Macroscopic Simulation Research Articles

Mesoscopic homogenization method of mechanical properties of fused filament fabrication structures considering void shapes and filament interfaces

Abstract The Fused Filament Fabrication process (FFF) is an additive manufacturing process for thermoplastic polymers based on material extrusion. It offers a large range of material options and high potential for manufacturing parts with complex geometry. Mechanical properties of parts produced with this method are, however, highly anisotropic and depend on process parameters and resulting inner mesostructures. The relationships between process parameters, mesostructures and mechanical properties are complex. Characteristics of the FFF mesostructures, such as voids and the interfaces between filaments, cannot yet be sufficiently taken into account in macroscopic design methods. In this work, a method for homogenising mechanical properties is developed. This is based on the inner FFF mesostructure: shape and size of the voids are determined using micrographs and the size of the coalescence areas between the filaments is also estimated. Representative volume elements with periodic boundary conditions are then created in a finite element environment and homogenised mechanical properties are derived. These are compared with analytical and experimental values, and the results are discussed. The method presented here provides an approach on how different characteristics of FFF mesostructures can be transferred to macroscopic simulations. Results of the numerical approach are in good agreement with the experimental data.

Enhancing Mixed Traffic Flow with Platoon Control and Lane Management for Connected and Autonomous Vehicles

As autonomous driving technology advances, connected and autonomous vehicles (CAVs) will coexist with human-driven vehicles (HDVs) for an extended period. The deployment of CAVs will alter traffic flow characteristics, making it crucial to investigate their impacts on mixed traffic. This study develops a hybrid control framework that integrates a platoon control strategy based on the “catch-up” mechanism with lane management for CAVs. The impacts of the proposed hybrid control framework on mixed traffic flow are evaluated through a series of macroscopic simulations, focusing on fundamental diagrams, traffic oscillations, and safety. The results illustrate a notable increase in road capacity with the rising market penetration rate (MPR) of CAVs, with significant improvements under the hybrid control framework, particularly at high MPRs. Additionally, traffic oscillations are mitigated, reducing shockwave propagation and enhancing efficiency under the hybrid control framework. Four surrogate safety measures, namely time to collision (TTC), criticality index function (CIF), deceleration rate to avoid a crash (DRAC), and total exposure time (TET), are utilized to evaluate traffic safety. The results indicate that collision risk is significantly reduced at high MPRs. The findings of this study provide valuable insights into the deployment of CAVs, using control strategies to improve mixed traffic flow operations.

Synergy of chelating agents and surfactants on the wettability and pore structure of coal dust: Experimental study and molecular simulation

To reduce the hazards of coal dust pollution to miner health and the environment, and to realize efficient wetting and settling of coal dust, this paper evaluates the wettability of tetrasodium glutamate diacetate (GLDA)–aliphatic alcohol polyoxyethylene ether sodium sulfate (AES), hereafter termed G–A, by selecting the surfactant through macroscopic experiments and microscopic simulations. With the help of molecular simulation to study the synergistic mechanism of the surfactants and chelating agents, the functional group changes and mesoscopic modification of coal dust particles were evaluated in combination with characterization experiments. Comprehensive analysis showed that the G-A solution had the best wettability with a low surface tension of 22.77 mN/m, the diffusion rate of the solution increased to 1.25°/s, and the contact angle with the coal dust decreased to 18° within 12 s. After infiltration, the median particle size of coal dust reached 38.140 μm, which increased by 148 %. The pores and slits on the surface of the coal dust particles are further increased, providing surfactants with more extensive adsorption sites, and the proportion of hydrophilic groups on the surface of coal increased by 8.42 %, with the consequent improvement of wettability. This study provides a theoretical basis for the research and development of more environmentally friendly and efficient dust reducing agents in the field of spray dust reduction.

Investigation of the history-dependent nonlinear micro-viscoplasticity behavior of dual-phase steel using crystal plasticity finite element method

During tensile loading–unloading cycles, steels composed of different phases may exhibit history-dependent nonlinear micro-viscoplasticity behavior. To analyze the mechanism of the evolution of the elastic behavior, in this study, loading–unloading experiments were conducted for dual-phase steels, comprising martensite and ferrite, with a thickness of 1.1 mm and a tensile strength of 980 MPa. To investigate the complex elastic behavior at the microscale, a 3D representative volume element modeling the steel microstructure was generated and the elastic response was examined using the rate-dependent crystal plasticity finite element method. The differences of the plastic deformation in the ferritic and martensitic phases were analyzed. To describe the history-dependent nonlinear micro-viscoplasticity behavior for macroscopic simulations, a micro-viscoplasticity model was developed. The developed material model successfully captured the repeated loading–unloading behavior of DP980 steel.

