Multiscale Mechanics and Optimization of Gastropod Shells

A vast majority of mollusks grow a hard shell for protection. The structure of these shells comprises several levels of hierarchy that increase their strength and their resistance to natural threats. This article focuses on nacreous shells, which are composed of two distinct layers. The outer layer is made of calcite, which is a hard but brittle material, and the inner layer is made of nacre, a tough and ductile material. The inner and outer layers are therefore made of materials with distinct structures and properties. In this article, we demonstrate that this system is optimum to defeat attacks from predators. A two-scale mod- eling and optimization approach was used. At the macroscale, a two-layer finite element model of a seashell was developed to capture shell geometry. At the microscale, a representative volume element of the microstructure of nacre was used to model the elastic modulus of nacre as well as a multiaxial failure criterion, both expressed as function of microstructural parameters. Experiments were also performed on actual shells of red abalone to validate the results obtained from simulations and gain insight into the way the shell fails under sharp perforation. Both optimization and experimental results revealed that the shell displays optimum performance when two modes of failure coincide within the structure. Finally, guidelines for designing two-layer shells were proposed to improve the performance of engineered protective systems undergoing similar structural and loading conditions.

Behaviour of granular matter under gravity-induced stress gradient:A two-dimensional numerical investigation

Gravity is the most important load source in mining and geotechnical engineering,which causes both the stress level and stress gradient inside geomaterials.Different from the stress level,the influence of gravity-induced stress gradient on the behaviour of the material is still unknown.An in-deep study on it will help to promote the understanding of material behaviour,especially for those cases related to unconventional gravity such as terrestrial ng physical modelling and extraterrestrial resource exploitation(g is the terrestrial gravitational acceleration).In this study,a high-order homogenization for granular materials is proposed at first,in which the stress gradient is drawn into the constitutive representation by adopting a representative volume element(RVE).The consolidation and shear strength behaviour of RVE are then investigated by performing numerical biaxial tests.The results show that all the compressibility,shear strength,shear stiffness,volumetric deformation,and critical state behaviour show a stress gradient dependence.A coupling between stress gradient,stress level,and material properties is also observed.These observations suggest that,besides the stress level,extra attention needs to be paid to material responses related to stress gradient during engineering practices.

Multiscale Homogenization Analysis of Alkali–Silica Reaction (ASR) Effect in Concrete

The alkali silica reaction (ASR) is one of the major long-term deterioration mechanisms occurring in con- crete structures subjected to high humidity levels, such as bridges and dams. ASR is a chemical reaction between the silica existing inside the aggregate pieces and the alkali ions from the cement paste. This chemical reaction produces ASR gel, which imbibes additional water, leading to gel swelling. Damage and cracking are subsequently generated in concrete, resulting in degradation of its mechanical proper- ties. In this study, ASR damage in concrete is considered within the lattice discrete particle model (LDPM), a mesoscale mechanical model that simulates concrete at the scale of the coarse aggregate pieces. The authors have already modeled successfully ASR within the LDPM framework and they have calibrated and validated the resulting model, entitled ASR-LDPM, against several experimental data sets. In the pre- sent work, a recently developed multiscale homogenization framework is employed to simulate the macroscale effects of ASR, while ASR-LDPM is utilized as the mesoscale model. First, the homogenized behavior of the representative volume element (RVE) of concrete simulated by ASR-LDPM is studied under both tension and compression, and the degradation of effective mechanical properties due to ASR over time is investigated. Next, the developed homogenization framework is utilized to reproduce experimental data reported on the free volumetric expansion of concrete prisms. Finally, the strength degradation of prisms in compression and four-point bending beams is evaluated by both the mesoscale model and the proposed multiscale approach in order to analyze the accuracy and computational ef - ciency of the latter. In all the numerical analyses, different RVE sizes with different inner particle realiza- tions are considered in order to explore their effects on the homogenized response.

