Plasticity Model Research Articles

An efficient nonlocal integral method based on the octree algorithm

The nonlocal integral method typically requires a very high computing cost to search neighborhood integration points for calculating the nonlocal variable, which limits its application in large-scale problems. This paper proposes an efficient nonlocal integral method based on the octree algorithm, in which the integration point information is stored in the tree data structure to accelerate the search task. Firstly, the fundamental principles and implementation details of using the octree algorithm to search neighborhood integration points are described in detail. Subsequently, a Mohr-Coulomb nonlocal damage plastic model is presented as the application object of the proposed method. The model is implemented further in the ABAQUS using the octree-based nonlocal method and the return mapping algorithm enhanced by a line search method. Finally, two typical boundary value problems are simulated to verify the effectiveness and to assess the computational efficiency of the proposed nonlocal method. For the given test environment, the octree algorithm can achieve up to 100 times speedup at the integration point level compared to the traversal algorithm, and the developed efficient nonlocal method can achieve up to 7.9 times speedup at the boundary value problem level compared to the original nonlocal method.

Corrected Method for Scaling the Structural Response Subjected to Blast Load

In scale-down tests of ship structures subjected to a blast load, the accuracy of the predicted response of a prototype is affected by the material substitution and geometric distortion between a scaled model and a full-size structure; this is known as incomplete similarity. To obtain a more accurate response from a prototype during small-size tests, a corrected method for scaling the response of thin plates and stiffened plates under a blast load was derived. In addition, based on numerical simulations of explosion responses by employing the elastic–plastic model and the Johnson–Cook constitutive model, it was found that using the average yield stress derived from the equivalent plastic strain energy in the ideal elastic–plastic model can obtain consistent structural responses. Moreover, a method for calculating the distortion factor caused by the yield stress of different materials was proposed. Furthermore, it was demonstrated that the average effective plastic strain between the prototype and the corrected model is equal, and based on this, a similarity prediction method was established to correct the distortions caused by yield stress and the thickness of blast loaded plates. The results indicate that the proposed correction method can compensate for the differences caused by distorted factors of yield stress and thickness, with the maximum error in the structure’s peak displacement being less than 3%.

From process to property: multi-physics modeling of dislocation dynamics and microscale damage in metal additive manufacturing

AbstractMetal additive manufacturing (AM) has the potential to tailor the mechanical performance of materials. Due to the complex thermal history and unique microstructure, AM materials are reported to contain distinct dislocation networks with a high dislocation density, which affect the plastic deformation behavior and fracture. However, it is challenging to experimentally observe the formation of such dislocation structures. In this work, a multi-scale multi-physics crystal plasticity modeling framework that integrates the process-structure-property relationship in metal AM is developed. The temperature field obtained from thermal-fluid flow simulations of the AM process and the microstructure from the phase field model of grain growth are combined into thermo-mechanical crystal plasticity simulations to obtain grain-scale thermal stresses. These stresses are used as input to simulate the evolution of dislocation structures within individual grains. Taking AM 316L stainless steel as the material of interest, the effect of initial dislocation configuration on the slip plane and cross-slip mechanism on the dislocation structure formation are investigated. Furthermore, a phase field damage model is implemented to study the initiation of microscale damage and their relationship with dislocation structures, which is a main novelty of this work. This modeling framework provides comprehensive simulations of all aspects of metal AM and offers insights into the dislocation mechanisms and damage formation at microscale in AM materials, which could be used to guide the manipulation of the mechanical properties of AM materials.

Through-thickness Work Hardening Variation in Thick High Strength Steel Plates: A Novel Inverse Characterization Method

Due to the production process, thick high strength steel plates potentially exhibit inhomogeneous plastic material behavior through the thickness. For example, the initial yield stress and work hardening behavior might vary through the plate thickness. In order to establish a reliable plasticity model that can be used in finite element simulations to optimize forming processes or to investigate the structural integrity of large structures, this material behavior needs to be characterized. A straightforward characterization method consists of slicing the thick high strength steel plate and conducting standard tensile tests. However, this approach comes with a large experimental effort. A novel specimen is proposed enabling to inversely identify the work hardening behavior at distinct locations through the thickness of a thick steel plate. To this end, a tensile specimen with circular pockets at different depths is used. The strain fields within the pockets are captured using digital image correlation (DIC). finite element model updating (FEMU) is used to inversely identify a predefined strain hardening law for each pocket. First, the procedure is optimized and numerically verified using virtual experiments generated by a finite element model with a known variation of the work hardening behavior. Finally, the procedure is experimentally validated by characterizing the strain hardening behavior of a 10 mm thick S690QL grade.