Morphological characteristics of low-asphalt RAP and influence of its reaction product during combustion heating on regenerated asphalt

To provide reference for regeneration of the finely separated low-asphalt reclaimed asphalt pavement (RAP), the macroscopic and microscopic laboratory testing and quantum chemical simulation were combined. The morphological characteristics of the basalt and limestone low-asphalt RAP were analyzed. The low-asphalt RAP needs to be dried before regeneration, so the reaction mechanism and product of the asphalt film on its surface during drying were clarified. The product influence on the temperature resistance and fatigue performance of the virgin asphalt was studied, so as to consider their mixing during the subsequent regeneration process. Result shows that the gradation of limestone low-asphalt RAP is coarser and particles are slenderer than basalt with the same particle size grade. The 5–10 mm low-asphalt RAP particles are slenderer than those in the 10–20 mm grade. In the drying cylinder, asphalt basically generate no new functional groups below 200℃, while the asphalt film on the low-asphalt RAP surface undergoes pyrolysis to produce carbon black with the particle size around 100μm in the combustion heating area. The most easily oxidation or pyrolysis site in asphalt molecule is the carbon atom connected to the benzene ring. The pyrolysis of asphalt molecules to generate free radicals in the local oxygen deficient environment is the prerequisite for the carbon black formation, and pyrolysis requires higher temperature than oxidation because of its higher energy barrier. As the carbon black content increases, the penetration and ductility of asphalt decrease, the softening point increases, the high-temperature performance is enhanced, the low-temperature performance is weakened, and the fatigue performance is not significantly affected. As the particle size of carbon black increases, the decrease range in penetration, ductility and low-temperature performance of asphalt declines, the increase or improvement range of softening point and high-temperature performance enhanced, while the fatigue performance still shows no significant and regular change.

Machine Learning Aided Modeling of Granular Materials: A Review

AbstractArtificial intelligence (AI) has become a buzzy word since Google’s AlphaGo beat a world champion in 2017. In the past five years, machine learning as a subset of the broader category of AI has obtained considerable attention in the research community of granular materials. This work offers a detailed review of the recent advances in machine learning-aided studies of granular materials from the particle-particle interaction at the grain level to the macroscopic simulations of granular flow. This work will start with the application of machine learning in the microscopic particle-particle interaction and associated contact models. Then, different neural networks for learning the constitutive behaviour of granular materials will be reviewed and compared. Finally, the macroscopic simulations of practical engineering or boundary value problems based on the combination of neural networks and numerical methods are discussed. We hope readers will have a clear idea of the development of machine learning-aided modelling of granular materials via this comprehensive review work.

Study on viscoelastic properties and rheological properties of SBS modified asphalt for road use with service life

SBS modified asphalt is an important material in the construction of high-grade highway, and its performance changes directly affect the pavement performance. In this study, SBS modified asphalt was extracted from the actual pavement with different service years, and the rheological properties of SBS modified asphalt with different service years were studied by macroscopic test and microscopic molecular dynamics simulation. The macroscopic test results show that the needle penetration value of SBS modified asphalt increases by 50.6 % after two years of service, and the viscosity of SBS modified asphalt increases by 54.8 % after 12 years of service. With the increase of service life, G∗ and G″ of SBS modified asphalt showed an increasing trend, and δ and G’’/G’ showed a decreasing trend. The molecular dynamics simulation results of SBS modified asphalt were consistent with the macroscopic experimental results. The rheological properties of SBS modified asphalt showed a decreasing trend with the service life, and the interfacial energies between SBS modified asphalt and aggregate also showed a decreasing trend. The research in this paper will provide a theoretical basis for the future study of the deterioration law of SBS modified asphalt and the formulation of road maintenance plan.

Micro-Macro Coupling Study on the Mechanical Properties of Continuous Fiber-Reinforced Composites.