Stress Analysis of Wire Strands by Mesoscale Mechanics

Steel wire ropes have wide application in a variety of engineering fields such as ocean engineering and civil engineering.The stress calculation for steel wire ropes is of crucial importance when conducting strength and fatigue analyses.In this study,we performed a finite element analysis of single-strand steel wire ropes.For the geometric modeling,we used an analytic geometry of space method.We established helical line equations and used the coordinates of the contact points.The finite-element model was simplified using the periodic law.Periodic boundary conditions were used to simulate a wire strand of infinite length under tensile strain,for which we calculated the cross-sectional stresses and inner forces.The results showed that bending and torsion moments emerged when the wire strand was under tensile load.In some cases,the bending stress reached 18%of the tensile stress,and the torsion stress reached 29%of the tensile stress,which means that the total stress was higher than the nominal stress.Whereas in ear-lier studies,a conservative prediction of nominal stress was not possible,the results of our strength and fatigue analyses were more conservative.

Elastoplastic analysis of AA7075-O aluminum sheet by hybrid micro-scale representative volume element modeling with really-distributed particles and in-situ SEM experimental testing

This paper addresses the challenge of reconstructing randomly distributed second-phase particlestrengthened microstructure of AA7075-O aluminum sheet material for computational analysis.The particle characteristics in 3D space were obtained from focused ion beam and scanning electron microscopy(FIB-SEM)and SEM-based Electron Backscatter Diffraction/Energy Dispersive X-ray Spectrometry(EBSD/EDS)techniques.A theoretical framework for analysis of elastic-plastic deformation of such3D microstructures is developed.Slip-induced shear band formation,void initiation,growth and linkage at large plastic strains during uniaxial tensile loading were investigated based on reconstructed 3D representative volume element(RVE)models with real-distribution of particles and the results compared with experimental observations.In-situ SEM interrupted tension tests along transverse direction(TD)and rolling direction(RD),employing microscopic-digital image correlation(μ-DIC)technique,were carried out to investigate slip bands,micro-voids formation and obtain microstructural strain maps.The resulting local strain maps were analyzed in relation to the experimentally observed plastic flow localization,failure modes and local stress maps from simulations of RVE models.The influences of particle size,shape,orientation,volume fraction as well as matrix-particle interface properties on local plastic deformation,global stress-strain/strain-hardening curves and interfacial failure mechanisms were studied based on 3D RVE models.When possible,the model results were compared with in-situ tensile test data.In general,good agreement was observed,indicating that the real 3D microstructure-based RVE models can accurately predict the plastic deformation and interfacial failure evolution in AA7075-O aluminum sheet.

Three Phase Composite Cylinder Assemblage Model for Analyzing the Elastic Behavior of MWCNT-Reinforced Polymers

Evolution of computational modeling and simulation has given more emphasis on the research activities related to carbon nanotube(CNT)reinforced polymer composites recently.This paper presents the composite cylinder assemblage(CCA)approach based on continuum mechanics for investigating the elastic properties of a polymer resin reinforced by multi-walled carbon nanotubes(MWCNTs).A three-phase cylindrical representative volume element(RVE)model is employed based on CCA technique to elucidate the effects of inter layers,chirality,interspacing,volume fraction of MWCNT,interphase properties and temperature conditions on the elastic modulus of the composite.The interface region between CNT and polymer matrix is modeled as the third phase with varying material properties.The constitutive relations for each material system have been derived based on solid mechanics and proper interfacial traction continuity conditions are imposed.The predicted results from the CCA approach are in well agreement with RVE-based finite element model.The outcomes reveal that temperature softening effect becomes more pronounced at higher volume fractions of CNTs.

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.

DAMAGE MECHANISM ANALYSIS OF 2D 1×1 BRAIDED COMPOSITES UNDER UNIDIRECTIONAL TENSION

Coupling with the periodical displacement boundary condition,a representative volume element(RVE) model is established to simulate the progressive damage behavior of 2D1×1 braided composites under unidirectional tension by using the nonlinear finite element method.Tsai-Wu failure criterion with various damage modes and Mises criterion are considered for predicting damage initiation and progression of yarns and matrix.The anisotropic damage model for yarns and the isotropic damage model for matrix are used to simulate the microscopic damage propagation of 2D1×1braided composites.Murakami′s damage tensor is adopted to characterize each damage mode.In the simulation process,the damage mechanisms are revealed and the tensile strength of 2D1×1braided composites is predicted from the calculated average stress-average strain curve.Numerical results show good agreement with experimental data,thus the proposed simulation method is verified for damage mechanism analysis of 2D braided composites.

