Finite Element Simulations on Failure Behaviors of Granular Materials with Microstructures Using a Micromechanics-Based Cosserat Elastoplastic Model

This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstructures are expressed as sums of microstructural information.The microstructures under consideration can be classified into three categories:a medium-dense microstructure,a dense microstructure consisting of one-sized particles,and a dense microstructure consisting of two-sized particles.Subsequently,the Cosserat elastoplastic model,along with its finite element formulation,is derived using the extended Drucker-Prager yield criteria.To investigate failure behaviors,numerical simulations of granular materials with different microstructures are conducted using the ABAQUS User Element(UEL)interface.It demonstrates the capacity of the proposed model to simulate the phenomena of strain-softening and strain localization.The study investigates the influence of microscopic parameters,including contact stiffness parameters and characteristic length,on the failure behaviors of granularmaterials withmicrostructures.Additionally,the study examines themesh independence of the presented model and establishes its relationship with the characteristic length.A comparison is made between finite element simulations and discrete element simulations for a medium-dense microstructure,revealing a good agreement in results during the elastic stage.Somemacroscopic parameters describing plasticity are shown to be partially related to microscopic factors such as confining pressure and size of the representative volume element.

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

Micromechanics of rock damage: Advances in the quasi-brittle field

Constitutive models play an essential role in numerical modeling and simulation of nonlinear deformation, progressive damage and failure of rock-like materials and structures. Recent advances in the quasi-brittle field show that upscaling methods by homogenization have provided a new efficient way to derive macroscopic formulations of rocks from their microstructure information and local properties and then to model nonlinear mechanical behaviors identified at laboratory. This paper aims first at relating the mechanical phenomena on sample scale to their respective mechanisms on microscale. Main focus is put on unilateral effects due to crack’s opening/closure transition, material anisotropy induced by crack growth in some preferred directions and multiphysical coupling at microcracks. After a brief introduction to the linear homogenization method and its application to crack problems, we present some recent advances achieved in the combined homogenization/thermodynamics framework, including anisotropic unilateral damage-friction coupling, theoretical failure prediction in conjunction with deformation analyses, poromechanical coupling, analytical solutions and numerical implementation with application to typical brittle rocks.

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR MICROCRACKED SOLIDS

Micromechanics models have been developed For the determination of the elastic moduli of microcracked solids based on different approaches and interpretations, including the dilute or non-interacting solution, the Mori-Tanaka method, the self-consistent method, and the generalized self-consistent method. It is shown in the present study that all these micromechanics models can be unified within an energy-equivalence framework, and that they differ only in the way in which the microcrack opening and sliding displacements are evaluated. Relevance to the differential methods and the verification of these models are discussed.

A THEORY OF EFFECTIVE THERMAL CONDUCTIVITY FOR MATRIX-INCLUSION-MICROCRACK THREE-PHASE HETEROGENEOUS MATERIALS BASED ON MICROMECHANICS

The effective thermal conductivity of matrix-inclusion-microcrack three-phase heterogeneous materials is investigated with a self-consistent micromechanical method (SCM) and a random microstructure finite element method(RMFEM). In the SCM, microcracks are assumed to be randomly distributed and penny-shaped and inclusions to be spherical, the crack effect is accounted for by introducing a crack density parameter, the effective thermal conductivity is derived which relates the macroscopic behavior to the crack density parameter. In the RMFEM, the highly irregular microstructure of the heterogeneous media is accurately described, the interaction among the matrix-inclusion-microcracks is exactly treated, the inclusion shape effect and crack size effect are considered. A Ni/ZrO2 particulate composite material containing randomly distributed, penny-shaped cracks is examined as an example. The main results obtained are: (1) the effective thermal conductivity is sensitive to the crack density and exhibits essentially a linear relationship with the density parameter: (2) the inclusion shape has a significant effect on the effective thermal conductivity and a polygon-shaped inclusion is more effective in increasing or decreasing the effective thermal conductivity than a sphere-shaped one; and (3) the SCM and RMFEM are compared and the two methods give the same effective property in the case in which the matrix thermal conductivity A, is greater than the inclusion one lambda(2). In the inverse case of lambda(1) < lambda(2), the two methods as the as the inclusion volume fraction and crack density are low and differ as they are high. A reasonable explanation for the agreement and deviation between the two methods in the case of lambda(1) < lambda(2) is made.

