基于微形态模型的颗粒材料中波的频散现象研究

基于颗粒材料冲击与波动响应特性的调控波传播行为的超材料设计受到广泛关注,设计这类材料需要对颗粒材料的波传播机制及调控机理有深入认识. 波在颗粒材料中传播的频散现象及频率带隙等行为与材料的非均匀性密切相关,通常讨论频散现象是基于弹性理论框架建立微结构连续体或高阶梯度连续体等广义连续体模型来进行. 本研究基于细观力学给出了一个颗粒材料的微形态连续体模型. 在该模型中,考虑了颗粒的平动和转动,且颗粒间的相对运动分解为两部分:即宏观平均运动和细观真实运动. 基于此分解,提出了一个完备的变形模式,得到了对应于不同应变及颗粒间运动的宏细观本构关系. 结合宏观变形能的细观变形能求和表达式,获得了基于细观量表示的宏观本构模量. 应用所建议模型考察了波在弹性颗粒介质的传播行为,给出了不同形式的波的频散曲线,结果显示此模型具有预测频率带隙的能力.      

Multi-scale micromorphic theory for hierarchical materials

For the design of materials, it is important to faithfully model macroscopic materials response together with mechanisms and interactions occurring at the microstructural scales. While brute-force modeling of all the details of the microstructure is too costly, many of the current homogenized continuum models suffer from their inability to capture the correct underlying deformation mechanisms—especially when localization and failure are concerned. To overcome this limitation, a multi-scale continuum theory is proposed so that kinematic variables representing the deformation at various scales are incorporated. The method of virtual power is then used to derive a system of coupled governing equations, each representing a particular scale and its interactions with the macro-scale. A constitutive relation is then introduced to preserve the underlying physics associated with each scale. The inelastic behavior is represented by multiple yield functions, each representing a particular scale of microstructure, but collectively coupled through the same set of internal variables. The theory is illustrated by two applications. First, a one-dimensional example of a three-scale material is presented. After the onset of softening, the model shows that the localization zone is distributed according to two distinct length scale determined by the model. Second, a two-scale continuum model is introduced for the failure of porous metals. By comparing the theory to a direct numerical simulation (DNS) of the microstructure for a specimen in tension, we show that the model capture the main physics, and at the same time, remains computationally affordable.     

Micromorphic approach for finite gradient-elastoplasticity fully coupled with ductile damage: Formulation and computational aspects

It is well established that the use of inelastic constitutive equations accounting for induced softening, leads to pathological space (mesh) and time discretization dependency of the numerical solution of the associated Initial and Boundary Value Problem (IBVP). To avoid this drawback, many less or more approximate solutions have been proposed in the literature in order to regularize the IBVP and to obtain numerical solutions which are, at convergence, much less sensitive to the space and the time discretization. The basic idea behind these regularization techniques is the formulation of nonlocal constitutive equations by introducing some effects of characteristic lengths representing the materials microstructure. In this work, using the framework of generalized nonlocal continua, a thermodynamically-consistent micromorphic formulation using appropriate micromorphic state variables and their first gradients, is proposed in order to extend the classical local constitutive equations by incorporating appropriate characteristic internal lengths. The isotropic damage, the isotropic and the kinematic hardenings are supposed to carry the targeted micromorphic effects. First the theoretical aspects of this fully coupled micromorphic formulation is presented in details and the proposed generalized balance equations as well as the fully coupled micromorphic constitutive equations deduced. The associated numerical aspects in the framework of the classical Galerkin-based FE formulation are briefly discussed in the special case of micromorphic damage. Specifically, the formulation of 2D finite elements with additional degrees of freedom (d.o.f.), the dynamic explicit global resolution scheme as well as the local integration scheme, to compute the stress tensor and the state variables at each integration point of each element, are presented. Application is made to the typical uniaxial tension specimen under plane strain conditions in order to chow the predictive capabilities of the proposed micromorphic model, particularly against its ability to give (at convergence) a mesh independent solution even for high values of the ductile damage (i.e., the macroscopic cracks).     

