Antiplane magneto-electro-elastic effective properties of three-phase fiber composites

In the present work, applying the asymptotic homogenization method (AHM), the derivation of the antiplane effective properties for three-phase magneto-electro-elastic fiber unidirectional reinforced composite with parallelogram cell symmetry is reported. Closed analytical expressions for the antiplane local problems on the periodic cell and the corresponding effective coefficients are provided. Matrix and inclusions materials belong to symmetry class 6mm. Numerical results are reported and compared with the eigenfunction expansion-variational method (EEVM) and other theoretical models. Good agreements are found for these comparisons. In addition, with the herein implemented solution, it is possible to reproduce the effective properties of the reduced cases such as piezoelectric or elastic composites obtaining good agreements with previous reports.     

Towards a homogenized plasticity theory which predicts structural and microstructural size effects

We study an idealized bending problem where two types of size effects are present – one induced by the non-uniform (macro) deformation, the other due to the (internal) resistance at grain boundaries. Classical models are not able to capture either of the two types of size dependent behavior. A remedy is to adopt a gradient crystal plasticity formulation which allows one to study the direct influence of different microstructural properties on the material response. However, it is computationally expensive to do so for a typical engineering problem since the discretization has to be done at a sub-granular level. In this paper, a homogenization theory is proposed such that the small deformation gradient crystal plasticity framework by Cermelli and Gurtin [Cermelli, P., Gurtin, M.E., 2002. Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations. Int. J. Solids Struct. 39, 6281–6309] translates from the micro to macro level consistently. Microstructural properties thus propagate naturally to the macro scale and the homogenized solutions compare well with the fine scale analyses for the two limit cases – microhard and microfree conditions. Three length scale parameters, i.e. the intrinsic length scale, grain size and the foil thickness, manifest themselves in the homogenized solution, thus capturing both types of size effects. We further discuss on the interplay and competition between the two size effects.     

Modeling of anisotropic softening phenomena: Application to soft biological tissues

A thermodynamically consistent dissipative model is proposed to describe softening phenomena in anisotropic materials. The model is based on a generalized polyconvex anisotropic strain energy function represented by a series. Anisotropic softening is considered by evolution of internal variables governing the anisotropic properties of the material. Accordingly, evolution equations are formulated and anisotropic conditions for the onset of softening are defined. In numerical examples, the model is applied to simulate the preconditioning behavior of soft biological tissues subjected to cyclic loading experiments. The results suggest that the general characteristics of preconditioning with different upper load limits are well captured including hysteresis and residual deformations. A model for the Mullins effect is obtained as a special case and shows very good agreement with experimental data on mouse skin.     

Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties

In this paper, we present the homogenization of an anisotropic hollow layered tube with discontinuous elastic coefficients. We focus on some aspects of technological importance, such as the effective coefficients of anisotropic materials, the behavior of the homogenized displacements and stresses, the discontinuities of in-plane shear, hoop and longitudinal stresses, the homogenization-induced anisotropy in the isotropic case. We conclude that the problem of cylindrically anisotropic tubes under extension, torsion, shearing and pressuring is stable by homogenization and we define the effective tensor of the material elastic coefficients. Some numerical examples confirm the theoretical results.     

Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates

A new approach is proposed for estimating the macroscopic behavior of two-phase nonlinear composites with random, particulate microstructures. The central idea is to model composites by sequentially laminated constructions of infinite rank whose macroscopic behavior can be determined exactly. The resulting estimates incorporate microstructural information up to the two-point correlation functions, and require the solution to a Hamilton–Jacobi equation with the inclusion concentration and the macroscopic fields playing the role of ‘time’ and ‘spatial’ variables, respectively. Because they are realizable, by construction, these estimates are guaranteed to be convex, to satisfy all pertinent bounds, to exhibit no duality gap, and to be exact to second order in the heterogeneity contrast. Sample results are provided for two- and three-dimensional power-law composites, and are compared with other homogenization estimates, as well as with numerical simulations available from the literature. The estimates are found to give physically sensible predictions for all the cases considered, even for extreme values of the nonlinearity and heterogeneity contrast. Interestingly, in the case of isotropic porous materials under hydrostatic loadings, the estimates agree exactly with standard Gurson-type models for viscoplastic porous media.     

