Multi-scale Finite Element Analysis Research Articles

Deep learning framework for multiscale finite element analysis based on data-driven mechanics and data augmentation

In this study, a deep learning framework for multiscale finite element analysis (FE2) is proposed. To overcome the inefficiency of the concurrent classical FE2 method induced by the repetitive analysis at each macroscopic integration points, the distance-minimizing data-driven computational mechanics is adopted for the FE2 analysis. Macroscopic strain and stress data are directly assigned to the material points of the macroscopic finite element models without constitutive model. Here, the macroscopic problems are solved with the offline macroscopic material genome database, without solving the microscopic problems simultaneously. The novelty of the proposed approach lies in using a deep neural network to enable adaptive sampling points without prior knowledge of the specific mechanical problem. The proposed data augmentation framework updates the sampling points gradually using the distance minimization algorithm with the mechanistic constraints, including the equilibrium and compatibility equations. Particularly, the deep neural network plays a crucial role as a guide in the phase space sampling process, facilitating the efficient use of sparse data. Thus, this method shows high feasibility and significantly improves the computational efficiency of offline computing.

Effects of nonlinear hyper‐viscoelasticity and matrix/fiber debonding on the mechanical properties of short carbon fiber/styrene‐butadiene rubber composites under cyclic uniaxial loading using a multiscale finite element model

AbstractA multiscale finite element analysis was performed for short carbon fiber (SCF) reinforced rubber composites under uniaxial tensile loading with periodic geometries and random distributions of the short fibers. Three different zones were considered, including the rubber matrix, SCF as the inclusion phase, and a thin matrix layer as the interphase. A nonlinear hyper‐viscoelastic model was selected for the matrix, while linear viscoelastic and elastic models were considered for the interphase and reinforcing phases, respectively. The analyses were carried out on an incremental basis from a lower loading‐unloading rate of 10 mm/min to a higher rate of 100 mm/min. Two interface conditions were considered between the polymer matrix and the SCF phases: perfect bonding and partial debonding. The partial debonding was modeled via extended FEM (XFEM) with a crack initiation criterion. An integral averaging technique was employed to predict stress and strain at the macro‐scale. Based on the observations in this work, hysteresis and energy dissipation decrease with the addition of the short fibers to the neat rubber and surface modification of the fibers under three‐cycle loading. For example, in the first cycle and for a constant stress of 0.45 MPa, the strain value decreases from 0.25 to 0.17 MPa at the loading‐unloading rate of 10 mm/min. The high‐fidelity model developed in this work for short fiber/rubber composites is able to predict the stress and strain responses of the SCF/SBR composites, confirming the accuracy of the utilized multiscale approach.

Superficial zone chondrocytes can get compacted under physiological loading: A multiscale finite element analysis.

Recent in vivo and in vitro studies have demonstrated that superficial zone (SZ) chondrocytes within articular layers of diarthrodial joints die under normal physiologic loading conditions. In order to further explore the implications of this observation in future investigations, we first needed to understand the mechanical environment of SZ chondrocytes that might cause them to die under physiological sliding contact conditions. In this study we performed a multiscale finite element analysis of articular contact to track the temporal evolution of a SZ chondrocyte's interstitial fluid pressure, hydraulic permeability, and volume under physiologic loading conditions. The effect of the pericellular matrix modulus and permeability was parametrically investigated. Results showed that SZ chondrocytes can lose ninety percent of their intracellular fluid after several hours of intermittent or continuous contact loading, resulting in a reduction of intracellular hydraulic permeability by more than three orders of magnitude. These findings are consistent with loss of cell viability due to the impediment of cellular metabolic pathways induced by the loss of fluid. They suggest that there is a simple mechanical explanation for the vulnerability of SZ chondrocytes to sustained physiological loading conditions. Future studies will focus on validating these specific findings experimentally. STATEMENT OF SIGNIFICANCE: As with any mechanical system, normal 'wear and tear' of cartilage tissue lining joints is expected. Yet incidences of osteoarthritis are uncommon in individuals younger than 45. This counter-intuitive observation suggests there must be an intrinsic repair mechanism compensating for this wear and tear over many decades of life. Recent experimental studies have shown superficial zone chondrocytes die under physiologic loading conditions, suggesting that this repair mechanism may involve cell replenishment. To better understand the mechanical environment of these cells, we performed a multiscale computational analysis of articular contact under loading. Results indicated that normal activities like walking or standing can induce significant loss of intracellular fluid volume, potentially hindering metabolic activity and fluid transport properties, and causing cell death.