Material force in micromorphic plasticity

Micromorphic theory envisions a material body as a continuous collection of deformable particles with finite size and inner structure. It is considered as the most successful top-down formulation of a two-level continuum model, in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure. In this work, we revisit the original micromorphic theory and further construct a mathematical theory of micromorphic plasticity with generalized strain-based return mapping algorithm. The concept of material forces, which may also be referred as Eshelbian mechanics, was first derived for micromorphic thermo-visco-elastic solid, and, now in this work, it is extended to the micromorphic plasticity. The balance law of pseudo-momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo-momentum, and material forces are derived. Following this formulation, the failure mechanisms of micromorphic thermo-visco-elastoplastic materials can be further investigated.     

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.     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

A micromechanical model of toughening behavior in the dual-phase composite

The fabrication of a special kind of dual-phase composite consisting of a hard matrix and ductile phase, such as metals with bimodal grain size distribution, is a promising strategy for improving the tensile ductility of nanocrystalline (nc)/ultrafine-grained (ufg) materials (Wang et al., 2002). This strategy is, however, challenged by the low reproducibility from low controllability of microstructural parameters and the existence of counterexamples (Prasad et al., 2009). The key to meet these challenges is to control the bimodal microstructural parameters to enable quantificational investigation of the relation between mechanical properties and microstructural parameters, and then set up a correlative quantitative model. In this paper, a new micromechanical model based on the propagation and multiplication of localized deformation bands is developed. To assess the model, a series of hypo-eutectoid Cu–Al alloys with controllable bimodal structures are prepared and their stress–strain curves in tension, together with those of bimodal copper (Wang et al., 2002) and bimodal Al–Mg alloys (Han et al., 2005) are predicted. Close agreement between the model-predicted and experimental results is obtained. The strength and uniform ductility of bimodal materials are observed in strong relation to the microstructural and constitutive parameters of volume fraction, strain hardening coefficient, and size of the coarse-grained ductile phase. Additionally, appropriate microstructural and constitutive parameters to achieve effective toughening can also be estimated according to the model.     

A three-dimensional progressive damage model for fibre-composite materials

This note presents a damage model for fibre-composite materials based in the approach by Matzenmiller et al. [Matzenmiller, A., Lubliner, J., Taylor, R.L., 1995. A constitutive model for anisotropic damage in fiber-composites. Mech. Mater. 20, 125]. In this work, the model is developed in a three-dimensional context with modified formulation for the constitutive law and damage evolution. An orthotropic composite subjected to mixed failure modes is assumed in this development. Its formulation and implementation details are provided.     

A unified theory for cavity expansion in cohesive-frictional micromorphic media

This paper presents a unified theory for both cylindrical and spherical cavity expansion problems in cohesive-frictional micromorphic media. A phenomenological strain-gradient plasticity model in conjunction with a generalized Mohr–Coulomb criterion is employed to characterize the elasto-plastic behavior of the material. To solve the resultant two-point boundary-value problem (BVP) of fourth-order homogeneous ordinary differential equation (ODE) for the governing equations which is not well-conditioned in certain cases, several numerical methods are developed and are compared in terms of robustness, efficiency and accuracy. Using one of the finite difference methods that shows overall better performance, both cylindrical and spherical cavity expansion problems in micromorphic media are solved. The influences of microstructural properties on the expansion response are clearly demonstrated. Size effect during the cavity expansion is captured. The proposed theory is also applied to a revisit of the classic problem of stress concentration around a cavity in a micromorphic medium subjected to isotropic tension at infinity, for which some conclusions made in early studies are revised. The proposed theory can be useful for the interpretation of indentation tests at small scales.     