A self-consistent plasticity theory for modeling the thermo-mechanical properties of irradiated FCC metallic polycrystals

A self-consistent theoretical framework is developed to model the thermo-mechanical behaviors of irradiated face-centered cubic (FCC) polycrystalline metals at low to intermediate homologous temperatures. In this model, both irradiation and temperature effects are considered at the grain level with the assist of a tensorial plasticity crystal model, and the elastic-visocoplastic self-consistent method is applied for the scale transition from individual grains to macroscopic polycrystals. The proposed theory is applied to analyze the mechanical behaviors of irradiated FCC copper. It is found that: (1) the numerical results match well with experimental data, which includes the comparison of results for single crystals under the load in different directions, and for polycrystals with the influences of irradiation and temperature. Therefore, the feasibility and accuracy of the present model are well demonstrated. (2) The main irradiation effects including irradiation hardening, post-yield softening, strain-hardening coefficient (SHC) dropping and the non-zero stress offset are all captured by the proposed model. (3) The increase of temperature results in the decrease of yield strength and SHC. The former is attributed to the weakened dislocation–defect interaction, while the latter is due to the temperature-strengthened dynamic recovery of dislocations through the thermally activated mechanism. The present model may provide a theoretical guide to predict the thermo-mechanical behaviors of irradiated FCC metals for the selection of structural materials in nuclear equipment.     

A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations

This study develops a small-deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation. The theory is based on a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:

•

the microstresses to depend on , the gradient of the plastic strain-rate, and

•

the free energy ψ to depend on the Burgers tensor .

The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for the plastic strain. The microstresses are strictly dissipative when ψ is independent of the Burgers tensor, but when ψ depends on G the gradient microstress is partially energetic, and this, in turn, leads to a back stress and (hence) to Bauschinger-effects in the flow rule. It is further shown that dependencies of the microstresses on lead to strengthening and weakening effects in the flow rule.Typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with flow, and, as an aid to numerical solutions, a weak (virtual power) formulation of the nonlocal flow rule is derived.     

A one-dimensional theory of strain-gradient plasticity: Formulation, analysis, numerical results

This study develops a one-dimensional theory of strain-gradient plasticity based on: (i) a system of microstresses consistent with a microforce balance; (ii) a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; (iii) a constitutive theory that allows

•

the free-energy to depend on the gradient of the plastic strain, and

•

the microstresses to depend on the gradient of the plastic strain-rate.

The constitutive equations, whose rate-dependence is of power-law form, are endowed with energetic and dissipative gradient length-scales L and l, respectively, and allow for a gradient-dependent generalization of standard internal-variable hardening. The microforce balance when augmented by the constitutive relations for the microstresses results in a nonlocal flow rule in the form of a partial differential equation for the plastic strain. Typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with flow, and properties of the resulting boundary-value problem are studied both analytically and numerically. The resulting solutions are shown to exhibit three distinct physical phenomena:

(i)

standard (isotropic) internal-variable hardening;

(ii)

energetic hardening, with concomitant back stress, associated with plastic-strain gradients and resulting in boundary layer effects;

(iii)

dissipative strengthening associated with plastic strain-rate gradients and resulting in a size-dependent increase in yield strength.

     

Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: A three-dimensional theory based on thermodynamics with internal state variables

In the vicinity of the glass transition, glass-forming materials exhibit pronounced frequency-dependent changes in the mechanical material properties, the thermal expansion behaviour and the specific heat. The frequency dependence becomes apparent under harmonic stress, strain or temperature excitations. The Prigogine-Defay ratio is a characteristic number which connects the changes in magnitude of these quantities at the glass transition. In order to represent the thermoviscoelastic properties of glass-forming materials in continuum mechanics, a three-dimensional approach which is based on the Gibbs free energy as thermodynamic potential is developed in this article. The Gibbs free energy depends on the stress tensor, the temperature and a set of internal variables which is introduced to take history-dependent phenomena into account. In the vicinity of an equilibrium reference state, the specific Gibbs free energy is approximated up to second order terms. Evaluating the Clausius-Duhem inequality, the constitutive relations for the strain tensor, the entropy and the internal variables are derived. In comparison with other approaches, the entropy, the strain tensor and the internal variables are functionals not only of the stress tensor but also of the temperature. Applying harmonic temperature- or stress-controlled excitations, complex frequency-dependent relations for the specific heat under constant stress, for the thermal expansion coefficients as well as for the dynamic mechanical compliance are obtained. The frequency-dependence of these quantities depicts the experimentally observed behaviour of glass-forming materials as published in literature. Under the assumption of isotropic material behaviour, it is shown that the developed theory is compatible with the Prigogine-Defay inequality for arbitrary values of the material parameters.     

A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part II: Finite deformations

This paper generalizes to finite deformations our companion paper [Gurtin, M.E., Anand, L., 2004. A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations. Journal of the Mechanics and Physics of Solids, submitted]. Specifically, we develop a gradient theory for finite-deformation isotropic viscoplasticity in the absence of plastic spin. The theory is based on the Kröner–Lee decomposition F = F^eF^p of the deformation gradient into elastic and plastic parts; a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:

• the microstresses to depend on D^p, the gradient of the plastic stretching,

• the free energy ψ to depend on the Burgers tensor G = F^pCurlF^p.

