Multi-scale Finite Element Analysis Research Articles

Investigation of the effects of volume fraction, aspect ratio and type of fibres on the mechanical properties of short fibre reinforced 3D printed composite materials

AbstractMechanical behaviour of 3D-printed composite parts is affected by the volume fraction, aspect ratio and type of fibre reinforcement. Although in the literature experimental approaches have been used to characterise the effects of the above factors on the mechanical properties of 3D printed parts, time and cost of the manufacturing process as well as the uncertainty associated with a large number of experimental techniques are the key issues. This study aims to address these challenges by developing a methodology based on a multi-scale Finite Element (FE) analysis of representative volume element (RVE) of 3D printed composite parts to predict the effective orthotropic properties. To account for the effects of fibre features, RVEs were modelled considering variables of volume fraction, aspect ratios and type of short fibres. To study the main and interaction effects of the above variables on the mechanical properties of 3D printed composite parts, a structured approach based on the Design of Experiments is used. The FE stress analysis of the RVE provides an understanding about the potential failure modes such as interfacial debonding between fibres and matrix, interlayer and intralayer delamination that may occur in load-bearing 3D printed composite parts. The FE computed mechanical properties are validated against experimental data through a series of mechanical testing of flexure, Iosipescu, and short beam shear which were conducted in conjunction with the Digital Image Correlation technique. As a result, certainty is obtained in using the proposed approach for a fast iterative design of 3D printed composite parts prior to industrial applications.

Coupling μ-computed tomography and multi-scale modelling to assess the mechanical performance of material extrusion metal components

The porosity defects arising in objects produced by metal Material Extrusion (MEX) additive manufacturing affect the macroscopic mechanical behaviour. This paper presents a new approach integrating μ-computed tomography (μXCT) and multi-scale finite element analysis to evaluate the mechanical performance of components fabricated by metal MEX. The porosity information from μXCT is mapped into the finite element model, allowing to define the volume fraction of porosity to each finite mesh element. Then, the Mori-Tanaka homogenization technique is used to estimate the effective mechanical properties in each integration point, assuming a representative volume element composed by a metal matrix with a void. The reliability of the proposed approach was assessed using tensile specimens of stainless steel 316L produced by metal MEX. The numerical predictions were compared with experimental measurements, namely the strain field evolution measured by digital image correlation (DIC). The results highlight the detrimental influence of the porosity distribution, evaluated in the specimen using μXCT, on the strain distribution during the loading stage. The numerical predictions are in agreement with the experimental measurements, i.e. the difference is lower than 11%. Therefore, the proposed approach offers valuable insights for evaluating the mechanical performance of components produced by metal MEX, focusing on the detrimental effects of porosity defects.

Multiscale finite element analysis of layer interface effects on cracking in semi-flexible pavements at different temperatures

This paper presents comprehensive research work on the crack initiation behavior of Semi Flexible Pavements (SFP) with the help of a one-way coupled multiscale modelling approach. The study focuses on elucidating the influence of layer interface conditions on potential cracking patterns under different temperature conditions. By integrating material properties at both local (mixture) and global (pavement) scales using a local de-homogenization approach, the interlocking effect was addressed within the asphalt binder's mesoscale properties. CT-image based mesostructure was employed to reconstruct the Representative Volume Element (RVE). Cohesive Zone Model (CZM) was utilized to simulate cracking initiation within the RVEs, with simulation results validated against practical engineering inspections. Additionally, a potential macroscopic failure index was introduced for SFP. It was found that the typical macroscopic failure indexes utilized for AC pavement may not be suitable for SFP due to the higher degree of heterogeneity. Analysis showed that SFP layer's coarse aggregate and cement grout at the bottom may experience compressive stress, while asphalt binder beneath the tire load may face high tensile stresses. Regardless of the interface conditions, top-down cracking was found to be the dominating failure mode in SFP. Besides, the vulnerable area in bonded interface SFP shifts from under tire load to the adjacent area with the rise in pavement temperature, while bottom-up cracking may appear only in unbonded interface SFP under low temperature conditions. Subsequent analysis demonstrated that top-down cracking is prominent in bonded interface SFP, especially at higher temperatures, compared to unbonded interface SFP. It is expected that critical observations for SFP highlighted above will certainly help in understanding critical failure modes and, hence, designing and constructing durable SFP structures.