Implementation of the Zienkiewicz–Pande Model into a Four‐Dimensional Lattice Spring Model for Plasticity and Fracture

ABSTRACTPlasticity and fracture problems have always been hot topics in numerical methods. In this work, a universal implementation procedure for the elasto‐plastic constitutive model is developed in the four‐dimensional lattice spring model (4D‐LSM), in which the Jaumann stress rate is incorporated to exclude the influence of the rigid rotation in the particle stress, expanding the ability of 4D‐LSM to deal with large elastic deformation problems by its own to large plastic deformation problems. As an example, the Zienkiewicz–Pande (ZP) constitutive model is implemented. Several numerical examples are carried out to check the performance of the implemented model. Through a comparison with analytical solutions, available experimental data, and other numerical results, the stability of the developed plastic framework and the correctness of the stress calculation scheme are verified. Meanwhile, numerical results show that the developed code is capable of solving elasto‐plastic large deformation problems. With the advantage of 4D‐LSM in handling fracture problems, the ability of the embedded model to solve plastic fracture problems is verified with a simple maximum deformation failure criterion.

Modeling the elastic–plastic contact forces and deformations of nonrotationally symmetric lunar dust particles

The sharp morphological features of lunar dust particles generate significant elastic–plastic contact forces and deformations upon contact with material surfaces, which considerably affect the mechanical properties of lunar dust particles, including their contact, collision, adhesion, transport, and wear characteristics. Despite these severe effects, valid models considering the contact characteristics of typical sharp-featured lunar dust particles are currently lacking. This study proposes an elastic–plastic contact model for nonrotationally symmetric lunar dust particles showing typical sharp features. Detailed derivations of the expressions for various physical responses observed when lunar dust particles establish normal contacts with elastic and elastic–plastic half-spaces under adhesive conditions are also provided. These include derivations for elastic forces, elastic–plastic forces, contact areas, pull-off forces, residual displacements, and plastic deformation areas. Furthermore, the tangential pull-off force during the tangential loading of lunar dust particles is derived, and the tangential contact characteristics are explored. Comparisons of the results of the proposed model with those of previous experiments reveal that the proposed model shows errors of only 6.06 % and 1.03 % in the maximum indentation depth and residual displacement, respectively. These errors are substantially lower than those of conventional spherical models (60.30 % and 60.13 %, respectively), confirming the superior accuracy of the proposed model. Furthermore, the discrete element method is employed to analyze the effects of normal and tangential contacts, dynamic characteristics, and plastic deformations on the considered lunar dust particles. The results are then compared with those of existing contact models. They reveal that maximum elastic–plastic forces under normal contact conditions are positively correlated with the initial velocity but negatively correlated with the lateral angle. Furthermore, the tangential pull-off force is positively correlated with the normal force and surface energy. In addition, the contact duration of lunar dust particles is positively correlated with their initial velocities, while the residual displacement is negatively correlation. For instance, as the initial velocity increases from 10 to 50 m/s, the maximum elastic–plastic force increases from 37.64 to 321.72 mN. Comparisons of the proposed model with other contact models reveal that the maximum elastic–plastic force of the elastic–plastic triangular pyramid model is only 14.93 % that of the cylindrical model, 34.23 % that of the spherical model, and 76.27 % that of the conical model, indicating significant reductions in the maximum elastic–plastic force owing to the plastic deformations of particles with typical sharp features. Overall, the results of this study offer crucial insights into the mechanical characteristics of nonspherical lunar dust particles under various contact conditions, such as elastic–plastic and adhesive contacts, and can guide in situ resource utilization on the lunar surface and for craft landings.

On identifying dynamic length scales in crystal plasticity

Materials are often heterogeneous at various length scales, with variations in grain structure, defects, and composition which has a strong influence on the emergent macroscopic plastic behavior. In particular, heterogeneities lead to fluctuations in the plastic response in the form of jerky flow and ubiquitous strain bursts. One of the crucial aspects of plasticity modeling is scale bridging: In order to deliver physically correct crystal plasticity models, one needs to determine relevant microstructural length scales. In this paper we advance the idea that continuum descriptions of dislocation mediated plasticity cannot neglect dynamic correlations related to the avalanche behavior. We present an extensive weakest link analysis of crystal plasticity by means of three-dimensional discrete dislocation dynamics simulations with and without spherical precipitates. We investigate strain bursts and related length scales and conclude that while sufficiently strong obstacles to dislocation motion tend to confine the dislocation avalanches within well-defined sub-volumes, in pure dislocation systems the avalanches may span the system, implying that the dynamic length scale is, in fact, the size of the entire sample. Consequences of this finding on continuum modeling are thoroughly discussed.