Simulation and Experiment on the Low-Velocity Impact Response of Flax Fabric Reinforced Composites.

Natural fiber reinforced composites are increasingly used to fabricate structural components prone to suffering low-velocity impacts. The low-velocity impact response of flax fabric reinforced composites under different impact energies is experimentally studied and numerically simulated. A multi-scale finite element analysis strategy for the progressive damage prediction of flax fabric reinforced composites is developed. Micro- and meso-scale analyses are conducted to predict the effective properties of the woven unit cell. Macro-scale analysis is carried out subsequently to predict the impact response of composite laminates using the results of micro- and meso-scale analyses as inputs. Simulation results and experimental results both show that most of the impact energy is absorbed by the specimens when the impact energy is lower than 4 J, and the absorption ratio of impact energy slightly increases with the increase in impact energy. On the contrary, a dramatic decrease occurs in the absorption ratio when the impact energy is 6 J, due to the severe damage to the specimen. In addition, simulation results indicate that matrix shear damage and interlaminar damage are the primary failure modes of composites under high impact energy. The numerical results of impact force, absorbed energy, and damage morphologies on both sides for all specimens show good agreement with the experimental results.

Vibration stress relief on the machining of SiCp/6061Al composites by multi-scale finite element analysis

Vibration stress relief on the machining of SiCp/6061Al composites by multi-scale finite element analysis

Computational modeling of combined frost damage and alkali–silica reaction on the durability and fatigue life of RC bridge decks

A coupling model reflecting the interaction between freeze–thaw cycles (FTCs) and alkali–silica reactions (ASRs) is established from the microscale to the macroscale under the consideration of non-uniform environmental and mechanical conditions. At both material and structural levels with/without reinforcement, the deformation and damage patterns of specimens under single and coupled FTCs and ASRs were simulated by multiscale finite element analysis and partially verified by experiments. Furthermore, following different sources of damage actions, the remaining fatigue life of reinforced concentrate (RC) slabs under traffic loads was investigated. The results show that ASR-driven expansion is mainly governed by the arrangement of reinforcing bars, whereas FTC damage is mainly initiated from corners, edges, and surfaces of RC slab parts and closely relies on water supply. In addition, the severity of coupled damage (FTC and ASR) can be significantly greater than that of the sum of single ASR and FTC damage due to the gel-filling of pores and entrained air. Finally, in terms of the remaining fatigue life, the ASR could be occasionally beneficial for bridge decks under moving traffic loads due to gel-filled cracks and chemical prestressing. However, if cracks are empty or filled by condensed liquid water, the overall fatigue life will be significantly reduced.

Thermoplastic coating on fiber reinforced polymer composites by cold spray additive manufacturing

This work investigates the cold spray coating of nylon 6 on fiber-reinforced composite substrates. Deposition conditions are investigated by systematically varying the process parameters (impact velocity, temperature, carrier gas pressure, and flow rate) for two woven fiber-reinforced epoxy substrates with glass and carbon fiber reinforcements, resulting in deposition efficiencies exceeding 30%. Parametric studies are performed to identify the optimal system pressure and powder flow rates that lead to the successful deposition of the powder particles on composite substrates. It is observed that, upon impact, the particles undergo extensive plastic deformation without damaging the reinforcing fibers in the substrate. Microstructural observations reveal that the first (seeding) layer of nylon particles experiences a higher degree of plastic deformation due to the impact on a stiff substrate. The large plastic deformation in the impacting particles plays a key role in enabling adhesion to the substrate. The successive layers of deposited particles undergo less plastic deformation as they impact a comparatively softer pre-deposited nylon substrate. The underlying deposition mechanisms are further explored using multiscale finite element analyses. Results obtained in this work demonstrate the feasibility of cold spray deposition of thermoplastic particles on fiber-reinforced composites without imposing significant damage to the substrate.

Physically recurrent neural networks for path-dependent heterogeneous materials: Embedding constitutive models in a data-driven surrogate

Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite element analysis (FE2) due to the exceedingly high computational costs often associated with it and the high number of similar micromechanical analyses involved. To tackle the issue, using surrogate models to approximate the microscopic behavior and accelerate the simulations is a promising and increasingly popular strategy. However, several challenges related to their data-driven nature compromise the reliability of surrogate models in material modeling. The alternative explored in this work is to reintroduce some of the physics-based knowledge of classical constitutive modeling into a neural network by employing the actual material models used in the full-order micromodel to introduce non-linearity. Thus, path-dependency arises naturally since every material model in the layer keeps track of its own internal variables. For the numerical examples, a composite Representative Volume Element with elastic fibers and elasto-plastic matrix material is used as the microscopic model. The network is tested in a series of challenging scenarios and its performance is compared to that of a state-of-the-art Recurrent Neural Network (RNN). A remarkable outcome of the novel framework is the ability to naturally predict unloading/reloading behavior without ever seeing it during training, a stark contrast with popular but data-hungry models such as RNNs. Finally, the proposed network is applied to FE2 examples to assess its robustness for application in nonlinear finite element analysis.