Multiscale Finite Element Analysis of Yield-point Phenomenon in Ferrite–Pearlite Duplex Steels

Multiscale Finite Element Analysis of Yield-point Phenomenon in Ferrite–Pearlite Duplex Steels

A multiscale finite element analysis model for predicting the effect of micro-aeration on the fragmentation of chocolate during the first bite

The emerging need to reduce the calorific value of foods, while simultaneously improving the consumer perception drives the quest for developing new food structures that satisfy both criteria. Aiming to shed light on the influence that micro-aeration has on the breakdown of chocolate during the early stages of the oral processing, this paper summarises the development of multi scale, in silico Finite Element (FE) models for the first bite. A micro-mechanical analysis was first employed to predict the impact on the mechanical properties of chocolate at two microaeration levels, i.e. f=10vol% and f=15vol%. The estimated elastic, plastic and fracture properties from the micromechanical model were subsequently fed into a macroscopic simulation of the first bite. Both micromechanical and the macromechanical models for the 10vol% and 15vol% porosity chocolate are compared to experimental data for validation purposes. The micromechanical models are compared to data from literature on mechanical testing of the same two chocolate materials whereas the first bite macromechanical model was compared to in vitro experimental data obtained in this study using a 3D printed molar teeth test rig mounted to a mechanical tester. Finally, the particle size distribution of the fragmented chocolate during the first bite was estimated from the in silico model and compared to in vivo literature data on the same chocolate materials and in vitro experimental data from this work. All comparisons between the in silico models and the in vitro/in vivo data led to good agreement. Our modelling methodology provides a cost-efficient tool for the investigation of new food structures that reduce the calorific value while enhancing the taste perception.

Multiscale Finite Element Analysis of Yield-point Phenomenon in Ferrite–Pearlite Duplex Steels

Multiscale Finite Element Analysis of Yield-point Phenomenon in Ferrite–Pearlite Duplex Steels

Implicit multiscale finite element analysis of polymer physics-based multiscale constitutive model for elastomers

This paper proposes a multiscale visco-hyperelastic constitutive model that can predict the material behavior bridging molecular properties to response at the continuum level and its integration within implicit finite element analysis. The proposed model incorporates all parameters having actual physical meaning obtained from molecular simulations based on the tube theory. Despite the advantages that the constitutive equation was determined from molecular network characteristics, applications of the model have been restricted to the simple shape of Finite Element (FE) models with a few cases of specific deformations, owing to its complexity and absence of the implicit formulation. Therefore, the application of the model to the 3D implicit FE analysis with a tangent stiffness was proposed by applying numerical differentiation with the complex step derivative approximation (CSDA) method. Combined with the Neo-Hookean hyperelasticity model, the results from the example analysis applied to the tensile specimen model were examined to manifest the visco-hyperelastic characteristics of elastomers under cyclic loading, stability of the analysis, and further discussion on the visco-hyperelastic constitutive model were proposed.

Multiscale finite element analysis model of needle-punched carbon/carbon composites

The mechanical properties of matrix, fiber bundle, and chopped fiber felt are evaluated by means of micromechanical analysis. An equivalent matrix model composed of matrix and chopped fiber felt material is established, which together with fiber bundle is used as the basic component of single cell. Based on the mesostructural characteristics of NP C/C composites, the local structure is divided into five typical unit cells to characterize the five representative microstructures of NP C/C composites, and the mechanical properties of the five typical unit cells are calculated, respectively. According to the true distribution of needle holes, the five typical unit cells are arranged to form a representative volume element model of NP C/C composites. The Cai–Wu failure criterion is used to determine the failure of the five typical unit cells model, and the periodic boundary condition is applied to the tension and compression simulation of the NP C/C composites, the progressive damage law of the model is analyzed. The results show that the prediction of mechanical properties of the composites under unidirectional tensile load and unidirectional compression load are in good agreement with the experimental data.