Behaviour of AZ91 magnesium alloy in tension and torsion: experimental investigations and numerical modelling

Abstract This study is concerned with the evaluation of the most appropriate plasticity model for simulating the behaviour of the AZ91 magnesium alloy in terms of accuracy and analysis times, based on experimental data obtained from tensile and torsion tests. The material was supplied in ingot form, was subsequently cut using and automated saw and ISO 6892 round specimens were obtained through lathing. The test data was used to calibrate three hardening functions, namely the multi-linear hardening, Johnson-Cook power law hardening and the Ramberg Osgood plasticity model, with the former determining the best results.

Early developmental alterations of CA1 pyramidal cells in Dravet syndrome

Dravet Syndrome (DS) is most often caused by heterozygous loss-of-function mutations in the voltage-gated sodium channel gene SCN1A (Nav1.1), resulting in severe epilepsy and neurodevelopmental impairment thought to be cause by reduced interneuron excitability. However, recent studies in mouse models suggest that interneuron dysfunction alone does not completely explain all the cellular and network impairments seen in DS. Here, we investigated the development of the intrinsic, synaptic, and network properties of CA1 pyramidal cells in a DS model prior to the appearance of overt seizures. We report that CA1 pyramidal cell development is altered by heterozygous reduction of Scn1a, and propose that this is explained by a period of reduced intrinsic excitability in early postnatal life, during which Scn1a is normally expressed in hippocampal pyramidal cells. We also use a novel ex vivo model of homeostatic plasticity to show an instability in homeostatic response during DS epileptogenesis. This study provides evidence for the early effects of Scn1a haploinsufficiency in pyramidal cells in contributing to the pathophysiology of DS.

Concurrent experimental testing and computational micromechanical modeling of a UD NCF GFRP composite ply

The current research work presents a detailed and thoroughly validated computational micromechanical modeling methodology to study the damage initiation and propagation in a uni-directional (UD) glass fiber-reinforced non-crimp fabric (NCF) composite ply. Under the applied transverse tension and compression loads, the effect of various microscale material and geometrical parameters on the ply level stress–strain behavior is studied. To this end, along with the distinctly modeled individual microscale constituents of the UD NCF composite ply (axial fibers, backing fibers, and matrix), the generated RVE (Representative Volume Element) model consists of manufacturing-induced defects and variabilities such as voids as well as the backing fiber’s out-of-plane waviness. The fiber/matrix interface failure behavior in the generated RVE model is simulated using cohesive zone formulations that follow bi-linear traction-separation law. Whereas the hydrostatic pressure-dependent non-linear stress–strain response followed by the fracture of the epoxy matrix is captured using the linear Drucker-Prager plasticity model coupled with the stress triaxiality-based failure criterion. The backing fibers stress–strain and failure behavior is modeled using the linear elastic and isotropic material model in conjunction with the maximum stress criterion.The proposed numerical methodology is thoroughly validated both qualitatively and quantitatively by conducting detailed experiments on a neat epoxy as well as at the composites laminate level. Upon comparing the experimental and computational results, the observed knee or slope change in the bi-linear stress–strain response of the UD NCF composite ply under transverse tension is attributed to the loss of the load-carrying ability of the axial fiber bundle due to fiber/matrix interface debonding followed by the ply splitting. Under the application of transverse compression load, the composite ply failure behavior is governed by the formation of a dominant matrix plastic shear band in the axial fiber bundles, which is in turn triggered by the fiber/matrix interface failure. Under the applied loads in the matrix-dominated direction, the presented research work provides a detailed insight into the microscale damage initiation and propagation in a UD NCF composite ply and its consequent influence on the macroscale stress–strain response.

Predictive mechanical property and fracture behavior in high-carbon steel containing high-density carbides via artificial RVE modeling

The mechanical properties and fracture behavior of high-carbon steel are closely related to the microstructural characteristics. This work developed the artificial representative volume element (RVE) model to explore the effects of microstructural characteristics on mechanical properties and fracture behavior of high-carbon steel containing high-density carbides under uniaxial tension. A series of RVEs with different ferrite grain sizes, particle volume fractions, and particle sizes were generated based on the RSA algorithms. The mechanism-based plasticity model and the three uncoupled damage models were implemented into the RVE modeling. The model parameters were calibrated by the corresponding simulation between in-situ μ DIC and microstructure-based RVE simulation. The predicted mechanical properties and fracture strain from the RVE simulation were in good agreement with the experimental results. Simulated results from a series of RVEs quantified the effects of ferrite grain sizes, particle volume fractions, and particle sizes on strength, elongation, and damage evolution of high-carbon steel containing high-density carbides: strength increases with increasing particle volume fraction while elongation decreases, as well as excessively large or small grain and particle size were not favored to improve elongation. These results were attributed to the damage and internal stress partition.