Micromechanics-Based Elastic Fields of Closed-Cell Porous Media

Fluid-filled closed-cell porous media could exhibit distinctive features which are influenced by initial fluid pressures inside the cavities.Based on the equivalent farfield method,micromechanics-based solutions for the local elastic fields of porous media saturated with pressurized fluid are formulated in this paper.In the present micromechanics model,three configurations are introduced to characterize the different state the closed-cell porous media.The fluid-filled cavity is assumed to be a compressible elastic solid with a zero shear modulus,and the pressures in closed pores are represented by eigenstrains introduced in fluid domains.With the assumption of spheroidal fluidfilled pores,the local stress and strain fields in solid matrix of porous media are derived by using the Exterior-Point Eshelby tensors,which are dependent of the Poisson’s ratio of solid matrix and the locations of the investigated material points outside the spheroidal fluid domain.The reliability and accuracy of the analytical elastic solutions are verified by a classical example.Moreover,for finite volume fraction of the fluid inclusions,the local elastic fields of the porous media subjected to the initial fluid pressure and external load are obtained.The results show that the present micromechanics model provides an effective approach to characterize the local elastic fields of the materials with closed-cell fluid-filled pores.

Review:A Critical Assessment on the Predictability of 14 Micromechanics Models for the Stiffness and Strength of UD Composites

Any micromechanics model initially developed for predicting stiffness (elastic property) of a composite can be used to predict its strength with a reasonable accuracy,as long as the homogenized stresses in the matrix are converted into its true values. A critical assessment on the predictability of 14 famous micromechanics models for stiffness and strength of UD (unidirectional) composites was made in this work against the benchmark data provided in three world-wide failure exercises (WWFEs). Bridging Model exhibited the highest accuracy in both the stiffness and strength predictions. Moreover,it was the only consistent model in the internal stress calculation. Non-consistency implies that a full three-dimensional (3D)approach should be used to predict the effective property of the composite. The paper also showed that the smallest fiber volume in an RVE (representative volume element) led to the best approximation to a composite property.

MICROMECHANICS ANALYSES OF INTERFACE CRACK

A new mechanics model based on Peierls concept is presented in this paper, which can clearly characterize the intrinsic features near a tip of an interfacial crack. The stress and displacement fields are calculated under general combined tensile and shear loadings. The near tip stress fields show some oscillatory behaviors but without any singularity and the crack faces open completely without any overlapping when remote tensile loading is comparable with remote shear loading. A fracture criterion for predicting interface toughness has been also proposed, which takes into account for the shielding effects of emitted dislocations. The theoretical toughness curve gives excellent prediction, as compared with the existing experiment data.

MICROMECHANICS ANALYSIS ON EVOLUTION OF CRACK IN VISCOELASTIC MATERIALS

A preliminary analysis on crack evolution in viscoelastic materials was presented. Based on the equivalent inclusion concept of micro-mechanics theory, the explicit expressions of crack opening displacement delta and energy release rate G were derived, indicating that both delta and G are increasing with time. The equivalent modulus of the viscoelastic solid comprising cracks was evaluated. It is proved that the decrease of the modulus comes from two mechanisms: one is the viscoelasticity of the material; the other is the crack opening which is getting larger with time.

A micromechanics-based finite element model for the constitutive behavior of polycrystalline ferromagnets

A micromechanics-based finite element model for the constitutive behavior of polycrystalline ferromagnets is developed. In the model, the polycrystalline solid is assumed to comprise numerous single crystals with randomly distributed crystallographic orientations, and the single crystals, in turn, consist of ferromagnetic domains, each of which is represented by a cubic element. The dipole directions of the domains are randomly assigned to simulate the crystallographic nature of ferromagnetic polycrystals. A switching criterion for the domains is specified at the microscopic level. The macroscopic constitutive behavior is obtained by averaging the microscopic/local behavior of each domain. The developed model has been applied to the simulation of a ferromagnetic material. With appropriate material parameters adopted, hysteresis loops of the predicted magnetic induction versus magnetic field and those of the strain versus magnetic field are shown to agree well with experimental observations.