UNDERSTANDING THE BIOMECHANICAL RESPONSE OF PROGRESSIVE THREAD DENTAL IMPLANTS USING MULTI-SCALE FINITE ELEMENT ANALYSIS

Implant osseointegration is an important factor dictating its long-term efficacy in situ. Along with various biological factors, it is greatly influenced by the mechanical stimulus at the peri-implant bone. The present study aims to understand the biomechanical response of progressive thread dental implants using multi-scale-based finite element analysis employing macro and micro models of bone. μ-CT images of a cadaveric human mandible of its premolar region were obtained, along with CT scan of the same region to generate computational models. Total of six dental implants were designed having regular and progressive thread depths. Three different stages of healing of the bone-implant assembly were simulated parametrically. The biomechanical environment at the peri-implant bone was analyzed considering the 'Mechanostat' hypothesis. The obtained results revealed that bone strain is significantly higher during the initial healing phase when the bone is weakest. During this phase, implant stress and its displacement in both buccolingual and coronoapical directions are also noticeably higher. Also, displacements of progressive thread implants were lower in all the healing phases as compared to the implants with constant thread depth. The observations of this μ FEA study highlights the clinical applicability of a progressive thread dental implant as it generates larger functional surface area, thus engages higher trabeculae and therefore is suitable for weaker bone conditions. Furthermore, by comparing the stress values at bone and implant between the two bone models, the CT-based model having inhomogeneous material was deemed suitable as an alternative to computationally expensive μ FEA.

Multiscale characterization and design of cellulose composites based on polymers with movable cross-links

To combine the conflicting properties of impact resistance, stiffness, and toughness, we focused on composite materials reinforced with cellulose nanofibers and polymers with movable cross-links using cyclic macromonomers and analyzed their mechanical properties through experiments and computational simulations. Based on the experimental foundation, the mechanical properties of cellulose nanofibers modified with citric acid and flexible crosslinked polymer composites using cyclodextrin were investigated. On the other hand, multi-scale finite element analysis simulation based on homogenization theory was employed to systematically clarify the effects of aspect ratio and content ratio of cellulose fibers by considering polymer blending and modification of molecular structure in the base material. For modification of the matrix polymers and the fiber morphologies, the elastic modulus of the cellulose composite was comprehensively organized by the fiber contribution based on strain energy. A design method for cellulose composites based on fiber contribution proportion was also developed. The design method was applied to a new cellulose composite with a different polymer of the matrix, and it was demonstrated that the elastic modulus can be predicted with an error of less than 10 %.

Fabrication, Evaluation, and Multiscale Simulation of Piezoelectric Composites Reinforced Using Unidirectional Carbon Fibers for Flexible Motion Sensors

AbstractPiezoelectric composite materials can convert mechanical energy into electrical energy, thus promoting battery‐free motion‐sensing systems. However, their substandard mechanical performance limits the capability of sensors developed using flexible piezoelectric materials. This study introduces a novel design strategy for preparing high‐strength flexible piezoelectric composite materials comprising unidirectional carbon fiber–reinforced potassium sodium niobate (K0.5Na0.5NbO3) nanoparticle–filled epoxy resin (UDCF/KNN–EP). The fibers significantly improve the Young's modulus of UDCF/KNN–EP along the fiber direction, which reaches 282.5 MPa. Moreover, the composite exhibits excellent stretchability and piezoelectric response () in the cross‐fiber direction under cyclic tensile loading. Multiscale finite element analysis is performed via simulation, which allows theoretical examination of the experimental results and the material's mechanical response mechanism. Finally, UDCF/KNN–EP is seamlessly incorporated into athletic gear and used to measure the impact caused by baseball catching and track footfall patterns. This study harnesses the superior strength of carbon fibers to enhance the durability and dependability of self‐powered sensors without compromising flexibility in specific directions.