As a key and weak point of continuous fiber-reinforced composites (CFRCs), the interface between the fiber and the matrix is vulnerable to failure under external loads, with its performance directly affecting the overall properties of CFRCs. Hence, a micro-macro coupling method that considered the microscopic properties of the interface was utilized to analyze and predict the mechanical properties of CFRCs more accurately. The microscopic mechanical parameters of the fiber-matrix interface, which were obtained using molecular dynamics, were transferred to the representative volume element (RVE). The stiffness matrix of the CFRC, required for the macroscopic finite element model, was then calculated using a unified periodic homogenization method based on the RVE and assigned to the finite element model for a macroscopic simulation. Nylon/continuous carbon fiber specimens were fabricated through additive manufacturing, with the tensile and bending strengths of the specimens obtained through tensile and three-point bending tests. The tensile strength of the experimental specimen was 200.1 MPa, while the result of the simulation containing the interface was 205.5 MPa, indicating a difference of less than 5% between the two. In contrast, the result of the simulation without an interface was 317.7 MPa, representing a high error of 58.7% compared with the experimental results. Moreover, the bending strength, Young's modulus, and flexural modulus results with and without an interface showed the same trend as that for the tensile strength. This illustrates the effectiveness of the proposed micro-macro coupling method for analyzing and predicting the mechanical properties of CFRCs.

Choice-based macroscopic lane-change prediction model for weaving areas

This paper introduces two macroscopic lane change models, separately for small vehicles (passenger cars and vans) as well as heavy vehicles. The model is structured using a Nested Logit discrete choice framework. The model was estimated and validated using unique trajectory data collected from a busy weaving section in Antwerp, Belgium. The models exhibit an average and maximum rate of inaccurate prediction results, amounting to 11% and 16%, respectively. Additionally, the model underestimates the total number of lane change maneuvers, with a margin of no more than 4.1–7.7%. This study aims to fill the gap in macroscopic lane change models, which mainly depend on theoretical underpinnings, by including empirical data from the analysis of more than 31,000 observed maneuvers. Furthermore, it differentiates among three maneuver intents, a unique alternative-specific discrete choice framework. This differentiation allows for the consideration of drivers’ systematic taste variations. In contrast to other models that utilize empirical datasets and are heavily dependent on expensive video-based data, including the entire traffic flow, this study introduces a novel approach for estimating the position and frequency of maneuvers by using just a small fraction (1–2%) of vehicle trajectories, supplemented by loop detector data, therefore eliminating the need for information from surrounding vehicles. Additionally, the work’s uniqueness is its validation methods extending beyond just numerical evaluations. The practical usability and usefulness of the model are shown in real-world traffic circumstances. Finally, the model is integrated in the context of a macroscopic simulation that represents a highly consistent lane balance based on the Scalable Quality Value statistics.

Integrating crystal plasticity and experimentation for investigating the size effect on the deformation characteristics of AISI304 microtubes manufactured by free bending technology

During the deformation process of micro-bending, the size effect resulting from the variation in the grain size of the microtubes is the primary factor affecting the bending behavior. The current study on free bending mainly focuses on using macroscopic finite element simulation and experimental analysis to investigate the factors affecting the bending radius and forming quality. However, due to the size effect, the practices and insights gained from macroscopic forming may not directly apply to microforming. Thus, this study aims to reveal and explain the reason for the increase in the bending radius of microtubes with decreasing grain size by combining experimental investigations with crystal plasticity finite element modeling (CPFEM). It was determined that the grain size is a crucial consideration in the micro-bending process of microtubes. Additionally, the CPFEM approach can provide guidance for the process parameters of free bending forming of microtubes.

Impact assessment of future fleet compositions in vehicle emissions in urban areas: A methodological framework and a case study

This study explores the impact of emerging vehicle technologies on direct urban traffic emissions. It investigates emission reduction potential from shifts in fleet compositions and modal choices, especially considering climate change. To achieve this, three key research areas are explored for historical, current, and future scenarios (up to 2050): mode choice, emission factors for different vehicle categories, and diverse vehicle propulsion technologies. The estimation of the modal split is pivotal, developing a methodology utilizing Stated Preference survey data, discrete choice modeling, Monte Carlo simulations, and macroscopic traffic simulations. Future scenarios derive from the reference year’s modal split, and emission factors and fleet compositions are predetermined via an extensive literature review, aiding the assessment of their respective emissions. A subsequent sensitivity analysis identifies the impact of specific parameters on emissions, guiding future research focus. Study results underscore differences in greenhouse gas emissions and primary air pollutants between base and future scenarios.