Micromechanics of Thermal Conductive Composites:Review,Developments and Applications

Micromechanics investigations of composites with fiber-shaped reinforcement are extensively applied in the engineering design and theoretical analysis of thermal composites in the aerospace engineering and high-tech industry.In this paper,a critical review of various classical micromechanics approaches is provided based on the classification framework and the development of micromechanics tools.Several numerical micromechanics tools have been developed to overcome limitations through exactly/approximately solving the internal governing equations of microstructures.The connections and limitations of those models are also investigated and discussed,based on which three recently developed numerical or semi-analytical models are explained,including finite-element micromechanics,finite-volume direct averaging micromechanics,and locally exact homogenization theory,as well as machine learning tools.Since it is almost inevitable to mention the interfacial effects on thermal behavior of fibrous composites,we review the new mathematical relations that interrupt the original continuity conditions due to the existence of interphase/interface within unit cells.Generally speaking,the interphase/interface is demonstrated to play a significant role in influencing the effective coefficients and localized thermal fields.The present work also briefly reviews the application of micromechanics tools in emerging engineered woven composites,natural fibrous composites,and ablative thermal protection composites.It is demonstrated that sophisticated micromechanics tools are always demanded for investigating the effective and localized responses of thermal fibrous composites.

A macro-mesoscopic constitutive model for porous and cracked rock under true triaxial conditions

The complex mechanical and damage mechanisms of rocks are intricately tied to their diverse mineral compositions and the formation of pores and cracks under external loads.Numerous rock tests reveal a complex interplay between the closure of porous defects and the propagation of induced cracks,presenting challenges in accurately representing their mechanical properties,especially under true triaxial stress conditions.This paper proposes a conceptualization of rock at the mesoscopic level as a two-phase composite,consisting of a bonded medium matrix and frictional medium inclusions.The bonded medium is characterized as a mesoscopic elastic material,encompassing various minerals surrounding porous defects.Its mechanical properties are determined using the mixed multi-inclusion method.Transformation of the bonded medium into the frictional medium occurs through crack extension,with its elastoplastic properties defined by the DruckerePrager yield criterion,accounting for hardening,softening,and extension.MorieTanaka and Eshelby’s equivalent inclusion methods are applied to the bonded and frictional media,respectively.The macroscopic mechanical properties of the rock are derived from these mesoscopic media.Consequently,a True Triaxial Macro-Mesoscopic(TTMM)constitutive model is developed.This model effectively captures the competitive effect and accurately describes the stress-deformation characteristics of granite.Utilizing the TTMM model,the strains resulting from porous defect closure and induced crack extension are differentiated,enabling quantitative determination of the associated damage evolution.

Microstructures and micromechanical behaviors of high -entropy alloys investigated by synchrotron X-ray and neutron diffraction techniques: A review

High-entropy alloys(HEAs)possess outstanding features such as corrosion resistance,irradiation resistance,and good mechan-ical properties.A few HEAs have found applications in the fields of aerospace and defense.Extensive studies on the deformation mech-anisms of HEAs can guide microstructure control and toughness design,which is vital for understanding and studying state-of-the-art structural materials.Synchrotron X-ray and neutron diffraction are necessary techniques for materials science research,especially for in situ coupling of physical/chemical fields and for resolving macro/microcrystallographic information on materials.Recently,several re-searchers have applied synchrotron X-ray and neutron diffraction methods to study the deformation mechanisms,phase transformations,stress behaviors,and in situ processes of HEAs,such as variable-temperature,high-pressure,and hydrogenation processes.In this review,the principles and development of synchrotron X-ray and neutron diffraction are presented,and their applications in the deformation mechanisms of HEAs are discussed.The factors that influence the deformation mechanisms of HEAs are also outlined.This review fo-cuses on the microstructures and micromechanical behaviors during tension/compression or creep/fatigue deformation and the application of synchrotron X-ray and neutron diffraction methods to the characterization of dislocations,stacking faults,twins,phases,and intergrain/interphase stress changes.Perspectives on future developments of synchrotron X-ray and neutron diffraction and on research directions on the deformation mechanisms of novel metals are discussed.

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM （Discrete Element Method） and FEM （Finite Element Method）, a model is established to simulate the breakage of twodimensional sharp-edge particles, in which the simulated particles are assumed to have no cracks. Particles can, however, crush during different stages of the numerical analysis, if stress-based breakage criteria are fulfilled inside the particles. With this model, it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials. Two series of tests, with and without breakable particles, are simulated under different confining pressures based on conditions of biaxial tests. The results, presented in terms of micromechanical behavior for different confining pressures, are compared with macroparameters. The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated. Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.

