Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

Multi-Material Topology Optimization of 2D Structures Using Convolutional Neural Networks

In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.

Microstructure and thermal properties of dissimilar M300–CuCr1Zr alloys by multi-material laser-based powder bed fusion

Multi-material laser-based powder bed fusion (PBF-LB) allows manufacturing of parts with 3-dimensional gradient and additional functionality in a single step. This research focuses on the combination of thermally-conductive CuCr1Zr with hard M300 tool steel.Two interface configurations of M300 on CuCr1Zr and CuCr1Zr on M300 were investigated. Ultra-fine grains form at the interface due to the low mutual solubility of Cu and steel. The material mixing zone size is dependent on the configurations and tunable in the range of0.1–0.3 mm by introducing a separate set of parameters for the interface layers. Microcracks and pores mainly occur in the transition zone.Regardless of these defects, the thermal diffusivity of bimetallic parts with 50vol% of CuCr1Zr significantly increases by 70%–150%compared to pure M300. The thermal diffusivity of CuCr1Zr and the hardness of M300 steel can be enhanced simultaneously by applying the aging heat treatment.

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.

Evaluation of different crosslinking methods in altering the properties of extrusion-printed chitosan-basedmulti-material hydrogel composites

Three-dimensional printing technologies exhibit tremendous potential in the advancing fields of tissue engineering and regenerative medicine due to the precise spatial control over depositing the biomaterial.Despite their widespread utilization and numerous advantages,the development of suitable novel biomaterials for extrusion-based 3D printing of scaffolds that support cell attachment,proliferation,and vascularization remains a challenge.Multi-material composite hydrogels present incredible potential in this field.Thus,in this work,a multi-material composite hydrogel with a promising formulation of chitosan/gelatin functionalized with egg white was developed,which provides good printability and shape fidelity.In addition,a series of comparative analyses of different crosslinking agents and processes based on tripolyphosphate(TPP),genipin(GP),and glutaraldehyde(GTA)were investigated and compared to select the ideal crosslinking strategy to enhance the physicochemical and biological properties of the fabricated scaffolds.All of the results indicate that the composite hydrogel and the resulting scaffolds utilizing TPP crosslinking have great potential in tissue engineering,especially for supporting neo-vessel growth into the scaffold and promoting angiogenesis within engineered tissues.

A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

STUDY ON DESIGN TECHNIQUES OF A LONG LIFE HOT FORGING DIE WITH MULTI-MATERIALS

A new design technique for the long life hot forging die has been proposed. By finite element analysis, the reason .for the failure of hot forging die was analyzed and it was concluded that thermal stress is the main reason for the failure of hot forging die. Based on this conclusion, the whole hot forging die was divided into the substrate part and the heat-resistant part according to the thermal stress distribution. Moreover, the heat-resistant part was further subdivided into more zones and the material of each zone was reasonably selected to ensure that the hot forging die can work in an elastic state. When compared with the existing techniques, this design can greatly increase the service life because the use of multi-materials can alleviate the thermal stress in hot forging die.

Coating process of multi-material composite sand mold 3D printing

Sand mold 3 D printing technology is an advanced manufacturing technology which has great flexible manufacturing ability. A multi-material composite sand mold can control the temperature field of metallic parts during the pouring process, while the current sand mold 3 D printing technology can only fabricate a single material sand mold. The casting temperature field can not be adjusted by using single sand mold material with isotropous heat exchange ability during the pouring process. In this work, a kind of novel coating device was designed. Multi-material composite sand molds could be manufactured using the coating device according to the casting process demands of the final parts. The influences of curing agent content, coating velocity and scraper shape on compactness and surface roughness of the sand layer(silica sand and zircon sand) were studied. The shapes and sizes of transition intervals of two kinds of sand granules were also tested. The results show that, with the increase of the added volume of curing agent, the compactness of sand layer reduces and the surface roughness value rises. With the increase of the velocity of the coating device, the compactness of sand layer reduces and the surface roughness value rises similarly. In addition, the scraper with a dip angle of 72 degrees could increase the compactness value of the sand layer. The criteria of quality parmeters of the coating procedure are obtained. That is, the surface roughness(δ) of sand layer should be equal to or lesser than half of main size of the sand particles(Dm). The parameter H of the coating device which is the distance between the base of hopper and the surface of sand layer impacts the size of transition zone. The width of the transition zone is in direct proportion to the parameter H, qualitatively. Through the optimization of the coating device, high quality of multi-material sand layers can be obtained. This will provide a solution in manufacturing the multi-material composite sand mold.

