Effect of boundary conditions on shakedown analysis of heterogeneous materials

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.

Optimization of a digested sludge-derived mesoporous material as an efficient and stable heterogeneous catalyst for the photo-Fenton reaction

The anaerobic digestion of sludge has recently received increased interest because of the potential to transform organic matter into methane‐rich biogas. However, digested sludge, the residue produced in that process, still contains high levels of heavy metals and other harmful substances that might make traditional disposal difficult. We have devised a facile method of converting digested sludge into a mesoporous material that acts as an effective and stable heterogeneous catalyst for the photo‐Fenton reaction. A comparison of the removal of rhodamine B under different conditions showed that FAS‐1‐350, which was synthesized by mixing the digested sludge with a 1 mol/L（NH4）2Fe（SO4）2 solution followed by calcination at 350 °C, exhibited the best catalytic activity owing to its faster reaction rate and lower degree of Fe leaching. The results indicate that Fe^（2＋）‐loaded catalysts have significant potential to act as stable and efficient heterogeneous promoters for the photo‐Fenton reaction, with better performance than Fe^3＋‐loaded catalysts because the Fe（II）/Fe（III）compounds formed in the calcination process are necessary to sustain the Fenton reaction. This protocol provides an alternative, environmentally friendly method of reusing digested sludge and demonstrates an easily synthesized mesoporous material that effectively degrades azo dyes.

Extended multiscale finite element method for mechanical analysis of heterogeneous materials

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.

Volume Change of Heterogeneous Quasi-brittle Materials in Uniaxial Compression

The volumetric strain was categorized into elastic and plastic parts. The farmer camposed of axial and lateral strains is uniform and determined by Hooke＇s law ; however, the latter consisting of axial and lateral strains is a fuaction af thickness af shear band determined by grndieat-dependeat plasticity by cansidering the heterngeneity of quasi- brittle materials. The non- uniform lateral strain due to the fact that shear band was farmed in the middle of specimen was averaged within specimen to precisely assess the volumetric strain. Then, the analytical expression for volumetric strain was verified by comparison with two earlier experimental results for concrete and rack. Finally, a detailed parametric study was carried out to investigate effects of constitutive parameters （ shear band thickness, elastic and softening rnoduli ） and geometrical size of specimen（ height and width of specimen ） on the volume dilatancy.

Simultaneous multi-material embedded printing for 3D heterogeneous structures

In order to mimic the natural heterogeneity of native tissue and provide a better microenvironment for cell culturing,multi-material bioprinting has become a common solution to construct tissue models in vitro.With the embedded printing method,complex 3D structure can be printed using soft biomaterials with reasonable shape fidelity.However,the current sequential multi-material embedded printing method faces a major challenge,which is the inevitable trade-off between the printed structural integrity and printing precision.Here,we propose a simultaneous multi-material embedded printing method.With this method,we can easily print firmly attached and high-precision multilayer structures.With multiple individually controlled nozzles,different biomaterials can be precisely deposited into a single crevasse,minimizing uncontrolled squeezing and guarantees no contamination of embedding medium within the structure.We analyse the dynamics of the extruded bioink in the embedding medium both analytically and experimentally,and quantitatively evaluate the effects of printing parameters including printing speed and rheology of embedding medium,on the 3D morphology of the printed filament.We demonstrate the printing of double-layer thin-walled structures,each layer less than 200μm,as well as intestine and liver models with 5%gelatin methacryloyl that are crosslinked and extracted from the embedding medium without significant impairment or delamination.The peeling test further proves that the proposed method offers better structural integrity than conventional sequential printing methods.The proposed simultaneous multi-material embedded printing method can serve as a powerful tool to support the complex heterogeneous structure fabrication and open unique prospects for personalized medicine.

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.

Multi-Scale Analysis of Fretting Fatigue in Heterogeneous Materials Using Computational Homogenization

This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.