The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for F^p. The microstresses are strictly dissipative when ψ is independent of the Burgers tensor, but when ψ depends on G the microstresses are partially energetic, and this, in turn, leads to backstresses and (hence) Bauschinger-effects in the flow rule. The typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with viscoplastic flow, and, as an aid to numerical solution, a weak (virtual power) formulation of the nonlocal flow rule is derived. Finally, the dependences of the microstresses on D^p are shown, analytically, to result in strengthening and possibly weakening of the body induced by viscoplastic flow.     

PBX-1炸药的力学性能和本构关系

PBX的力学行为对其安全性有重要影响。为研究PBX-1的力学性能,以PBX-1为研究对象,进行准静态力学实验和SHPB(分离式霍普金森压杆)实验研究。结果表明,准静态压缩实验中,试样的裂纹出现在与加载方向大约成45°的最大剪应力方向。SHPB实验中,在应变率100~1 500 s^-1范围内,随着应变率的提高,PBX-1炸药的动态屈服强度、动态压缩强度和破坏应变不断提高。动态屈服强度逐渐从静态的2.77 MPa增加至16.1 MPa;压缩强度从7.46 MPa增加至16.1 MPa,破坏应变从6.23%增加到26.4%。同时,基于Z-W-T模型,建立了一种含损伤的动态黏弹性本构模型,在330~1 500 s^-1应变率范围内具有较高的精度,可以较好地描述PBX-1炸药在达到破坏前的动态力学行为。     

Thermally actuated shape-memory polymers: Experiments, theory, and numerical simulations

With the aim of developing a thermo-mechanically coupled large-deformation constitutive theory and a numerical-simulation capability for modeling the response of thermally actuated shape-memory polymers, we have (i) conducted large strain compression experiments on a representative shape-memory polymer to strains of approximately unity at strain rates of 10⁻³ and 10⁻¹ s⁻¹, and at temperatures ranging from room temperature to approximately 30 °C above the glass transition temperature of the polymer; (ii) formulated a thermo-mechanically coupled large-deformation constitutive theory; (iii) calibrated the material parameters appearing in the theory using the stress-strain data from the compression experiments; (iv) numerically implemented the theory by writing a user-material subroutine for a widely used finite element program; and (v) conducted representative experiments to validate the predictive capability of our theory and its numerical implementation in complex three-dimensional geometries. By comparing the numerically predicted response in these validation simulations against measurements from corresponding experiments, we show that our theory is capable of reasonably accurately reproducing the experimental results. As a demonstration of the robustness of the three-dimensional numerical capability, we also show results from a simulation of the shape-recovery response of a stent made from the polymer when it is inserted in an artery modeled as a compliant elastomeric tube.     

Homogenization of intergranular fracture towards a transient gradient damage model

This paper focuses on the intergranular fracture of polycrystalline materials, where a detailed model at the meso-scale is translated onto the macro-level through a proposed homogenization theory. The bottom-up strategy involves the introduction of an additional macro-kinematic field to characterize the average displacement jump within the unit cell. Together with the standard macro-strain field, the underlying processes are propagated onto the macro-scale by imposing the equivalence of power and energy at the two scales. The set of macro-governing equations and constitutive relations are next extracted naturally as per standard thermodynamics procedure. The resulting homogenized microforce balance recovers the so-called ‘implicit’ gradient expression with a transient nonlocal interaction. The homogenized gradient damage model is shown to fully regularize the softening behavior, i.e. the structural response is made mesh-independent, with the damage strain correctly localizing into a macroscopic crack, hence resolving the spurious damage growth observed in many conventional gradient damage models. Furthermore, the predictive capability of the homogenized model is demonstrated by benchmarking its solutions against reference meso-solutions, where a good match is obtained with minimal calibrations, for two different grain sizes.     

Multi-scale modeling of the mechanical response of plain weave composites and cellular solids

Multi-component materials with customized mechanical properties, such as textile composites and sandwich materials (cellular core with metallic or composite skin), show a great prospective for use in aerostructures. Understanding of the mechanical response of these materials is still in progress. In the present paper, the tensile response of plain weave composites as well as the compressive response of cellular solids are investigated using a multi-scale damage model. The model, implemented by means of the FE method, is based on homogenized progressive damage modeling of a representative unit-cell. Four failure modes have been considered in the failure analysis of the tows, while material property degradation was performed using a damage mechanics approach which takes into account strain softening. For the cellular solids, two different types of FE models were considered namely, a beam model and a shell model. Failure analysis and material property degradation of the struts were integrated into a bilinear material model. Simulations show a non-linear tensile response of the plain weave mainly attributed to matrix cracking and shear failures occurring at warp tows and resin-rich areas. For the cellular solid, preliminary elastic analyses show a customizability of the normal stiffness with regard to strut’s dimensions.     