Enhancement effect of two-tiered heterostructure in piezoelectric filler-dispersed polymer composites

The effect of two-tiered heterostructure was verified by computational simulations and prototype experiments as a new approach for improving the performance of piezoelectric (PE) filler-dispersed polymer materials. Multiscale finite element analysis (FEA) based on asymptotic homogenization theory was applied to systematically investigate the fundamental properties of 0–3 composites in the first level and the relationship between macroscopic piezoelectricity and connectivity of the constituent phases in the second level. Simulations indicated that macroscopic piezoelectricity can be improved by controlling the PE filler content of the constituent phases in the two-tiered heterostructure, and that the connectivity of the PE phases in the direction of the applied electric field can effectively enhancing piezoelectricity. Furthermore, the two-tiered heterostructure discovered by multiscale FEA was fabricated by the melt-casting, demonstrating a piezoelectricity improvement of approximately 480 %.

A simple machine learning-based framework for faster multi-scale simulations of path-independent materials at large strains

Coupled multi-scale finite element analyses have gained traction over the last years due to the increasing available computational resources. Nevertheless, in the pursuit of accurate results within a reasonable time frame, replacing these high-fidelity micromechanical simulations with reduced-order data-driven models has been explored recently by the modelling community. In this work, two classes of machine learning models are trained for a porous hyperelastic microstructure to predict (i) whether the microscopic equilibrium problem is likely to fail and (ii) the stress–strain response. The former may be used to identify critical macroscopic points where one may fall back to the high-fidelity analysis and possibly apply convergence bowl-widening techniques. For the latter, both a linear regression with polynomial features and artificial Neural Networks have been used, and the required stress–strain derivatives for solving the equilibrium problem have been derived analytically. A weight regularisation is introduced to stabilise the tangent operator and several strategies are discussed for imposing null stresses in undeformed configurations for both regression models. The regression techniques, here analysed exclusively in the context of porous hyperelastic materials, evidence very promising prospects to accelerate multi-scale analyses of solids under large deformation.

Multi-scale finite element analysis on the soft impact behavior of twill weave laminate

This work proposed an impact momentum flexibility (IMF) to precisely and concisely characterize the soft impact behavior of twill weave laminate based on multi-scale finite element analysis. A multi-scale finite element model taking into consideration the microstructure and properties of constituents is established for twill weave laminate. The equivalent properties of fiber tows and twill weave laminate are predicted by micro-scale model and meso-scale model, respectively. Then the soft impact behavior of the laminate is investigated by macro-scale model. The multi-scale model is validated on different scales by comparing the experimental and simulated results of quasi-static compression and soft impact. On this basis, the deformation and failure of the laminate under soft impact are analyzed. The soft impact response is categorized according to the damage morphology and impact velocity. Moreover, the IMF is proposed to depict the ability to resist soft impact deformation of the laminate, and can be further adopted to rank the soft impact property of different materials.

Multiscale finite element analysis of earthquake-induced damage on underground RC culverts: The role of reinforcing bar corrosion

This study conducted finite element (FE) analysis to investigate the effect of corrosion in the sidewall on the damage to underground reinforced concrete (RC) culverts under an earthquake. The rationality of the numerical model was validated through the analysis of quasi-static cyclic loading tests of corroded RC culverts. Based on the validated FE model, a nonlinear dynamic analysis of an underground RC culvert subjected to an earthquake was performed. Further, the global and local responses that were changed not only by the corrosion of the sidewall reinforcement, but also by shear reinforcement in the sidewall and magnitude of the earthquake were discussed comprehensively. The analysis results show that the global deformation of the underground RC culvert increases with a higher degree of corrosion of the sidewall reinforcement and that severe local shear crack damage can be concentrated on the concrete web when corrosion cracks exist. In addition, extremely serious damage was induced in the RC culvert when corrosion occurred in the sidewall without proper seismic provisions. Therefore, steel corrosion in an aging underground RC culvert with insufficient shear reinforcement should be closely monitored to prevent its collapse in the event of earthquakes.

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