A novel concurrent multiscale method based on the coupling of Direct FE2 and CPFEM

Performing concurrent simulations of macroscopic behaviors and microscopic structures using the crystal plasticity finite element method (CPFEM) presents a substantial difficulty with existing numerical techniques. To address this issue, a novel multi-scale method is proposed that couples CPFEM with a multiscale FEM, specifically Direct FE2. This facilitates the implementation of Direct CP-FE2 in this work. The micro representative volume elements (RVEs) equipped with a crystal plasticity constitutive model and the macro mesh are integrated into a monolithic solution scheme within the Direct FE2 framework. The proposed method integrates the multiscale simulation capability of Direct FE2 with the crystal plasticity model of CPFEM. Alpha titanium (α-Ti), which exhibits two distinct plastic mechanisms of slip and twinning, is chosen as the subject of investigation for conducting numerical experiments. The accuracy and efficiency of the Direct CP-FE2 model are evaluated through multiple plate tension and beam bending tests. The effective validation against the FEM model demonstrated the capability of Direct CP-FE2 to forecast macroscopic deformation behaviors. Meanwhile, the Direct CP-FE2 model can reveal the activation of slip/twinning systems and the evolution of crystal texture at a microscopic level. The influence of the grain orientation-dependent effect can be well considered into the macroscopic analysis with the help of Direct CP-FE2. Based on the testing examples, we demonstrate that the yield state of the macrostructure is enhanced when the crystal orientation is closer to the (0001) direction. Consequently, there exist very little crystal rotation behavior, hindering the evolution of the crystal texture.

Exploring the brittle-to-ductile transition and microstructural responses of [formula omitted]−TiAl alloy with a crystal plasticity model incorporating dislocation and twinning

γ−TiAl alloy, with its high specific strength and creep resistance, is ideal for aerospace engines and gas turbines, but its brittleness poses significant manufacturing and processing challenges. To address these issues, this study employs a crystal plasticity finite element method incorporating dislocation and twinning to analyze the brittle-to-ductile transition behavior of γ−TiAl alloy at different temperatures. Additionally, the Bayesian optimization methods are employed to efficiently and accurately obtain parameters related to numerical calculations of crystal plasticity. The results indicate that at room temperature, the high activation resistance of the slip systems in the α2 phase leads to limited slip activity, resulting in poor plasticity. However, at 750 °C and 850 °C, the strength of the slip systems decreases significantly, allowing more α2 phase lamellae in the γ-TiAl alloy to undergo greater plastic deformation. This enhancement in the plastic deformation capacity of the α2phase lamellae reduce the overall deformation incompatibility in the TiAl alloy, thereby improving the overall ductile of the γ-TiAl alloy.

3D strain heterogeneity and fracture studied by X-ray tomography and crystal plasticity in an aluminium alloy

Strong correlations between measured strain fields and crystal plasticity finite element (CP-FE) predictions based on the real microstructure are found for a plane strain tensile specimen made of 6016 T4 aluminium alloy. This is achieved using multimodal X-ray lab tomography giving access to both the initial grain structure and the strain evolution. The real microstructure of the central region of interest (ROI) of the undeformed specimen is obtained non destructively using lab-based diffraction contrast tomography (DCT) and meshing. An in situ tensile test, using absorption contrast tomography (ACT) is then performed for twelve loading increments up to fracture. Taking advantage of the plane strain condition, the evolution of the internal strain field is measured by two-dimensional digital image correlation (DIC) in the material bulk using the natural speckle provided by intermetallic particles. Early strain heterogeneities in the form of slanted bands, that are spatially stable over time, are revealed and the fracture path – determined from the post mortem scan – is found to coincide with the bands exhibiting maximum strain. CP-FE simulations are performed on the meshed microstructure of the specimen acquired by DCT and are compared with image correlation measurements. The measured strain fields are well described by 3D CP-FE predictions, whilst it is shown that neither a macroscopic anisotropic plasticity model nor a CP-FE simulation with random grain orientations could reproduce the measurements.

