discrete behaviors and structures. Further, the idea behind Eshelby’s equivalent eigenstrain principle is introduced to replace a defect distribution by an imagining displacement field (eigendisplacement) with the equivalent mechanical effect, and the triangular lattice Green's function technique is developed to solve the eigendisplacement field. The proposed method therefore allows handling of different types of microstructural defects as well as its arbitrary spatial distribution within a general and compact framework. Analytical closed-form estimations are derived, in the case of the dilute limit, for all the effective elastic moduli of stretch-dominated triangular lattices containing fractured cell walls and missing cells, respectively. Comparison with numerical results, the Hashin–Shtrikman upper bounds and uniform strain upper bounds are also presented to illustrate the predictive capability of the proposed method for lattice materials. Based on this work, we propose that not only the effective Young’s and shear moduli but also the effective Poisson’s ratio of triangular lattice materials depend on the number density of fractured cell walls and their spatial arrangements.     

Stability and chaotic motion in columns of nonlinear viscoelastic material

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Macroscopic elastic tensor of a regular incompressible porous composite material

Institute of Superhard Materials, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 1, pp. 37–43, January, 1995.     

Multiscale micromechanical modeling of the constitutive response of carbon nanotube-reinforced structural adhesives

Appropriate formulations are developed to allow for the atomistic-based continuum modeling of nano-reinforced structural adhesives on the basis of a nanoscale representative volume element that accounts for the nonlinear behavior of its constituents; namely, the reinforcing carbon nanotube, the surrounding adhesive and their interface. The newly developed representative volume element is then used with analytical and computational micromechanical modeling techniques to investigate the homogeneous dispersion of the reinforcing element into the adhesive upon both the linear and nonlinear properties. Unlike our earlier work where the focus was on developing linear micromechanical models for the effective elastic properties of nanocomposites, the present approach extends these models by describing the development of a nonlinear hybrid Monte Carlo Finite Element model that allows for the prediction of the full constitutive response of the bulk composite under large deformations. The results indicate a substantial improvement in both the Young’s modulus and tensile strength of the nano-reinforced adhesives for the range of CNT concentrations considered.     

Fracture of structural elements made of viscoelastic aging materials

International Applied Mechanics -     

Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

Polar plasticity of thin-walled composites made of ideal fibre-reinforced material

The present study investigates the influence that polar material response has on the plastic behaviour of thin-walled structures made of ideal fibre-reinforced materials (Spencer, 1972); or, equivalently, on the response of thin-walled fibrous composites within the first branch of the matrix dominated form (MDM) of the bimodal theory of plasticity (Soldatos, 2011, Dvorak and Bahei-El-Din, 1987). The plasticity studies mentioned above assume that fibres are infinitely thin and, therefore, perfectly flexible. They possess no bending stiffness and, hence, their negligible bending resistance cannot influence the developed stress state, which is accordingly described by a symmetric stress tensor. In contrast, the present study considers that if fibres resistant in bending are embedded in a material at high volume concentrations, their flexure produces couple-stress and, as a result of this kind of polar material behaviour, the stress tensor becomes non-symmetric. Under plane stress conditions that dominate behaviour of thin-walled structures, the stress-space and, therefore, conditions of plastic yield and relevant yield surfaces are thus four-dimensional. However, shapes and properties of initial yield surfaces relevant to the f₁-branch of MDM are studied comprehensively by considering their projection on particular planes of such a four-dimensional stress-space. It then becomes easier understood that, in the regime of polar material response, a thin-walled structure made of ideal fibre-reinforced material deforms plastically when suitable combinations of shear stress values are reached simultaneously, rather than when only one of two unequal shear stress components reaches some maximum absolute value. Thus, polar material plasticity dismisses the conventional concept of material yield stress in shear and replaces it with a pair of two independent yield moduli. Existence of the latter is perceived as a theoretical justification of the expectation that, due to the presence of fibres, two rather than one shear yield parameters of the composite should be present and accountable for. The non-zero values of those parameters are shown to exert paramount influence on the form of the yield surface of the ideal fibre-reinforced material of interest.     

Stability of plates made of a damageable physically nonlinear material

The bifurcation instability problem for rectangular plates made of physically nonlinear materials progressively damaged with increasing load is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 79–88, September 2006.     

Survey of optimum structural design

Minimum-weight structural designs have been developed for various types of behavior specifications including stiffness, elastic and plastic strength, and stability. Some of the important design techniques and principles are discussed together with a number of significant results and implications.