Scale transition of a higher order plasticity model – A consistent homogenization theory from meso to macro

Standard plasticity models cannot capture the microstructural size effect associated with grain sizes, as well as structural size effects induced by external boundaries and overall gradients. Many higher-order plasticity models introduce a length scale parameter to resolve the latter limitation – microstructural influences are not explicitly account for. This paper adopts two distinct length scales in the formulation, i.e. an intrinsic length scale (l) governing micro-processes such as dislocation pile-up at internal boundaries, as well as the characteristic grain size (L), and aims to unravel the interaction between these two length scales and the characteristic specimen size (H) at the macro level. At the meso-scale, we adopt the strain gradient plasticity model developed in Gurtin (2004) [Gurtin, M.E., 2004. A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. J. Mech. Phys. Solids 52, 2545–2568] which accounts for the direct influence of grain boundaries. Through a novel homogenization theory, the plasticity model is translated consistently from meso to macro. The two length scale parameters (l and L) manifest themselves naturally at the macro scale, hence capturing both types of size effects in an average sense. The resulting (macro) higher-order model is thermodynamically consistent to the meso model, and has the same structure as a micromorphic continuum. Finally, we consider a bending example for the two limiting cases – microhard and microfree conditions at grain boundaries – and illustrate the excellent match between the meso and homogenized solutions.     

材料非线性微-宏观分析的多尺度方法研究

介绍并比较了近年来在材料非线性微-宏观分析多级数值方法方面的研究工作. 针 对考虑材料内摩擦接触的颗粒材料多尺度计算问题，建立一种基于数值技术的多级分析方 法. 方法的特点是在对材料进行微观分析的基础上建立宏观材料的多尺度非线性数值本构模 型. 而对材料弹塑性多级分析问题，建立了基于转换场技术的算法，采用近似技术建立非线 性分析的本征应变矩阵，使方法具有表达简单与实现方便的特点. 给出了数值算例， 通过比较说明了方法的正确性与有效性.     

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.     

Coupled Solvent and Heat Transport of a Mixture of Swelling Porous Particles and Fluids: Single Time-Scale Problem

A three-spatial scale, single time-scale model for both moisture and heat transport is developed for an unsaturated swelling porous media from first principles within a mixture theoretic framework. On the smallest (micro) scale, the system consists of macromolecules (clay particles, polymers, etc.) and a solvating liquid (vicinal fluid), each of which are viewed as individual phases or nonoverlapping continua occupying distinct regions of space and satisfying the classical field equations. These equations are homogenized forming overlaying continua on the intermediate (meso) scale via hybrid mixture theory (HMT). On the mesoscale the homogenized swelling particles consisting of the homogenized vicinal fluid and colloid are then mixed with two bulk phase fluids: the bulk solvent and its vapor. At this scale, there exists three nonoverlapping continua occupying distinct regions of space. On the largest (macro) scale the saturated homogenized particles, bulk liquid and vapor solvent, are again homogenized forming four overlaying continua: doubly homogenized vicinal fluid, doubly homogenized macromolecules, and singly homogenized bulk liquid and vapor phases. Two constitutive theories are developed, one at the mesoscale and the other at the macroscale. Both are developed via the Coleman and Noll method of exploiting the entropy inequality coupled with linearization about equilibrium. The macroscale constitutive theory does not rely upon the mesoscale theory as is common in other upscaling methods. The energy equation on either the mesoscale or macroscale generalizes de Vries classical theory of heat and moisture transport. The momentum balance allows for flow of fluid via volume fraction gradients, pressure gradients, external force fields, and temperature gradients.     

钨合金的冲击动力学性质及细微观结构的影响

简单介绍了钨合金(主要为W-Ni-Fe)的制备工艺和常用热处理方法,其后着重从动 态力学性能、剪切带的实验观察和研究、细微观结构对材料力学性能的影响等几方 面总结和评述了近年来针对钨合金取得的主要结果.并在文章的最后初步提出了有 前景的几个研究方向.     