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.

Multi-scale finite element simulation on large deformation behavior of wood under axial and transverse compression conditions

Multi-scale finite element method is adopted to simulate wood compression behavior under axial and transverse loading. Representative volume elements (RVE) of wood microfibril and cell are proposed to analyze orthotropic mechanical behavior. Lignin, hemicellulose and crystalline-amorphous cellulose core of spruce are concerned in spruce nanoscale model. The equivalent elastic modulus and yield strength of the microfibril are gained by the RVE simulation. The anisotropism of the crystalline-amorphous cellulose core brings the microfibril buckling deformation during compression loading. The failure mechanism of the cell-wall under axial compression is related to the distribution of amorphous cellulose and crystalline cellulose. According to the spruce cell observation by scanning electron microscope, numerical model of spruce cell is established using simplified circular hole and regular hexagon arrangement respectively. Axial and transverse compression loadings are taken into account in the numerical simulations. It indicates that the compression stress-strain curves of the numerical simulation are consistent with the experimental results. The wood microstructure arrangement has an important effect on the stress plateau during compression process. Cell-wall buckling in axial compression induces the stress value drops rapidly. The wide stress plateau duration means wood is with large energy dissipation under a low stress level. The numerical results show that loading velocity affects greatly wood microstructure failure modes in axial loading. For low velocity axial compression, shear sliding is the main failure mode. For high velocity axial compression, wood occur fold and collapse. In transverse compression, wood deformation is gradual and uniform, which brings stable stress plateau.

Simulations of deformation and damage processes of SiCp/Al composites during tension

The deformation, damage and failure behaviors of 17 vol.% SiCp/2009AI composite were studied by micro- scopic finite element （FE） models based on a representative volume element （RVE） and a unit cell. The RVE having a 3D realistic microstructure was constructed via computational modeling technique, in which an interface phase with an average thickness of 50 nm was generated for assessing the effects of interracial properties. Modeling results showed that the RVE based FE model was more accurate than the unit cell based one. Based on the RVE, the predicted stress-strain curve and the fracture morphology agreed well with the experimental results. Furthermore, lower interface strength resulted in lower flow stress and ductile damage of interface phase, thereby leading to decreased elongation. It was revealed that the stress concentration factor of SiC was -2.0： the average stress in SiC particles reached -1200 MPa, while that of the composite reached -600 MPa.

Multi-scale thermodynamic analysis method for 2D SiC/SiC composite turbine guide vanes

Ceramic Matrix Composite （CMC） turbine guide vanes possess multi-scale stress and strain with inhomogeneity at the microscopic scale. Given that the macroscopic distribution cannot reflect the microscopic stress fluctuation, the macroscopic method fails to meet the requirements of stress and strain analysis of CMC turbine guide vanes. Furthermore, the complete thermodynamic properties of 2D woven SiC/SiC-CMC cannot be obtained through experimentation, Accordingly, a method to calculate the thermodynamic properties of CMC and analyze multi-scale stress and strain of the turbine guide vanes should be established. In this study, the multi-scale thermodynamic analysis is investigated. The thermodynamic properties of Chemical Vapor Infiltration （CVI） pro- cessed SiC/SiC-CMC are predicted by a Representative Volume Element （RVE） model with porosity, leading to the result that the relative error between the calculated in-plane tensile modulus and the experimental value is 4.2%. The macroscopic response of a guide vane under given conditions is predicted. The relative error between the predicted strain on the trailing edge and the experimental value is 9.7%. The calculation of the stress distribution of micro-scale RVE shows that the maximum value of microscopic stress, which is located in the interlayer matrix, is more than 1.5 times that of macroscopic stress in the same direction and the microscopic stress distribution of the interlayer matrix is related to the pore distribution of the composite.