Fretting wear characteristics of 60Si2MnA steel for high-speed railway rail fastener clips

ABSTRACT The fretting wear of rail fastener clips caused by wheel and rail vibrations can diminish their mechanical properties, negatively impacting high-speed train operation. However, the fretting wear characteristics of fastener clips are not yet known. In this work, the value range of the two key parameters of normal load and displacement amplitude of the fretting wear tests is determined by the multi-scale finite element analysis. Fretting wear tests are carried out systematically, and the fretting wear running characteristics and wear mechanism of the 60Si2MnA steel clip under normal service conditions are obtained. The results show that the clip has two fretting wear running regimes, the mixed fretting regime (MFR) and the gross slip regime (GSR). The wear mechanism in MFR is mainly characterized by abrasive wear, adhesive wear and oxidative wear. The wear mechanism in GSR is mainly characterized by abrasive wear, adhesive wear, oxidative wear, and fatigue wear.

Hierarchical Dynamic Bayesian Network-Based Fatigue Crack Propagation Modeling Considering Initial Defects.

Orthotropic steel decks (OSDs) are inevitably subjected to fatigue damage caused by cycled vehicle loads in long-span bridges. This study establishes a probabilistic analysis framework integrating the dynamic Bayesian network (DBN) and fracture mechanics to model the fatigue crack propagation considering mutual correlations among multiple fatigue details. Both the observations of fatigue crack length from field inspection and monitoring data of vehicle loads from the weight-in-motion (WIM) system are utilized. First, fracture mechanics-based uncertainty analysis is performed to determine the multiple uncertainty sources in the Paris crack propagation model, material property, and observation data of crack length. The uncertainty of monitoring data of vehicle loads is ignored because of its high accuracy; consequently, the vehicle-load-related uncertainty is spontaneously ignored, which is also demonstrated to be very small on the investigated actual bridges. Second, a hierarchical DBN model is introduced to construct mutual dependencies among various uncertainties and intra-correlations in the propagation process of multiple fatigue cracks at different components. Third, a stochastic traffic model is established based on the WIM monitoring data and multi-scale finite element analysis via substructure techniques to determine the probability distribution of vehicle-load-related parameters. After variable discretization, a refined exact inference algorithm in a forward–backward–forward manner is adopted to estimate the posterior distribution of equivalent initial crack length and update the established DBN model. Finally, the proposed method is demonstrated by a numerical case study and a typical application on an actual cable-stayed bridge with steel box girders using OSDs in China. The results show that the probability distribution of equivalent initial crack size can be spontaneously derived with a larger mean value than the results of conventional empirical analysis. Furthermore, the component-level fatigue reliability is tracked and predicted based on the established crack propagation model.

Effect of fibre aspect ratio and aggregation on nonlinear material property of random cellulose reinforced composites: A multiscale computational study

Multiscale finite element analysis based on the asymptotic homogenisation theory was performed on cellulose-fibre-reinforced plastics. Polypropylene, a thermoplastic resin, was used as the matrix, and the effect of the fibre morphology on the nonlinear response of the material was clarified. A new indicator, that is, the proportion of the fibre contribution based on strain energy, was applied to quantify the effect of reinforcing fibres in improving the mechanical properties. Representative volume element models of randomly oriented fibre dispersion were constructed using a random sequential adsorption algorithm, and the effects of the fibre aspect ratio and aggregation on the nonlinear response under a tensile load were clarified. Consequently, it was deduced that the elastic properties and maximum tensile stress fluctuated by 26.8 % and 39.6 %, respectively, depending on the fibre aspect ratio, and 5.95 % and 4.20 %, respectively, owing to fibre aggregation. Furthermore, by introducing the fibre contribution proportion, we found that both the fibre aspect ratio and aggregation belong to the secondary factor, and their influence can be evaluated almost uniformly by the increase rate determined from the fibre orientation distribution of the primary factor.