Numerical investigation of the oxy-fuel combustion in the fluidized bed using macroscopic model supported by CFD-DDPM

Oxy-fuel combustion (OFC) presents a promising strategy for reducing carbon emissions from coal combustion. Traditional multiphase flow models (MFM) used for OFC simulations face challenges in integration and optimization with systems like carbon capture and electrolysis. Constructing a cost-effective and versatile macroscopic model simulation is critical for the industrial application of OFC. This study employs CFD-DDPM to obtain fluid dynamics parameters and couples heat and mass transfer models to construct macroscopic model of OFC based on a fluidized bed. Through calculations of OFC using both the macroscopic model and CFD-DDPM, molar fractions of O2, CO2, NO, and SO2 under various combustion conditions were found consistent with experimental measurements. Predictions under Recirculated Flue Gas (RFG) conditions showed comparable O2 and CO2 molar fractions at 30 % O2 & RFG, with the macroscopic model achieving 10.3 % and 69.3 %, versus 6.9 % and 72 % in CFD-DDPM. This demonstrates the ability of a macroscopic model to predict the design of the OFC in the fluidized bed. Importantly, the computational time of the macroscopic model is over 99 % shorter than that of CFD-DDPM. Consequently, employing a rapid simulation based on the macroscopic model method enables efficient simulation of OFC systems and facilitates the integration of oxygen combustion systems with other technologies like electrolysis. This approach provides valuable guidance for the development and application of OFC technology.

Experimental and molecular simulation study on the influence of chain length and anion structure of ionic liquids on the wettability of highly hydrophobic bituminous coal

The wettability of bituminous coal is critical for the coal dust suppression and can be apparently modulated by ionic liquids. However, the modulation mechanism still remains elusive. Here, a combination of macroscopic experiments, mesoscopic characterization, and microscopic simulations (quantum mechanics and molecular dynamics) are leveraged to parse the effect on the wettability of coal dust surfaces of three novel ionic liquids ([C12MIm]Br, [BMIm]Br, [BMIm]Cl) featuring the varying chain lengths and anions in the coal-water system. The results show that the selected ionic liquids exert a distinct bridging function from traditional surfactants which invoke the hydrogen bonding interaction. This ionic liquids-mediated bridging mechanism heavily depends on their chain length structure, which can firstly penetrate deeply the internal pores of coal dusts and then adsorb on the coal surfaces to rapidly strike a dynamic equilibrium. Ionic liquids interacting with coal dust can primarily reduce the energy difference between polar and nonpolar interactions within coal dust, thereby enhancing the electrostatic interactions between coal dust and water molecules and effectively improving coal dust wetting properties. These findings provide a theoretical basis for the rational design of high-performance ionic liquids for coal mine dust control.

Simulation of microtextural evolution in omphacite: Ordering transformation kinetics as unexplored archives of slab eclogitization

Earth's subduction zone processes and surface environments are intricately governed by mass transfer phenomena at plate convergent boundaries. The determination of their rates and timings from high-pressure metamorphic rocks (e.g., eclogite), or remnants of ancient convergent boundaries, remains an ongoing challenge. Here, we proposed the potential and versatility of ordering transformation kinetics of omphacite, an essential mineral found in eclogite, as a dynamic recorder of the metamorphic history. Through macroscopic phase-field simulation, we explored the growth of antiphase domains (APDs) in metastable disordered omphacite, discussing the feasibility of constraining metamorphic reaction kinetics based on the size and morphology of omphacite APDs in eclogitized oceanic crust. Our simulation corroborated that omphacite nucleating later during the prograde metamorphism can exhibit an incompletely ordered state with sparsely distributed ordered domains, which suggests their usefulness in estimating the recrystallization timing of the omphacite. Additionally, we confirmed that the APD formation dynamics are significantly influenced by the initial cation configuration of the disordered matrix. This implies the APD morphology in natural omphacite under slab-surface conditions may reflect their precipitation kinetics. These findings provide valuable insights into the microtextural evolution of omphacite due to its ordering transformation, thereby enhancing our ability to interpret morphological features.

A hyperelastic approach for modeling the membrane behavior in finite element forming simulation of unidirectional non-crimp fabrics (UD-NCF)

Unidirectional non-crimp fabrics (UD-NCFs) are highly suitable for high-performance components due to their excellent lightweight potential. However, during forming they are prone to wrinkling and gapping compared to woven or biaxial textiles. Macroscopic simulation models can be used to efficiently predict these effects as well as the global forming behavior for complex geometries. Therefore, a new hyperelastic membrane model is proposed to describe the typical deformation of UD-NCFs based on superimposed shear, transverse tension and compression perpendicular to the fiber rovings. The model is parameterized using the forces and different ratios of superimposed strains obtained in experimental off-axis-tension-tests at bias angles of 30°, 45°and 60°. The resulting approach is validated by forming simulations of a hemisphere and tetrahedron geometry in different configurations and quantitative comparison to experimental tests. The model accurately predicts the forming behavior of UD-NCF with a good agreement of the global deformation behavior and local strains.