A fast numerical method of introducing the strengthening effect of residual stress and strain to tensile behavior of metal matrix composites

Thermal residual stress and strain(TRSS)in particle reinforced metal matrix composites(PRMMCs)are believed to cause strengthening effects,according to previous studies.Here,the representative volume element(RVE)based computational homogenization technique was used to study the tensile deformation of PRMMCs with different particle aspect ratios(AR).The influence of TRSS was assessed quantitatively via comparing simulations with or without the cooling process.It was found that the strengthening effect of TRSS was affected by the particle AR.With the average strengthening effect of TRSS,a fast method of introducing the strengthening effect of TRSS to the tensile behavior of PRMMCs was developed.The new method has reduced the computational cost by a factor 2.The effect of TRSS on continuous fiber-reinforced metal matrix composite was found to have a softening-effect during the entire tensile deformation process because of the pre-yield effect caused by the cooling process.

Two-scale modeling of granular materials:A FEM-FEM approach

In the present paper,a homogenization-based two-scale FEM-FEM model is developed to simulate compactions of visco-plastic granular assemblies.The granular structure consisting of two-dimensional grains is modeled by the microscopic finite element method at the small-scale level,and the homogenized viscous assembly is analyzed by the macroscopic finite element method at large-scale level.The link between scales is made using a computational homogenization method.The two-scale FEM-FEM model is developed in which each particle is treated individually with the appropriate constitutive relations obtained from a representative volume element,kinematic conditions,contact constraints,and elimination of overlap satisfied for every particle.The method could be used in a variety of problems that can be represented using granular media.

Influence of Lamellar Direction in Pearlitic Steel Wire on Mechanical Properties and Microstructure Evolution

During cold drawing of pearlitic steel wire, the lamellar structure becomes gradually aligned with the draw ing axis, which contributes to the ultra high strength. A direct simulation about the mechanical behaviors and microstructural evolution of pearlitic lamellae was presented. A representative volume element （RVE） containing one pearlitic colony was established based on the real transmission electron microscope （TEM） observation. The deformation of pearlitic colony during tension, shear and wire drawing were successfully simulated. The numerical results show that this metallographic texture leads to a strong anisotropy. The colony has higher yielding stress when the la mellar direction is parallel and perpendicular to the tensile direction. The lamellar evolution is strongly dependent on the initial direction and deformation mode. The formation of typical period shear bands is analyzed. In the wire draw ing, the pearlitic colony at the sub surface experiences a complex strain path： rotation, stretching along the die sur face, and rotation back.

The Micromechanics of Biological and Biomimetic Staggered Composites

Natural materials such as bone, tooth and nacre achieve attractive properties through the ＂staggered structure＂, which consists of stiff, parallel inclusions of large aspect ratio bonded together by a more ductile and tougher matrix. This seemingly simple structure displays sophisticated micromechanics which lead to unique combinations of stiffness, strength and toughness. In this article we modeled the staggered structure using finite elements and small Representative Volume Elements （RVEs） in order to explore microstructure-property relationships. Larger aspect ratio of inclusions results in greater stiffiless and strength, and also significant amounts of energy dissipation provided the inclusions do not fracture in a brittle fashion. Interestingly the ends of the inclusions （the junctions） behave as crack-like features, generating theoretically infinite stresses in the adjacent inclusions. A fracture mechanics criterion was therefore used to predict the failure of the inclusions, which led to new insights into how the interfaces act as a ＂＇soft wrap＂ for the inclusions, completely shielding them from excessive stresses. The effect of statistics on the mechanics of the staggered structure was also assessed using larger scale RVEs. Variations in the microstructure did not change the modulus of the material, but slightly decreased the strength and significantly decreased the failure strain. This is explained by strain localization, which can in turn be delayed by incorporating waviness to the inclusions. In addition, we show that the columnar and random arrangements, displaying different deformation mechanisms, lead to similar overall prop- erties. The guidelines presented in this study can be used to optimize the design of staggered synthetic composites to achieve mechanical performances comparable to natural materials.

The Meso-inhomogeneous Deformation of Pure Copper under Tension-Compression Cyclic Strain Loading

The investigation based on experiments and crystal plasticity simulation is carried out to undertake research on mesodeformation inhomogeneity of metals under cyclic loading at grain level.Symmetrical tension-compression cycle tests are performed on pure copper specimens to observe the inhomogeneous distribution of slip deformation and its evolution with cycle number.Cyclic hardening process and stable hysteretic behavior of pure copper under cyclic loading are simulated by applying a crystal plasticity constitutive model including nonlinear kinematic hardening associated with the polycrystalline representative volume element(RVE)constructed by Voronoi tessellation.Inhomogeneous deformation processes of materials under six different strain amplitudes are simulated by 1600 cycles,respectively.We discuss the variation law of the inhomogeneous meso-deformation distribution of material with the increase in cycle number,and research the rationality of characterizing the inhomogeneous deformation distribution and variation with the statistical standard deviation of the micro-longitudinal strain or the statistical average of the first principal strain based on the statistical analysis of the inhomogeneous deformation of the polycrystalline RVE model during the cycling process.It is found that these two parameters are related to and approximately inversely proportional to the length of measuring gauge.