Review of heterogeneous material objects modeling in additive manufacturing

This review investigates the recent developments of heterogeneous objects modeling in additive manufacturing(AM),as well as general problems and widespread solutions to the modeling methods of heterogeneous objects.Prevalent heterogeneous object representations are generally categorized based on the different expression or data structure employed therein,and the state-of-the-art of process planning procedures for AM is reviewed via different vigorous solutions for part orientation,slicing methods,and path planning strategies.Finally,some evident problems and possible future directions of investigation are discussed.

Irregular Characteristics and Parameter Assessment of Machined Surface of Heterogeneous Materials

Surface roughness is one of the main indexes in qua li ty assessment of machined components. Surface generation by material removal pro cess depends on the machining process mechanism. The material removal mechanisms are different for machining common materials and heterogeneous materials. Machi ned surface profiles of conventional engineering materials are determined by the moving tracks of tool edges on workpiece surface, the roughness mainly depends on the cutting parameters and the geometrical shape of cutting tool. Heterogeneo us materials consist of two or more separate materials, their properties vary fr om one phase to another and change along with measurement direction. When he terogeneous materials are cut, a quantity of machining-conduced imperfections o ccurs in the machined surface, part of the surface profiles do not directly result from the cutting of tool edges but from the imperfections, the surface te xture may confuse or disappears. The imperfections distribute randomly and their shapes are irregular, the spacing of profile peaks and valleys is irregular and un-periodical, therefore, they cannot be distinguished by wavelength. The prof iles of machined surface of heterogeneous materials have dense, narrow and sharp peaks and valleys. The amplitude distribution of profile peak and valley is dis persed and unsymmetrical, and usually the profile has a positive skewness. Ten p oint height of irregularities or root-mean-square deviation of the profile is more appropriate parameter than maximum height or arithmetical mean deviation of the profile for describing the height characteristics of roughness, and statist ical method and random process method are used to describe the irregularity distribution of the profile.

3-D NUMERICAL SIMULATION OF FRACTURE PROCESSES IN HETEROGENEOUS BRITTLE MATERIALS

By using the lattice model combined with finite element methods andstatistical techniques, a numerical approach is developed to establish mechanical models ofthree-dimensional heterogeneous brittle materials. A special numerical code is introduced, in whicha lattice model and statistical approaches are used to simulate the initial heterogeneity ofmaterial properties. The size of displacement-load step is adap-tively determined so that only fewelements would fail in each load step. When the tensile principal strain in an element exceeds theultimate strain of this element, the element is considered broken and its Young's modulus is set tobe very low. Some important behaviors of heterogeneous brittle materials are indicated using thiscode. Load-displacement curves and figures of three-dimensional fracture patterns are alsonumerically obtained, which are similar to those observed in laboratory tests.

NONLINEAR BUCKLING CHARACTERISTIC OF GRADED MULTIWEB STRUCTURE OF HETEROGENEOUS MATERIALS

The graded multiweb structure of heterogeneous anisotropic materials, which makes full use of the continuous, gradual and changing physical mechanical performance of material properties, has a widespread application in aeroplane aerofoil structure and automobile lightweight structure. On the basis of laminate buckling theory, the equivalent rigidity method is adopted to establish the corresponding constitutive relation and the non-linear buckling governing equation for the graded multiweb structure. In finding the solution, the critical load of buckling under different complicated boundary conditions together with combined loads were obtained and testification of the experimental analysis shows that the calculation results can satisfy the requirements of engineering design in a satisfactory way. Results obtained from the research say that： graded materials can reduce the concentrated stress on the interface in an effective way and weaken the effect of initial defect in materials and thereby improve the strength and toughness of materials.

A NEW APPROXIMATE SOLUTION TO THE MULTIPLE SCATTERING THEORY FOR THE ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS

The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.