A micromorphic electromagnetic theory

This work is concerned with the determination of both macroscopic and microscopic deformations, motions, stresses, as well as electromagnetic fields developed in the material body due to external loads of thermal, mechanical, and electromagnetic origins. The balance laws of mass, microinertia, linear momentum, moment of momentum, energy, and entropy for microcontinuum are integrated with the Maxwell’s equations. The constitutive theory is constructed. The finite element formulation of micromorphic electromagnetic physics is also presented. The physical meanings of various terms in the constitutive equations are discussed.     

Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models

A temperature-dependent anisotropic material model was developed for two aluminum alloys AA5182-O and AA5754-O and their anisotropy parameters were established. A coupled thermo-mechanical finite element analysis of the forming process was then performed for the temperature range 25–260 °C (77–500 °F) at different strain rates. In the developed model, the anisotropy coefficients for Barlat’s YLD2000-2d anisotropic yield function [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H., Chu, E., 2003. Plane stress yield function for aluminum alloy sheets – Part 1: Theory. Int. J. Plasticity 19, 1297–1319] in the plane-stress condition and the parameters for the isotropic strain hardening were established as a function of temperature. The temperature-dependent anisotropic yield function was then implemented into the commercial FEM code LS-DYNA as a user material subroutine (UMAT) using the cutting-plane algorithm for the integration of a general class of elastoplastic constitutive models [Abedrabbo, N., Pourboghrat, F., Carsley, J., 2006b. Forming of aluminum alloys at elevated temperatures – Part 2: Numerical modeling and experimental verification. Int. J. Plasticity 22 (2), 342–737]. The temperature-dependent material model was used to simulate the coupled thermo-mechanical finite element analysis of the stamping of an aluminum sheet using a hemispherical punch under the pure stretch boundary condition (no material draw-in was allowed). Simulation results were compared with experimental data at several elevated temperatures to evaluate the accuracy of the UMAT’s ability to predict both forming behavior and failure locations. Two failure criteria were used in the analysis; the M–K strain based forming limit diagrams (ε-FLD), and the stress based forming limit diagrams (σ-FLD). Both models were developed using Barlat’s YLD2000-2d anisotropic model for the two materials at several elevated temperatures. Also, as a design tool, the Genetic Algorithm optimization program HEEDS was linked with the developed thermo-mechanical models and used to numerically predict the “optimum” set of temperatures that would generate the maximum formability for the two materials in the pure stretch experiments. It was found that a higher temperature is not needed to form the part, but rather the punch should be maintained at the lowest temperature possible for maximum formability.     

Path-dependent failure of inflated aluminum tubes

Our recent investigation on the formability of Al alloy tubes under combined internal pressure and axial load is expanded by examining the effect of the loading path traced. A set of Al-6260-T4 tubes were loaded along orthogonal stress paths to failure and the results are compared to those of the corresponding radial paths. It is confirmed that failure strains are path-dependent, but also is demonstrated that failure stresses become path-dependent if the prestrain is significant. The experiments are simulated using the previously developed finite element models and the calibration of the Yld2000-2D [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.-H., Chu, E., 2003. Plane stress yield function for aluminum alloy sheets-part I: theory. Int. J. Plasticity 19, 1297--1319] anisotropic yield function shown in [Korkolis, Y.P., Kyriakides, S., 2008b. Inflation and burst of anisotropic aluminum tubes. Part II: an advanced yield function including deformation-induced anisotropy. Int. J. Plasticity 24, 1625–1637] to yield accurate predictions of rupture for nine radial paths. The models are shown to reproduce the path dependence of the failure stresses and strains quite well. A group of additional radial and corner paths are subsequently examined numerically to enrich the existing data on path-dependence of failure. It is again shown that the amount of plastic prestraining in either of the two directions influences the difference of the failure stresses and strains between the radial and the corner stress paths.     

A constitutive theory for shape memory polymers. Part II: A linearized model for small deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modelling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.