Homogenization theory for designing graded viscoelastic sonic crystals

In this paper,we propose a homogenization theory for designing graded viscoelastic sonic crystals（VSCs） which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material.We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC.The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement.According to the relation of the effective loss factor to the filling fraction,a graded VSC plate is easily and quickly designed.Then,the graded VSC may have potential applications in the vibration absorption and noise reduction fields.

Prediction of Transverse Permeability for Unidirectional Fiber Tows Based on the Homogenization Theory

The transverse permeability of unidirectional fiber tows is calculated using homogenization method.Each fiber tow consisting of 21 filaments is arranged in uniform square packing.Stokes governing equation is analogized with Lame equation used in the linear elasticity problem and is solved by the finite element code ANSYS.The prediction for transverse permeability of unidirectional fiber obtained by the homogenization approach is compared with other analytical methods.The result shows a good agreement with Kozeny-Carman equation and Gebart square packing model.A model for nonuniform fiber distribution and measurement technology are proposed.It can be found that the experimental result is in excellent agreement with predicted permeability in the nonuniform distribution model.

A homogenization method for nonlinear inhomogeneous elastic materials

Background Fast simulation techniques are strongly favored in computer graphics,especially for the nonlinear inhomogeneous elastic materials.The homogenization theory is a perfect match to simulate inhomogeneous deformable objects with its coarse discretization,as it reveals how to extract information at a fine scale and to perform efficient computation with much less DOF.The existing homogenization method is not applicable for ubiquitous nonlinear materials with the limited input deformation displacements.Methods In this paper,we have proposed a homogenization method for the efficient simulation of nonlinear inhomogeneous elastic materials.Our approach allows for a faithful approximation of fine,heterogeneous nonlinear materials with very coarse discretization.Modal analysis provides the basis of a linear deformation space and modal derivatives extend the space to a nonlinear regime;based on this,we exploited modal derivatives as the input characteristic deformations for homogenization.We also present a simple elastic material model that is nonlinear and anisotropic to represent the homogenized materials.The nonlinearity of material deformations can be represented properly with this model.The material properties for the coarsened model were solved via a constrained optimization that minimizes the weighted sum of the strain energy deviations for all input deformation modes.An arbitrary number of bases can be used as inputs for homogenization,and greater weights are placed on the more important low-frequency modes.Results Based on the experimental results,this study illustrates that the homogenized material properties obtained from our method approximate the original nonlinear material behavior much better than the existing homogenization method with linear displacements,and saves orders of magnitude of computational time.Conclusions The proposed homogenization method for nonlinear inhomogeneous elastic materials is capable of capturing the nonlinear dynamics of the original dynamical system well.

Multiscale Evaluation of Mechanical Properties for Metal-Coated Lattice Structures

With the combination of 3D printing and electroplating technique,metal-coated resin lattice is a viable way to achieve lightweight design with desirable responses.However,due to high structural complexity,mechanical analysis of the macroscopic lattice structure demands high experimental or numerical costs.To efficiently investigate the mechanical behaviors of such structure,in this paper a multiscale numerical method is proposed to study the effective properties of the metal-coated Body-Centered-Cubic(BCC)lattices.Unlike studies of a similar kind in which the effective parameters can be predicted from a single unit cell model,it is noticed that the size effect of representative volume element(RVE)is severe and an insensitive prediction can be only obtained from models containing multiple-unit-cells.To this end,the paper determines the minimum number of unit cells in single RVE.Based on the proposed method that is validated through the experimental comparison,parametric studies are conducted to estimate the impact of strut diameter and coating film thickness on structural responses.It is shown that the increase of volume fraction may improve the elastic modulus and specific modulus remarkably.In contrast,the increase of thickness of coating film only leads to monotonously increased elastic modulus.For this reason,there should be an optimal coating film thickness for the specific modulus of the lattice structure.This work provides an effective method for evaluating structural mechanical properties via the mesoscopic model.

A LOWER BOUND LIMIT ANALYSIS OF DUCTILE COMPOSITE MATERIALS

The plastic load-bearing capacity of ductile composites such as metal matrix composites is studied with an insight into the microstructures. The macroscopic strength of a composite is obtained by combining the homogenization theory with static limit analysis, where the temperature parameter method is used to construct the self-equilibrium stress field. An interface failure model is proposed to account for the effects of the interface on the failure of composites. The static limit analysis with the finite-element method is then formulated as a constrained nonlinear programming problem, which is solved by the Sequential Quadratic Programming （SQP） method. Finally, the macroscopic transverse strength of perforated materials, the macroscopic transverse and off-axis strength of fiber-reinforced composites are obtained through numerical calculation. The computational results are in good agreement with the experimental data.