ORIENTATION DISTRIBUTION FUNCTIONS FOR MICROSTRUCTURES OF HETEROGENEOUS MATERIALS (Ⅰ) ──DIRECTIONAL DISTRIBUTION FUNCTIONS AND IRREDUCIBLE TENSORS

In this two_part paper, a thorough investigation is made on Fourier expansions with irreducible tensorial coefficients for orientation distribution functions (ODFs) and crystal orientation distribution functions (CODFs), which are scalar functions defined on the unit sphere and the rotation group, respectively. Recently it has been becoming clearer and clearer that concepts of ODF and CODF play a dominant role in various micromechanically_based approaches to mechanical and physical properties of heterogeneous materials. The theory of group representations shows that a square integrable ODF can be expanded as an absolutely convergent Fourier series of spherical harmonics and these spherical harmonics can further be expressed in terms of irreducible tensors. The fundamental importance of such irreducible tensorial coefficients is that they characterize the macroscopic or overall effect of the orientation distribution of the size, shape, phase, position of the material constitutions and defects. In Part (Ⅰ), the investigation about the irreducible tensorial Fourier expansions of ODFs defined on the N_dimensional (N_D) unit sphere is carried out. Attention is particularly paid to constructing simple expressions for 2_ and 3_D irreducible tensors of any orders in accordance with the convenience of arriving at their restricted forms imposed by various point_group (the synonym of subgroup of the full orthogonal group) symmetries. In the continued work -Part (Ⅱ), the explicit expression for the irreducible tensorial expansions of CODFs is established. The restricted forms of irreducible tensors and irreducible tensorial Fourier expansions of ODFs and CODFs imposed by various point_group symmetries are derived.

Displacement Field Variable Modeling Method for Heterogeneous Materials in Wind Power Blade Core Plates

In order to study the mechanical properties of the heterogeneous core plate of the wind turbine blade,a modeling method of the core plate based on displacement field variables is proposed.Firstly,the wind turbine blade core plate was modeled according to the theory of modeling heterogeneous material characteristics.Secondly,the three-point bending finite element model of the wind turbine blade core plate was solved by the display dynamic equation to obtain the deformation pattern and force-deformation relationship of the core plate.Finally,the three-point bending static test was conducted to compare with the finite element analysis.The test results show that:the damage form of the wind turbine blade core plate includes elasticity,yield,and failure stages.The main failure modes are plastic deformation,core material collapse,and panel-core delamination.The failure load measured by the test is 1.59 kN,which is basically consistent with the load-displacement result obtained by the simulation,with a difference of only 1.9%,which verifies the validity and reliability of the model.It provides data references for wind turbine blade structure design.

Silicon-based optoelectronic heterogeneous integration for optical interconnection

The performance of optical interconnection has improved dramatically in recent years.Silicon-based optoelectronic heterogeneous integration is the key enabler to achieve high performance optical interconnection,which not only provides the optical gain which is absent from native Si substrates and enables complete photonic functionalities on chip,but also improves the system performance through advanced heterogeneous integrated packaging.This paper reviews recent progress of silicon-based optoelectronic heterogeneous integration in high performance optical interconnection.The research status,development trend and application of ultra-low loss optical waveguides,high-speed detectors,high-speed modulators,lasers and 2D,2.5D,3D and monolithic integration are focused on.

Toward Next-Generation Heterogeneous Catalysts:Empowering Surface Reactivity Prediction with Machine Learning

Heterogeneous catalysis remains at the core of various bulk chemical manufacturing and energy conversion processes,and its revolution necessitates the hunt for new materials with ideal catalytic activities and economic feasibility.Computational high-throughput screening presents a viable solution to this challenge,as machine learning(ML)has demonstrated its great potential in accelerating such processes by providing satisfactory estimations of surface reactivity with relatively low-cost information.This review focuses on recent progress in applying ML in adsorption energy prediction,which predominantly quantifies the catalytic potential of a solid catalyst.ML models that leverage inputs from different categories and exhibit various levels of complexity are classified and discussed.At the end of the review,an outlook on the current challenges and future opportunities of ML-assisted catalyst screening is supplied.We believe that this review summarizes major achievements in accelerating catalyst discovery through ML and can inspire researchers to further devise novel strategies to accelerate materials design and,ultimately,reshape the chemical industry and energy landscape.