Multiscale 3D finite element analysis of aluminum matrix composites with nanoµ hybrid inclusions

The present work proposed a multiscale finite element (FE) analytical approach to investigate the mechanical behavior of elasto-plastic aluminum matrix composites reinforced with nano-micro hybrid inclusions. To study the effect of microstructural effects, 3D representative volume elements (RVEs) of nano- and micro-scales are established, where the nano-RVE considers the aluminum matrix with carbon nanotubes (CNTs)-reinforcement whose homogenization is treated as the equivalent matrix (EM) phase for micro-RVE with SiC particles. The FE-based ABAQUS simulation is employed to recover the local stress distributions within RVE of either scales, and the corresponding effective stress–strain relationship, damage and failure behavior are calculated and predicted. Results generated from the present simulations are validated against the experimental measurement of CNTs/SiC/Al composites and good agreement is generally obtained. What’s more, several microstructural parameters are tested on the composites’ effective behavior, including the elaso-plastic constitutive relation and damage response of aluminum matrix, the elastic-brittle failure mechanical behavior of the micro-scale SiC particles. We also consider the traction-separation mechanical behavior at the SiC-Al interface. It is demonstrated that the present numerical method is suitable to study the comprehensive behavior of composites with hybrid inclusions.

Multiscale simulation on nonlinear mechanical properties of 3D printed cellulose composites

Polypropylene (PP), a major thermoplastic resin, is widely used in compression molding and injection molding due to its excellent mechanical properties and recyclability. In general, talc, an inorganic mineral product, is widely used as a reinforcing filler in PP. Talc has excellent chemical stability, electrical insulation, and affinity with organic materials. However, PP has a high coefficient of linear expansion, making it difficult to use with the fused deposition modeling 3D printers that have become increasingly popular in recent years because of warping of the printed structures. On the other hand, cellulose nanofiber (CNF) is a plant fiber that has been degraded to the nanoscale and is expected to be used as a reinforcing filler for composite materials because of its superior specific stiffness and specific strength. It is expected to reduce environmental impact compared to conventional reinforcing fillers due to its reduced CO2 emissions and high recyclability. In addition, the high aspect ratio and low coefficient of linear expansion of CNF can be expected to reduce thermal deformation of composite materials. In this study, the mechanical properties of PP composites reinforced by talc and CNF fillers were tested by multiscale finite element analysis. The contents of talc and CNF were changed, and the effects of adding each were clarified.

Heterogeneous mechanical properties along the building direction in direct laser deposited 17-4 PH steel

The present work thoroughly investigated the heterogeneous mechanical properties along the building direction in a direct laser deposited 17-4 PH part by tensile tests. From top to bottom (1# - 5#) in the as-built cuboid, the yield strength enhanced from ~729 MPa to ~1050 MPa, while the elongation decreased from ~4.69% to ~1.50%. The microstructure of samples was composed of main martensite, reversed austenite, and a large amount of NbC nano-particles. The discrepancy in chemical composition and dislocation density between the phases existed due to the heat accumulation as the increasing building height. The various reduced fraction of austenite in different samples after tensile tests, implying the diverse extent of strain-induced phase transformation. Besides, the average Schmid factor of the 1# sample was higher; thus its grain orientation was more conducive to plastic deformation, leading to lower yield stress. The kernel average misorientation (KAM) was higher and distributed uniformly near the fracture of the 1# sample, and showed better deformation compatibility in the microstructure. Based on the combination of microstructural models and the dislocation density micromechanical model, multiscale finite element analysis further found that larger particles advanced the movements of dislocations, inducing more intense plastic flow within the austenite grains, which enabled greater fractions of transformation in austenite to improve the overall elongation of the sample.

Uncertainty quantification for the representative volume element of geometrically monoclinic 3D printed concrete

3D concrete printing technology has been well developed and applied in various engineering fields. Anisotropy is one of the most important properties for the 3D printed cementitious material. Like fiber reinforced composite matters, if the material property is symmetric in only one plane, then the material is called as monoclinic with 13 independent elastic moduli in its constitutive law. In this study, multiscale finite element analysis of the monoclinic 3D printed cementitious material is made. Both material and geometrical randomness and uncertainty are quantified and investigated. At micro scale the material randomness is explored using nanoindentation technique. In addition, the geometrical uncertainty is analyzed through multiscale finite element method at meso scale. Then a stochastic finite element numerical experiment of 3D printed concrete simple supported beam under vertical loading is made based on the 13 independent stochastic elastic constants at macro scale. Computational methods proposed in this paper could be widely applied in 3D concrete printing industry.