Rheological discrimination and characterization of carrageenans and starches by Fourier transform-rheology in the non-linear viscous regime

Classical rheological methods are often insufficient to characterize and to differentiate the non-linear rheological behavior of polysaccharide systems such as carrageenan or starch. In this article the non-linear rheological method of characteristic functions is used to discriminate between the different polysaccharides. This method is based on the Fourier transform-rheology (FT-rheology). The response of a sample is decomposed using simple characteristic functions. We show that there are differences in the response of a number of carrageenan and starch samples, which are not distinguishable with classical rheometry.     

Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models

The deformation of a composite made up of a random and homogeneous dispersion of elastic spheres in an elasto-plastic matrix was simulated by the finite element analysis of three-dimensional multiparticle cubic cells with periodic boundary conditions. “Exact” results (to a few percent) in tension and shear were determined by averaging 12 stress-strain curves obtained from cells containing 30 spheres, and they were compared with the predictions of secant homogenization models. In addition, the numerical simulations supplied detailed information of the stress microfields, which was used to ascertain the accuracy and the limitations of the homogenization models to include the nonlinear deformation of the matrix. It was found that secant approximations based on the volume-averaged second-order moment of the matrix stress tensor, combined with a highly accurate linear homogenization model, provided excellent predictions of the composite response when the matrix strain hardening rate was high. This was not the case, however, in composites which exhibited marked plastic strain localization in the matrix. The analysis of the evolution of the matrix stresses revealed that better predictions of the composite behavior can be obtained with new homogenization models which capture the essential differences in the stress carried by the elastic and plastic regions in the matrix at the onset of plastic deformation.     

Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON

Within this two part series we develop a new material model for ceramic protection materials to provide an interface between microstructural parameters and bulk continuum behavior to provide guidance for materials design activities. Part I of this series focuses on the model formulation that captures the strength variability and strain rate sensitivity of brittle materials and presents a statistical approach to assigning the local flaw distribution within a specimen. The material model incorporates a Mie–Grüneisen equation of state, micromechanics based damage growth, granular flow and dilatation of the highly damaged material, and pore compaction for the porosity introduced by granular flow. To provide initial qualitative validation and illustrate the usefulness of the model, we use the model to investigate Edge on Impact experiments (Strassburger, 2004) on Aluminum Oxynitride (AlON), and discuss the interactions of multiple mechanisms during such an impact event. Part II of this series is focused on additional qualitative validation and using the model to suggest material design directions for boron carbide.     

Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation

This paper deals with some theoretical and experimental aspects of the behavior of periodic hyperelastic composites. We focus here on composites consisting of an elastomeric matrix periodically reinforced by long fibers. The paper is composed of three parts. The first part deals with the theoretical aspects of compressible behavior. The second-order theory of Ponte Castañeda (J. Mech. Phys. Solids 44 (1996) 827) is considered and extended to periodic microstructures. Comparisons with results obtained by the finite element method show that the composite behavior predicted by the present model is much more accurate for compressible than for incompressible materials. The second part deals with the extension of the method to incompressible behavior. A mixed formulation (displacement-pressure) is used which improves the accuracy of the estimate given by the model. The third part presents experimental results. The composite tested is made of a rubber matrix reinforced by steel wires. Firstly, the matrix behavior is identified with a tensile test and a shear test carried out on homogeneous samples. Secondly, the composite is tested under shearing. The experimentally measured homogenized stress is then compared with the predictions of the model.     

聚甲基丙烯酸甲酯/纳米有机改性蒙脱土复合材料的制备及其摩擦磨损性能研究

采用乳液插层法制备聚甲基丙烯酸甲酯/纳米有机改性蒙脱土复合材料,采用X射线衍射仪表征复合材料结构,考察有机改性蒙脱土(OMMT)含量对复合材料摩擦磨损性能的影响,并通过扫描电子显微镜观察分析复合材料磨损表面形貌.结果表明:所制备的纳米片状分散型复合材料的磨损率随OMMT含量增加先减小而后增加;摩擦系数随OMMT含量的变化趋势则相反,当OMMT含量为5%时,复合材料的磨损率最小,为PMMA的25%;当OMMT含量为6%时,摩擦系数最大,比PMMA增加8%.复合材料的磨损机制为粘着磨损和磨粒磨损,随着OMMT含量不同,2种机理的表现程度有所变化.