Covalent organic frameworks as heterogeneous catalysts

Covalent organic frameworks （COFs）, established as an emerging class of crystalline porous polymers with high surface area, structural diversity, and esignability, attract much interest and exhibit potential applications in catalysis. In this review, we summarize the use of COFs as a versatile platform to develop heterogeneous catalysts for a variety of chemical reactions. Catalytic COFs are categorized in accordance with the types of active sites, involving single functional active sites, bifunctional active sites, and metal nanoparticles （NPs） embedded in pores. Special emphasis is placed on the deliberate or incidental synthesis strategies, the stability, the heterogeneity, and the shape/size selectivity for COF catalysis. Moreover, a description of the application of COFs as photocatalysts and electrocatalysts is presented. Finally, the prospects of COFs in catalysis and remaining issues in this field are indicated.

Fabrication of ultrafine Pd nanoparticles on 3D ordered macroporous TiO_2 for enhanced catalytic activity during diesel soot combustion

Nanocatalysts consisting of three‐dimensionally ordered macroporous(3DOM)TiO2‐supported ultrafine Pd nanoparticles(Pd/3DOM‐TiO2‐GBMR)were readily fabricated by gas bubbling‐assisted membrane reduction(GBMR)method.These catalysts had a well‐defined and highly ordered macroporous nanostructure with an average pore size of 280 nm.In addition,ultrafine hemispherical Pd nanoparticles(NPs)with a mean particle size of 1.1 nm were found to be well dispersed over the surface of the 3DOM‐TiO2 support and deposited on the inner walls of the material.The nanostructure of the 3DOM‐TiO2 support ensured efficient contact between soot particles and the catalyst.The large interface area between the ultrafine Pd NPs and the TiO2 also increased the density of sites for O2 activation as a result of the strong metal(Pd)‐support(TiO2)interaction(SMSI).A Pd/3DOM‐TiO2‐GBMR catalyst with ultrafine Pd NPs(1.1 nm)exhibited higher catalytic activity during diesel soot combustion compared with that obtained from a specimen having relatively large Pd NPs(5.0 nm).The T10,T50 and T90 values obtained from the former were 295,370 and 415°C.Both the activity and nanostructure of the Pd/3DOM‐TiO2‐GBMR catalyst were stable over five replicate soot oxidation trials.These results suggest that nanocatalysts having a 3DOM structure together with ultrafine Pd NPs can decrease the amount of Pd required,and that this approach has potential practical applications in the catalytic combustion of diesel soot particles.

Modeling of material deformation behavior in micro-forming under consideration of individual grain heterogeneity

This study aims to develop a model to characterize the inhomogeneous material deformation behavior in micro-forming.First,the influence of individual grain heterogeneity on the deformation behavior of CuZn20 foils was investigated via tensile and micro-hardness tests.The results showed that different from thick sheets,the hardening behavior of grains in the deformation area of thin foils is not uniform.The flow stress of thin foils actually only reflects the average hardening behavior of several easy-deformation-grains,which is the reason that thinner foils own smaller flow stress.Then,a composite modeling method under consideration of individual grain heterogeneity was developed,where the effects of grain orientation and shape are quantitatively represented by the method of flow stress classification and Voronoi tessellation,respectively.This model provides an accurate and effective method to analyze the influence of individual grain heterogeneity on the deformation behavior of the micro-sized material.

Co-salen functionalized on graphene as an efficient heterogeneous catalyst for cyclohexene oxidation

Co-salen functionalized on graphene with an average pore size of 27.7 nm as a heterogeneous catalyst exhibited good catalytic activity and recyclability in cyclohexene oxidation.