Machine Learning-Driven Calibration of Traffic Models Based on a Real-Time Video Analysis

Accurate traffic simulation models play a crucial role in developing intelligent transport systems that offer timely traffic information to users and efficient traffic management. However, calibrating these models to represent real-world traffic conditions accurately poses a significant challenge due to the dynamic nature of traffic flow and the limitations of traditional calibration methods. This article introduces a machine learning-based approach to calibrate macroscopic traffic simulation models using real-time traffic video stream data. The proposed method for creating and calibrating a traffic simulation model has significantly improved the statistical correspondence between the generated vehicle characteristics and real data about cars on the simulated road section. The correspondence has increased from 37% to 73%. Machine learning models trained on generated data and tested on real data show improved accuracy rates. Mean absolute error, mean square error, and mean absolute percentage error decreased by more than two orders of magnitude. The coefficient of determination has also increased, approaching 1. This method eliminates the need to deploy wireless sensor networks, which can reduce the cost of implementing intelligent transport systems.

The Microstructure characteristic and Its influence on the stray grains of Nickel-based single crystal superalloys prepared by Laser directed energy deposition

The microstructure adjustment and the stray grains inhibition are important for the preparation of Nickel-based single crystal (SX) superalloys by laser directed energy deposition (L-DED). In this work, the single channel monolayer and single channel five-layers DD6 SX superalloys have been prepared by L-DED. The macroscopic simulations in the deposition processing and multiscale characterizations of deposition structure were used to analyze the formation and evolution mechanisms of unique precipitations and stray grains. Results shows that the larger laser power and higher powder feed rate have a positive impact on the epitaxial growth of columnar dendrite and the elimination of stray grains. The residual stress caused by the complex thermal cycles is not the direct reason that induce the formation of SGs, but the rapid movement of dislocations result in the formation of sub-grain boundary. According to the columnar transition to equiaxed theory (CET), temperature field simulation and analysis of element segregation behaviors, the element segregation results in the unique microstructure, include petal-shaped γ/γ′ eutectic and demarcation band with a thickness of a single γ/γ′ eutectic. Besides, the geometric size of γ/γ′ eutectic decrease with respect to the deposition height. With the change of height at deposition region, dendritic orientation deviations affect the uniformity of element segregation, resulting in variations in γ′ phase and γ/γ′ eutectic dimensions between dendritic core and the inter-dendrite zone at the microscopic level and manifesting as grain boundaries at the mesoscale. At the same time, the formation mechanisms of carbide and adjacent γ/γ′ eutectic leads to the misorientations between the dendrite core and the inter-dendrite zone, which also appears as stray grains at the mesoscopic scale.

Indium-free nonmetal and Nb co-doped anatase TiO2 transparent conductive oxide materials for photovoltaic applications: From first-principles calculations to macroscopic simulation

Various researchers have attempted to design indium-free transparent conductive materials. This study first employed density functional theory combined with the Hubbard U parameter to predict the photoelectric properties of nonmetal (B, C, N, F, P, and S) and Nb co-doped anatase TiO2. The results indicate that Ti0.875Nb0.125O1.96875N0.03125, Ti0.9375Nb0.0625O1.96875F0.03125, Ti0.875Nb0.125O1.96875P0.03125 and Ti0.9375Nb0.0625O1.96875S0.03125 possess characteristics of n-type semiconductors with high transmittance, exceptional thermal stability and wide bandgap. Notably, Ti0.9375Nb0.0625O1.96875S0.03125 exhibits optimal electronic conductivity due to its lower effective mass and higher electron concentration. Then, we used the SCAPS-1D solar cell simulation software to simulate the macroscopic characteristics of the MASnI3-based perovskite solar cell with Ti0.9375Nb0.0625O1.96875S0.03125 transparent conductive oxide layer based on the microscopic properties computed at the density functional theory level. A maximum efficiency of 27.17 % is obtained by regulating the thickness, electron affinity, and defect density of Ti0.9375Nb0.0625O1.96875S0.03125 layer and the thickness of MASnI3 absorber layer. The findings highlight the tremendous potential of Ti0.9375Nb0.0625O1.96875S0.03125 as an indium-free transparent conductive oxide candidate material for photovoltaic applications.