Multi-scale analysis of void evolution in large-section plastic mold steel during multi-directional forging

The void evolution of large-section plastic mold steel during multi-directional forging(MDF)was investigated using multiscale analysis.To simulate the forging process of the plastic mold steel(SDP1 steel)and realize micro-void reconstruction in a representative volume element(RVE),MDF experiment and void-characteristic evaluation of the SDP1 steel were carried out.Traditional upsetting and stretching forging(TUSF)and MDF were simulated to comparatively analyze the evolution of temperature,effective stress,and effective strain.By embedding RVE with a micro-void and using boundary condition by point tracking into the forging process,the single-void evolution in TUSF and MDF was studied.The effect of void orientation on single-void evolution was also investigated.The multi-scale analysis revealed the following results.(1)Compared with TUSF,MDF achieved a higher efficiency in void closure.(2)The closing efficiency of the void increased with the increase in angle h(the angle between the Z and long axes of the void).(3)The closing efficiency increased with the increase in the orientation angle during the forging process.On the basis of the important role of the main stress in each forging step on the void closure,an integral formula of the main stress was proposed.When main compressive-stress integration reached-0.4,the closed state of the void could be accurately determined.

Experimental and numerical investigation of failure mode in geometrically imperfect DP590 steel

Various microstructure-level finite element models were generated according to the real microstructure of DP590 steel to capture the mechanical behavior and fracture mode.The failure mode of the dual-phase(DP)steels,mainly resulting from microstructure-level inhomogeneity and initial geometrical imperfection,was predicted using the plastic strain localization theory.In addition,dog-bone-type tensile test specimens with different edge qualities were prepared and the deformation processes were recorded using a digital image correlation system.When the steel exhibited no initial geometrical imperfection,void initiation was triggered by decohesion between martensite and ferrite which was predicted based on the severe strain concentration,or tensile stress in areas where stress triaxiality and strain values were high.Final failure was caused by shear localization in the vicinity.Moreover,the initial geometrical imperfections severely affected the overall ductility and failure mode of the DP590steel.When initial geometrical imperfections were deeply ingrained,an incipient crack began at the site of initial geometrical imperfection,and then caused progressive damage throughout the microstructure,from the area of shear localization to the final fracture.Overall,the depth of the geometrical imperfection was the critical factor in determining whether internal decohesion or a local crack plays a dominant role.

Multiscale analysis of composite material reinforced by randomly-dispersed particles

A multiscale analysis method is presented in which detailed information on the microscopic level is incorporated into macroscopic models capable of simulating damage evolution and ultimate failure.The composite considered is reinforced by randomly-dispersed particles,which reflects the statistical characteristics of real materials,such as cement-based materials.Specifically,a three-dimensional material body is decomposed into many unit cells.Each unit cell is reinforced by a cylindrical particle,the orientation of which is characterized by three Euler angles generated by the random number generator.Based on a detailed finite element analysis,the material properties of the representative volume element are obtained.As verification,the properties of the cylindrical particles are set equal to those of the matrix and the computed‘composite’properties reduce exactly to those of the‘isotropic’material,as expected.Through coordinate transformation,the effective material properties of each unit cell are calculated.The assembly of stiffness matrices of all unit cells leads to the stiffness matrix of the whole specimen.Under the simple tension loading condition,the initial damaged unit cell can be identified according to the vonMises yield criterion.The stiffness of the damaged unit cell will then be reduced to zero and it will cause stress redistribution and trigger further damage.It was found that the reinforcement is effective to mitigate and arrest the damage propagation,and therefore prolongs the material’s lifetime.These results suggest that the hierarchical coupling approaches used here may be useful for material design and failure protection in composites.