A robust algorithm for moving interface of multi-material fluids based on Riemann solutions

In the paper, the numerical simulation of interface problems for multiple material fluids is studied. The level set function is designed to capture the location of the material interface. For multi-dimensional and multi-material fluids, the modified ghost fluid method needs a Riemann solution to renew the variable states near the interface. Here we present a new convenient and effective algorithm for solving the Riemann problem in the normal direction. The extrapolated variables are populated by Taylor series expansions in the direction. The anti-diffusive high order WENO difference scheme with the limiter is adopted for the numerical simulation. Finally we implement a series of numerical experiments of multi-material flows. The obtained results are satisfying, compared to those by other methods.

CONSERVATION LAW AND APPLICATION OF J- INTEGRAL IN MULTI-MATERIALS

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.

Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties.To characterize the random-field uncertainties with a reduced set of random variables,the Karhunen-Lo`eve(K-L)expansion is adopted.The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization.Under dividing the design domain,the volume fraction of each preset gradient layer is extracted.Based on the ordered solid isotropic microstructure with penalization(Ordered-SIMP),a functionally graded multi-material interpolation model is formulated by individually optimizing each preset gradient layer.The periodic constraint setting of the gradient layer is achieved by redistributing the average element compliance in sub-regions.Then,the method of moving asymptotes(MMA)is introduced to iteratively update the design variables.Several numerical examples are presented to verify the validity and applicability of the proposed method.The results demonstrate that the periodic functionally graded multi-material topology can be obtained under different numbers of sub-regions,and robust design structures are more stable than that indicated by the deterministic results.

Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

This study establishes amultiscale andmulti-material topology optimization model for thermoelastic lattice structures(TLSs)consideringmechanical and thermal loading based on the ExtendedMultiscale Finite ElementMethod(EMsFEM).The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint,respectively.The Solid Isotropic Material with Penalization(SIMP)interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure.The modified volume preserving Heaviside function(VPHF)is utilized to obtain a clear 0/1 material of truss microstructure.Compared with the classic topology optimization of single-material TLSs,multi-material topology optimization can get a better structural design of the TLS.The effects of temperatures,size factor,and mass fraction on optimization results have been presented and discussed in the numerical examples.

Abnormal interfacial bonding mechanisms of multi-material additive-manufactured tungsten-stainless steel sandwich structure

Tungsten(W)and stainless steel(SS)are well known for the high melting point and good corrosion resistance respectively.Bimetallic W-SS structures would offer potential applications in extreme environments.In this study,a SS→W→SS sandwich structure is fabricated via a special laser powder bed fusion(LPBF)method based on an ultrasonic-assisted powder deposition mechanism.Material characterization of the SS→W interface and W→SS interface was conducted,including microstructure,element distribution,phase distribution,and nano-hardness.A coupled modelling method,combining computational fluid dynamics modelling with discrete element method,simulated the melt pool dynamics and solidification at the material interfaces.The study shows that the interface bonding of SS→W(SS printed on W)is the combined effect of solid-state diffusion with different elemental diffusion rates and grain boundary diffusion.The keyhole mode of the melt pool at the W→SS(W printed on SS)interface makes the pre-printed SS layers repeatedly remelted,causing the liquid W to flow into the sub-surface of the pre-printed SS through the keyhole cavities realizing the bonding of the W→SS interface.The above interfacial bonding behaviours are significantly different from the previously reported bonding mechanism based on the melt pool convection during multiple material LPBF.The abnormal material interfacial bonding behaviours are reported for the first time.

A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods

A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.

Application of Gridless Method to Simulation of Compressible Multi-Material Flows

The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fits was adopted to approximate the spatial derivatives of a point on the base of the points in its circular support domain,and the basis function was linear. The HLLC( Harten-Lax-van Leer-Contact) scheme was used to calculate the inviscid flux. On the material interfaces,the gridless points were endued with a dual definition corresponding to different materials. The moving velocity of the interface points was updated by solving the Riemann problem. The interface boundary condition was built by using the Ghost Fluid Method( GFM).Computations were performed for several one and two dimensional typical examples. The numerical results show that the interface and the shock wave are well captured,which proves the effectiveness of gridless method in dealing with multi-material flow problems.

