PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD

The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.     

A version of Hill＇s lemma for Cosserat continuum

On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.     

THEORY OF NONLOCAL ASYMMETRIC ELASTIC SOLIDS

In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum fieM theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic fiteld theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation, We show that there is the nonlocal body moment in the nonlocal elastic solids. The noniocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.     

BASIC THEOREMS IN LINEAR MICROMORPHIC THERMOELECTROELASTICITY AND THEIR PRIMARY APPLICATION

As a natural extension of the micromorphic continuum theory, the linear theory of micromorphic thermoelectroelasticity is developed to characterize the nano-micro scale behavior of thermoelectroelastic materials with remarkable microstructures. After the basic governing equations are given and the reciprocal theorem is deduced, both the generalized variational principle and the generalized Hamilton principle for mixed boundary-initial value problems of micromorphic thermoelectroelastodynamics in convolution form are established. Finally, as a primary application, steady state responses of an unbounded homogeneous isotropic micromorphic thermoelectroelastic body to external concentrated loads with mechanical, electric, and thermal origins are analyzed.     

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF FULLY BACKED SANDWICH PLATES UNDER LOCALIZED IMPULSIVE LOADING

An analytical model is developed to assess the elastic-plastic dynamic response of fully backed sandwich plates under localized impulse load.The core is modeled as an elastic-perfectly plastic foundation.The top face sheet is treated as an individual plate resting on the foundation.The elastic-plastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique.The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed.The model can be used to predict the impulse-induced local effect on fully backed sandwich plates.     

A micropolar mixture theory of multi-component porous media

A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen＇s model.     

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

In this paper,the nonlinear dynamic behavior of a string-beam coupled system subjected to external,parametric and tuned excitations is presented.The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system which are described by a set of ordinary differential equations with two degrees of freedom.The case of 1:1 internal resonance between the modes of the beam and string,and the primary and combined resonance for the beam is considered.The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system and obtain approximate solutions up to and including the second-order approximations.All resonance cases are extracted and investigated.Stability of the system is studied using frequency response equations and the phase-plane method.Numerical solutions are carried out and the results are presented graphically and discussed.The effects of the different parameters on both response and stability of the system are investigated.The reported results are compared to the available published work.     

Thermodynamic and rate variational formulation of models for inhomogeneous gradient materials with microstructure and application to phase field modeling

In this work,thermodynamic models for the energetics and kinetics of inhomogeneous gradient materials with microstructure are formulated in the context of continuum thermodynamics and material theory.For simplicity,attention is restricted to isothermal conditions.The materials of interest here are characterized by(1) first- and secondorder gradients of the deformation field and(2) a kinematic microstructure field and its gradient(e.g.,in the sense of director,micromorphic or Cosserat microstructure).Material inhomogeneity takes the form of multiple phases and chemical constituents,modeled here with the help of corresponding phase fields.Invariance requirements together with the dissipation principle result in the reduced model field and constitutive relations.Special cases of these include the wellknown Cahn-Hilliard and Ginzburg-Landau relations.In the last part of the work,initial boundary value problems for this class of materials are formulated with the help of rate variational methods.     

Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension

A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory. Transition sets of the system and 40 groups of bifurcation diagrams are obtained. The local bifurcation is found, and shows the overall character- istics of bifurcation. Based on the. relationship between parameters and the topological bifurcation solutions, motion characteristics with different parameters are obtained. The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.     

基于参数变分原理的Cosserat连续体弹塑性分析

基于参数变分原理,提出了Cosserat模型弹塑性计算的算法,给出了基于Cosserat理论的参数最小势能原理,基于所提出的变分方程,建立了Cosserat理论弹塑性分析的参数二次规划模型,进一步将算法应用于平面应变软化问题计算中,获得的结果具有良好的非网格依赖性.     