MICRO/MACROMECHANICAL PLASTIC LIMIT ANALYSES OF COMPOSITE MATERIALS AND STRUCTURES

The load-bearing capacities f ductile composite materials andstructures are studied by means of a combined micro/macromechanicsapproach. Firstly, on the microscopic scale, the aim is to get themacroscopic strength domains by means of the homogenization theory ofmicromechanics. A representative volume element (RVE) is selected toreflect the microstructures of the composite materials. Byintroducing the homogenization theory into the kinematic limittheorem of plastic limit analysis, an optimization format to directlycalculate the limit loads of the RVE is obtained. And the macroscopicyield criterion can be deter- mined according to the relation betweenmacroscopic and microscopic fields.

An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems

The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information.This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented.

ON THE SOLUTIONS OF NAVIER-STOKES EQUATIONS AND THE THEORY OF HOMOGENEOUS ISOTROPIC TURBULENCE

The present paper is a further development of our previous work in solving the wholeproblem of the homogeneous isotropic turbulence from the nitial period to the final period ofdecay. An expansion method is developed to obtain the axinlly symmetrical solution of theNavier-Stokes equations of motion in the form of an infinite set of nonlinear partial differen-tial equations of the second order. For the present we solve the zeroth order approximation.By using the method of Fourier transform, we get a nonlinear nitegro-differential equationfor the amplitude function in the wave number space.It is also the dynamical equation forthe energy spectrum. By choosing a suitable initial condition, we solve this equation numerically. The energyspectrum function and the energy transfer spectrum function thus calculated satisfy the spec-trum form of the karman-Howarth equation exactly. We Lave computed the energy spectrumfunction, the energy transfer function the decay of turbulent energy, the integral scale, Taylormicroscale, the double and triple velocity correlations on the whole range from the initialperiod to the final period of decay. As a whole all these calculated statistical physicalquantities agree with experiments very wall except a few cases with small discrepancies at largeseparations.

Dynamic mechanical characterization and optimization of particle-reinforced W-Ni-Fe composites

A visco-plastic rate-dependent homogenization theory for particle-reinforced composites was derived and the equivalent elastic constants and the equivalent visco-plastic parameters of these composites were obtained. A framework of homogenization the- ory for particle-reinforced W-Ni-Fe composites, a kind of tungsten alloy, was established. Based on the homogenization theory and a fixed-point iteration method, a unit cell model with typical microstructnres of the composite was established by using dynamic analysis program. The effects of tungsten content, tungsten particle shape and particle size and interface strength on the mechanical properties and the crack propagation of the W-Ni-Fe composite are analyzed under quasi-static and dynamic loadings. The stress-strain curves of the composite are given and the relation between the macro-mechanical characteristics and the microstructure parameters is explored, which provides an important theoretical basis for the optimization of the W-Ni-Fe composites.

Modeling of Mesoscale Creep Behaviors and Macroscale Creep Responses of Composite Fuels Under Irradiation Conditions

A finite-strain homogenization creep model for composite fuels under irradiation conditions is developed and verified,with the irradiation creep strains of the fuel particles and matrix correlated to the macroscale creep responses,excluding the contributions of volumetric strain induced by the irradiation swelling deformations of fuel particles.A finite element(FE)modeling method for uniaxial tensile creep tests is established with the irradiation effects of nuclear materials taken into account.The proposed models and simulation strategy are numerically implemented to a kind of composite nuclear fuel,and the predicted mesoscale creep behaviors and the macroscale creep responses are investigated.The research results indicate that:(1)the macroscale creep responses and the mesoscale stress and strain fields are all greatly affected by the irradiation swelling of fuel particles,owing to the strengthened mechanical interactions between the fuel particles and the matrix.(2)The effective creep rates for a certain case are approximately two constants before and after the critical fission density,which results from the accelerated fission gas swelling after fuel grain recrystallization,and the effects of macroscale tensile stress will be more enhanced at higher temperatures.(3)The macroscale creep contributions from the fuel particles and matrix depend mainly on the current volume fractions varying with fission density.(4)As a function of the macroscale stress,temperature,initial particle volume fraction and particle fission rate,a multi-variable mathematical model for effective creep rates is fitted out for the considered composite fuels,which matches well with the FE predictions.This study supplies important theoretical models and research methods for the multi-scale creep behaviors of various composite fuels and provides a basis for simulation of the thermal–mechanical behavior in related composite fuel elements and assemblies.

Global stabilisation for a class of uncertain non-linear systems:a novel non-recursive design framework

In this paper,a novel global non-recursive stabilisation design framework is addressed for a class of inherent non-linear systems with the presence of system uncertainties and external nonvanishing disturbances.By virtue of the facility that the weighted homogeneity brings into the system synthesis procedure,a non-recursive design method is proposed to yield a globally effectiveness robust controller with its expression following a quasi-linear manner.By proceeding with a rigorous non-recursive stability analysis framework,which covers both global asymptotical and finite-time convergence cases,the common recursively treated derivative items in backsteppingbased methods are totally avoided.Inspired by the homogeneous domination technique,a scaling gain performed as a bandwidth factor is introduced into the original system and hence the robustness of the controlled system can be adjusted to meet the practical performance requirements.A numerical example and its control performance simulations are given to illustrate the effectiveness and simplicity of the proposed controller design framework.