Simulation study on fatigue behavior of wrap-around weld at rib-to-floorbeam joint in a steel-UHPC composite orthotropic bridge deck

As an innovative cement-based material, the ultra-high performance concrete (UHPC) has been recently utilized to reinforce the orthotropic steel bridges. Based on an in-situ steel-UHPC composite orthotropic deck bridge, both the field testing and multi-scale finite element analysis modelling were conducted to investigate the fatigue behavior of wrap-around weld at rib-to-floorbeam (RF) joint, and factors influencing stress were further studied to achieve an infinite fatigue life. It is found that a primary tensile stress cycle is jointly produced by the axle group of truck, while a small reversal compressive cycle will be generated when the axle is directly located on the floorbeam. The stress behavior of fatigue detail is extremely sensitive to the localized effect of axle loading instead of entire truck configuration. Since significant stress concentration and high stress gradient exist in the wrap-around weld, it is essential to utilize the hot-spot stress approach rather than nominal stress approach. The wrap-around weld presents an obvious out-of-plane bending deformation, which results from the torsion effect and Poisson’s effect. The Dong’s structural stress reveals that the surface stress is dominated by bending stress. The application of bulkhead can greatly improve the fatigue performance of wrap-around weld. Both the large-scale rib and U-shaped rib are preferable, which are available to achieve an infinite fatigue life without extra fabrication procedure.

A Multiscale Finite Element Analysis of Balloon Kyphoplasty to Investigate the Risk of Bone-Cement Separation In Vivo.

During the past decade there has been a significant increase in the number of vertebral fractures being treated with the balloon kyphoplasty procedure. Although previous investigations have found kyphoplasty to be an effective treatment for reducing patient pain and lowering cement-leakage risk, there have been reports of vertebral recollapse following the procedure. These reports have indicated evidence of in vivo bone-cement separation leading to collapse of the treated vertebra. The following study documents a multiscale analysis capable of evaluating the risk of bone-cement interface separation during lying, standing, and walking activities following balloon kyphoplasty. Results from the analysis found that instances of reduced cement interlock could initiate both tensile and shear separation of the interface region at up to 7 times the failure threshold during walking or up to 1.9 times the threshold during some cases for standing. Lying prone offered the best protection from interface failure in all cases, with a minimum safety factor of 2.95. The results of the multiscale analysis show it is essential for kyphoplasty simulations to take account of the micromechanical behavior of the bone-cement interface to be truly representative of the in vivo situation after the treatment. The results further illustrate the importance of ensuring adequate cement infiltration into the compacted bone periphery during kyphoplasty through a combination of new techniques, tools, and biomaterials in a multifaceted approach to solve this complex challenge.

Multiscale Finite Element Analysis of Needle-Punched C/SiC Composites through Subcell Modeling

Multiscale Finite Element Analysis of Needle-Punched C/SiC Composites through Subcell Modeling

In-situ effect in cross-ply laminates under various loading conditions analyzed with hybrid macro/micro-scale computational models

In this work, multi-scale finite element analyses based on three-dimensional (3D) hybrid macro/micro-scale computational models subjected to various loading conditions are carried out to examine the in-situ effect imposed by the neighboring plies on the failure initiation and propagation of cross-ply laminates. A detailed comparative study on crack suppression mechanisms due to the effect of embedded laminar thickness and adjacent ply orientation is presented. Furthermore, we compare the results of in-situ transverse failure strain and strength between the computational models and analytical predictions. Good agreements are generally observed, indicating the constructed computational models are highly accurate to quantify the in-situ effect. Subsequently, empirical formulas for calculating the in-situ strengths as a function of embedded ply thickness and different ply angle between embedded and adjacent plies are developed, during which several material parameters are obtained using a reverse fitting method. Finally, a new set of failure criteria for σ22-τ12, σ22-τ23, and σ11-τ12 accounting for the in-situ strengths are proposed to predict laminated composites failure under multi-axial stress states. This study demonstrates an effective and efficient computational technique towards the accurate prediction of the failure behaviors and strengths of cross-ply laminates by including the in-situ effects.

Multiscale Investigations of RC Shear Wall Buildings

ABSTRACT The precise description of reinforced concrete shear wall (RCSW) systems under severe dynamic loading remains a difficult research question owing to the intrinsically multi-scale underlying mechanisms, ranging from building’s irregularity to individual core walls, and even to the millimeter length-scales nonlinear shear over cracks and progressive steel bar buckling. This study adopted a parallel multiscale finite element analysis platform that can link the millimeter-level microphysical phenomena to the entire building-level dynamic responses in order to analyze weak pre-1980 buildings that lack modern codes such as boundary elements of walls. Results offer physically sound rationales behind the multi-scale damage behaviors.