Multi-Material Topology Optimization of Structures Using an Ordered Ersatz Material Model

This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint.A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost.Different from the traditional material penalization scheme,the algorithm is established on the ordered ersatz material model,which linearly interpolates Young’s modulus for relaxed design variables.To achieve a multi-material design,the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values.For the convergent element-based solution,the multiple level-set functions are constructed to tentatively extract the smooth interface between two adjacent materials.Some 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed algorithm and the possible advantage of the multi-material designs over the traditional solid-void designs.

Advanced Welding Technology for Highly Stressable Multi-Material Designs with Fiber-Reinforced Plastics and Metals

Organic sheets made out of fiber-reinforced thermoplastics are able to make a crucial contribution to increase the lightweight potential of a design. They show high specific strength- and stiffness properties, good damping characteristics and recycling capabilities, while being able to show a higher energy absorption capacity than comparable metal constructions. Nowadays, multi-material designs are an established way in the automotive industry to combine the benefits of metal and fiber-reinforced plastics. Currently used technologies for the joining of organic sheets and metals in large-scale production are mechanical joining technologies and adhesive technologies. Both techniques require large overlapping areas that are not required in the design of the part. Additionally, mechanical joining is usually combined with “fiber-destroying” pre-drilling and punching processes. This will disturb the force flux at the joining location by causing unwanted fiber- and inter-fiber failure and inducing critical notch stresses. Therefore, the multi-material design with fiber-reinforced thermoplastics and metals needs optimized joining techniques that don’t interrupt the force flux, so that higher loads can be induced and the full benefit of the FRP material can be used. This article focuses on the characterization of a new joining technology, based on the Cold Metal Transfer (CMT) welding process that allows joining of organic sheets and metals in a load path optimized way, with short cycle times. This is achieved by redirecting the fibers around the joining area by the insertion of a thin metal pin. The path of the fibers will be similar to paths of fibers inside structures found in nature, e.g. a knothole inside of a tree. As a result of the bionic fiber design of the joint, high joining strengths can be achieved. The increase of the joint strength compared to blind riveting was performed and proven with stainless steel and orthotropic reinforced composites in shear-tests based on the DIN EN ISO 14273. Every specimen joined with the new CMT Pin joining technology showed a higher strength than specimens joined with one blind rivet. Specimens joined with two or three pin rows show a higher strength than specimens joined with two blind rivets.

OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD

Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained.

Specialty optical fibers for advanced sensing applications

Optical fiber technology has changed the world by enabling extraordinary growth in world-wide communications and sensing.The rapid development and wide deployment of optical fiber sensors are driven by their excellent sensing performance with outstanding flexibility,functionality,and versatility.Notably,the research on specialty optical fibers is playing a critical role in enabling and proliferating the optical fiber sensing applications.This paper overviews recent developments in specialty optical fibers and their sensing applications.The specialty optical fibers are reviewed based on their innovations in special structures,special materials,and technologies to realize lab in/on a fiber.An overview of sensing applications in various fields is presented.The prospects and emerging research areas of specialty optical fibers are also discussed.

DIC Based Strain and Damage Analysis of Large Scale Steel to Composite Adhesive Joints Subjected to Tension and Compression Loading

This paper reports an experimental study of the mechanical response to tensile and compressive force of large scale steel to composite joints adhesively bonded with a thin layer of vinylester resin.In one specimen,the length of the reinforcing fibres in contact with the steel substrate has been reduced by saw cutting at both ends of the joint.This damaged specimen and four intact specimens were subjected to quasi-static tensile testing;six specimens were used for compression testing.The strain distribution at the composite surface and at the steel to hardwood connection of the specimen was monitored by digital image correlation(DIC).DIC allowed identifying the onset of damage in the tensile tested joints near the interface of the composite layer and the steel-hardwood connection.Both tensile and compression tested specimens failed due to significant peel strain concentration at the composite near the connection of steel and hardwood.The average strength of a specimen tested in compression was about 66%higher than the average strength of a specimen tested in tension.The strain concentration zone in the damaged specimen was away from the introduced saw cuts.As a result the damaged and intact tensile specimens showed the same failure strength and stiffness.All specimens failed by adhesive failure between the composite-hardwood interface.