A generalized micromechanics constitutive theory of single crystal with thermoelastic martensitic transformation

Based on the crystallography theory of martensitic transformation and Hill-Rice’s internal variable constitutive theory, a generalized micromechanics constitutive model is established to describe the thermoelastic martensitic transformation and reorientation of single crystal. This model can describe the macroscopic constitutive behavior due to the microstructure changes of forward transformation, reverse transformation and reorientation in single crystal under complex thermodynamic loading condition. The theoretical predictions agree well with the available experiment.

A continuum model of jointed rock masses based on micromechanics and its integration algorithm

The paper is devoted to proposing a constitutive model based on micromechanics. The joints in rock masses are treated as penny-shaped inclusion in solid but not through structural planes by considering joint density, closure effect, joint geometry. The mechanical behavior of the joints is represented by an elasto-plastic constitutive law. Mori-Tanaka method is used to derive the relationship between the joint deformations and macroscopic strains. The incremental stress-strain relationship of rock masses is formulated by taking the volume average of the representative volume element. Meanwhile, the behavior of joints is obtained. By using implicit integration algorithms, the consistent tangent moduli are proposed and the method of updating stresses and joint displacements is presented. Some examples are calculated by ABAQUS user defined material subroutine based on this model.

Theoretical analysis and experiment of micromechanics and mechanics-optics coupling of distributed optic-fiber crack sensing

The micromechanical behaviors and mechanics-optics coupling effects of optic-fiber-concrete complex in the distributed optic-fiber sensing concrete-crack technology,which was used in health monitoring of Wu Gorge Bridge on Yangtze River and a large dam successfully,have been investigated.A micromechanical theoretical analysis method and micromechanical frictional contact bi-interface model,as well as a modified optical theoretical analysis method of the mechanics-optics coupling effects are presented.A series of verification experiments,including mechanical experiments and mechanics-optics coupling experiments,have been preformed.The results of micromechanical theoretical analysis and the analysis of the modified theory of mechanics-optics coupling along with mechanical and optical experimental data are shown to be in close agreement.Both the micromechanical theory and the modified theory of mechanics-optics coupling with their analysis methods can not only enhance credibility of this novel distributed sensing technology but also provide a way to understand its sensing mechanism and optimize its technical details and system.

Modeling the Interaction between Vacancies and Grain Boundaries during Ductile Fracture

The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenomenon remains not fully understood.This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects.This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy.Subsequently,a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries.This model is first verified and validated through comparison with some available analytical solutions,demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy.A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation.The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries,potentially facilitating void nucleation in ductile fracture.

Micromechanics-based analysis for predicting asphalt concrete modulus

The elastic modulus of asphalt concrete(AC) is an important material parameter for pavement design.The prediction and determination of elastic modulus,however,largely depends on laboratory tests which cannot reflect explicitly the influence of the microstructure of AC.To this end,a micromechanical model based on stepping scheme is adopted.Consideration is given to the influence of interfacial debonding and interlocking effect between the aggregates and asphalt mastic using the concept of effective bonding.Tests on asphalt mixture with various microstructures are conducted to verify the proposed approach.It is shown that the prediction is generally in agreement with experimental results.Parameters affecting the elastic modulus of AC are also discussed in light of the proposed method.

Micromechanics of composites with interface effects

In terfaces that exist in composites greatly influence their mechanical and conductive properties.There are usually three interface models to characterize the elastic and conductive properties of the interface in composites.For elastic problems,they are the interface stress model(ISM),linear spring model(LSM),and interphase model.For conductive problems,they are the high conducting(HC)interface model,low conducting(LC)interface model,and interphase model.For elastic problems with the interface effects,they can be divided into two types.The first kind of elastic problem concerns the solution of boundary value problems and aims to predict the effective properties of composites with interface effects.The second kind of elastic problem concerns the surface/interface stress effects on the elastic properties of nanostructured materials,which is usually characterized by the ISM.In this paper,three aspects in the elastic problems with interface effects are first reviewed,i.e.,equivalent relations among the three interface models,Eshelby formalism,and micromechanical frameworks.Special emphasis is placed on the ISM to show how classical models can be extended to the nano-scale by supplementing the interface elasticity to the basic equations of the classical elastic problems.Then,the conductive problems of the composites with the interface effects are also reviewed,and the general frameworks for predicting the effective conductivity of the composites are given.Finally,scaling laws depicting the size-dependent elastic and conductive properties of the composites are discussed.