平面Cosserat模型有限元分析的4和8节点单元与分片试验研究

经典连续体理论不包括物质内部尺度，当考虑应变软化问题时，有限元结果对网格具有很强的依赖性。与经典连续介质力学理论不同，Cosserat连续体模型在传统平动自由度的基础上添加了一独立的旋转自由度，在本构模型中引入了内尺度参数。本文研究了基于Cosserat理论的平面4和8节点等参元以及8（4）节点线、角位移混合插值等参单元，给出Cosserat单元分片试验的实施过程。最后将单元运用到小孔应力集中问题的分析当中，通过计算结果与理论解的比较，表明了4和8节点以及8（4）节点等参元的适用性，为问题的非线性分析打下基础。     

三维Cosserat连续体模型与微结构尺寸相关效应的有限元分析

分析了三维Cosserat连续体理论中的应力应变特征,推导了三维Cosserat连续体的有限元方程,基于ABAQUS计算软件提供的用户单元子程序(UEL)接口编写了弹性Cosserat连续体三维20节点有限元程序,并分析了微悬臂梁自由端的挠度问题和微杆扭转问题。通过与基于经典连续体理论的解析解及有限元数值计算结果进行比较,表明所发展的三维Cosserat连续体有限元能有效地模拟微结构尺寸相关效应问题,即随着微结构尺寸与材料内部长度参数的接近,基于Cosserat连续体有限元分析得到的微梁的挠度以及微杆的转角与经典连续体的解析解及有限元解相比越来越小;反之,Cosserat连续体有限元的计算结果与经典连续体的解析解及有限元数值解较为一致。     

Computational multiscale methods for granular materials

The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolves, it is demonstrated to develop computational multiscale methods using discrete particle assembly-Cosserat continuum modeling in micro- and macro- scales, respectively. The computational homogenization method and the bridge scale method along the concurrent scale linking approach are briefly introduced. Based on the weak form of the Hu-Washizu variational principle, the mixed finite element procedure of gradient Cosserat continuum in the frame of the second-order homogenization scheme is developed. The meso-mechanically informed anisotropic damage of effective Cosserat continuum is characterized and identified and the microscopic mechanisms of macroscopic damage phenomenon are revealed.     

梯度增强Cosserat连续体的广义Hill定理

基于经典Cauchy连续体的Hill定理,在平均场理论的框架下导出了梯度增强Cosserat连续体细、宏观均匀化方法的广义Hill定理。在梯度增强Cosserat连续体中,不仅宏观样条点上的应变和应力张量,而且它们的梯度均作用于与该样条点相关联的细观表征元（RVE）。依据此广义Hill定理,对梯度增强Cosserat连...     

Transversely isotropic material: nonlinear Cosserat versus classical approach

We consider a specific case of unidirectional reinforced material under applied tensile load. The reinforcement of the material is inclined with 45° to the direction of the tensile resultant. Different approaches are discussed: one experiment and three computational models. Two models use the classical Cauchy continuum theory whereas the third computational model is based on a Cosserat continuum. It is well known that test specimen with inclination between unidirectional reinforcement and tensile direction show, besides Poissons effect, additional deformation perpendicular to the load direction. The classical transversely isotropic continuum theory predicts this deformation as typical S-shape. In the Cosserat continuum the orientation of the inner structure is incorporated. Thus, structural parameters influence the deformation. With the proposed geometrically non-linear Cosserat model classical and non-classical behaviour can be modelled. In the non-classical case, the transverse deformation is not described by one S-shape but by multiple S-shaped modes. The additional rotational parameters in the Cosserat continuum are responsible for the non-classical behaviour which is due to non-symmetric strain.     

Finite element modeling of micropolar-based phononic crystals

The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of virtual work and Bloch–Floquet boundary conditions. The periodic boundary conditions are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Results in terms of band structures for different material cells and mechanical parameters are provided.     

Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes occurring in the internal heterogeneous structure. These models tend to be intensive from the computational point of view as they adopt an “a priori” discretization anchored to the major material heterogeneities (e.g. grains in particulate materials and aggregate pieces in cementitious composites) and this hampers their use in the numerical simulations of large systems. In this work, this problem is addressed by formulating a general multiple scale computational framework based on classical asymptotic analysis and that (1) is applicable to any discrete model with rotational degrees of freedom; and (2) gives rise to an equivalent Cosserat continuum. The developed theory is applied to the upscaling of the Lattice Discrete Particle Model (LDPM), a recently formulated discrete model for concrete and other quasi-brittle materials, and the properties of the homogenized model are analyzed thoroughly in both the elastic and the inelastic regime. The analysis shows that the homogenized micropolar elastic properties are size-dependent, and they are functions of the RVE size and the size of the material heterogeneity. Furthermore, the analysis of the homogenized inelastic behavior highlights issues associated with the homogenization of fine-scale models featuring strain-softening and the related damage localization. Finally, nonlinear simulations of the RVE behavior subject to curvature components causing bending and torsional effects demonstrate, contrarily to typical Cosserat formulations, a significant coupling between the homogenized stress–strain and couple-curvature constitutive equations.