Significance of fluid properties, pore structure, and surface chemistry in CMK series mesoporous carbon materials for N2/CH4/CO2 separation

We employed a combination of macroscopic approaches (Ideal Adsorption Solution Theory, IAST, and Two-Dimensional Equation of State, 2D-EOS) and microscopic molecular simulations to explore the adsorption and separation of N2, CH4, and CO2 in mesoporous materials CMK-1, CMK-3, and CMK-5. Our findings reveal that these behaviors are intricately linked to the material's structure, surface properties, and the adsorbed fluid type. For nonpolar N2/CH4 supercritical fluid, both macroscopic theories align remarkably well with molecular simulations. For gas mixtures with a supercritical gas (N2 or CH4) and a subcritical gas (CO2), the impact of material structure on adsorption and separation varies. While both adsorption theories perform well for CMK-3, with excellent agreement to simulations, only IAST accurately predicts CMK-1. This discrepancy indicates that 2D-EOS has a less satisfactory predictive accuracy for CMK-1 compared to CMK-3 due to structural differences. The hexagonal arrangement of nanorods in CMK-3 leads to a more uniform adsorption site, while CMK-1's diverse adsorption sites, including nanorod surfaces and inter-rod grooves, contribute to a more complex adsorption behavior. In CMK-5, a unique jump in the CO2 adsorption selectivity is observed, attributed to a phase transition within the pores. Interestingly, this transition-induced jump defies accurate prediction by common theoretical models, except for IAST, which correctly predicts trends in selectivity and adsorption amounts. This phenomenon is specific to CMK-5's dual-pore structure, where most CO2 adsorption occurs inside the pipes until saturation, followed by adsorption on the external surface. Examining the impact of –COOH and –OH functional groups on adsorption behavior, we find minimal influence on separation in nonpolar N2–CH4 fluid, independent of the material type. However, in CO2-containing systems, the –COOH functional group has a substantial impact, highlighting its significance in influencing adsorption behavior.

DLP printed 3D gyroid structure: Mechanical response at meso and macro scale

Rapid prototyping (RP) technology enables the fabrication of complex geometries, making lattice structures increasingly popular. Lattice structures, known as cellular materials, have garnered significant attention over the past two decades due to their ability to optimise mass distribution in components. These structures excel in mechanical properties, catering to energy absorption (bending-dominated structures) and structural performance (stretch-dominated structures). In this paper, we investigate the behaviour of stretch-dominated lattice structures using periodic surface models, specifically focusing on sheet-based Gyroid cells, to allow for a more efficient macroscale modelling. We study cells and scaffolds of different sizes, considering various triply periodic minimal surface thicknesses and relative densities ranging from approximately 0.2 to 0.65. We explore load applications in directions different from the unit cell's principal axes and analyse the strain rate effect on both bulk and cellular material. The lattice structures are manufactured using epoxy resin and digital light processing (DLP) technology. In the range of relative density investigated, both in quasi-static and dynamic conditions, a linear trend is observed for Young's modulus and compression yield strength. To extend the quasi-static results to the dynamic regime, we employ a more generalized normalization technique. This approach divides Young's modulus and compression yield strength by the behaviour of the base material at a specific strain rate, facilitating the correlation of mechanical properties across the two loading regimes. Based on experimental findings, we implemented and calibrated a bi-linear material model for describing, in macroscale, triply periodic minimal surface (TPMS) Gyroid structures. The model coefficients are parameterized with respect to relative density. In addition, the presented material law was compared with that proposed by Gibson-Ashby. Furthermore, we evaluated the anisotropy of both the base material and the unit cell. The first one is done by testing the 3D printed samples in directions different from the printing one, the latter by using the Zener factor. The anisotropy evaluation confirmed the isotropic behaviour of the unit cell within the range of relative density and test conditions investigated. Finally, we perform linear elastic 3D macroscopic and mesoscopic model simulations for combined shear-compression tests using the implemented bi-linear material model and the anisotropic stiffness matrix (obtained through the homogeneous formulation) for the macroscale, and the base material for the mesoscopic one. The results demonstrate the suitability of the proposed equivalent material model for studying the TPMS Gyroid structure in the elastic regime, both in quasi-static and dynamic states. This allows for an efficient FE modelling process of complex lattice structures.