Investigation of the failure mechanisms of Zr alloy with Cr2AlC coatings using in-situ bending tests: Experiments and simulations

The failure mechanisms of Cr2AlC-coated zirconium samples under different mechanical loading conditions have been investigated by combining in-situ bending tests and finite element simulations. The results of interrupted in-situ bending tests reveal that new critical cracks are mainly initiated in the Cr2AlC coating layer, followed by subsequent propagation into the Zr substrate with increasing plastic deformation. The formation of new critical cracks in Cr2AlC material is described using the maximum principal stress criterion. A stress state-dependent damage mechanics model combined with an advanced plasticity model is used to capture the ductile fracture behavior of the Zr substrate. Finite element simulations have been performed to identify the failure properties of coating and substrate materials, leading to the accurate reproduction of experimental fracture behavior.

Mechanical and failure behaviors of adhesively bonded dissimilar materials joints incorporating bio-inspired morphological irregularities

Adhesive dissimilar material joints between stainless steel grade 316L and polyethylene terephthalate glycol (PETG) plastic were examined, in which irregular interface morphologies inspired by natural sutures were incorporated. The joint interfaces exhibited various teeth-like, non-repetitive zigzag patterns based on a pseudo-randomization method and sutural interdigitation index. Effects of their irregularities on mechanical and failure characteristics of adhesive butt joints were studied by means of experiments and FE simulations. The cohesive zone model, Drucker-Prager plasticity model and ductile failure criterion were applied for the interface and PETG, respectively. Predicted load-displacement curves of joints with different teeth profiles were well validated. The degree of irregularity became higher to 20%, 40%, and 60%, the joint strengths decreased by 1.47%, 5.39%, and 11.95%, while the total energies to failure increased by 110.74%, 129.33%, and 161.23%, accordingly. More inhomogeneous morphologies led to earlier local damage initiation, but enhanced damage evolution range by impeding abrupt joint separation. Smaller teeth angles provided higher joint strength, whereas significant declines of bonding strength were observed by too acute teeth angle due to excessive stress localization and resulting teeth breakage. The teeth angle of 45º enabled the superior joint performance owing to a proper combination of interlocking and large adhesive force under shear stress state. Finally, a key insight for designing an optimal dissimilar joint with morphological irregularities was provided.

Experimental and digital twinning in ZnAlMg coatings

Twinning is a major deformation mechanism in various materials, especially when few dislocation slip systems are operative. It is the case of zinc-rich coatings in galvanised steel sheets, made of pancake grains on a substrate and where the slip systems with a non-vanishing component along the c-axis present high critical resolved shear stress values. In addition, the abrupt lattice orientation change associated to twinning, the stress relaxation during its propagation and the localised nature of its early stages make it difficult to reproduce this deformation mechanism by using classical crystal plasticity models conceived for dislocation slip. In this sense, this work proposes a hierarchy of three twinning models in combination with a dislocation slip crystal plasticity model, for the case of a ZnAlMg coating. These three models are: a relaxed-Taylor model applied to individual crystal orientations of the coating, a “pseudo-slip” model for twinning and a localised twinning model. The latter incorporates a linear softening in the material law accounting for the unstable twinning initiation and enforces twinning lattice reorientation. A microstructure portion extracted from an in-situ SEM tensile experiment on galvanised steel is used to perform 3D full-field finite element simulations within a finite strain formulation. SEM observations and EBSD acquisitions are used to compare simulation and experimental results during the different steps of the in-situ SEM test, regarding the deformation and damage modes of the zinc-rich coating. The focus is set on twinning evolution inside some individual grains, and the pros and the cons of the three models are finally discussed.

A generalized, computationally versatile plasticity model framework - Part II: Theory and verification focusing on shear anisotropy

Shear-dominated deformation (SHDD) is pivotal in sheet metal forming; however, comprehensive modeling of plastic anisotropy in SHDD, specifically shear anisotropy considering both yield stress and plastic flow, has been inadequately addressed in existing literature. In this work, a generalized constitutive framework is introduced on the basis of stress triaxiality-dependent state variable to accurately emulate plastic anisotropy and the physics-based shear constraint in SHDD. The framework is capable to seamlessly integrate with existing yield criteria, preserving computational efficiency and versatility. Notably, the yield function, anisotropic parameters, and their optimization or analytical determination for the non-shear deformation state remain unaltered. When integrated with the Hill48 yield function, featuring either one or two anisotropic parameters within the generalized constitutive framework, precise characterization of yield strength and plastic flow in SHDD is achieved. The applicability of the framework extends to various anisotropic yield functions such as the widely employed Yld2k-2d and the sixth-order polynomial (Poly6) function as a class of associated flow rule-based yield functions, and one non-quadratic yield function for non-associated flow rule scenarios. Experimental validation with two engineering sheet metals, high-strength dual-phase steel DP980 and high-strength aluminum alloy AA7075-T6, was conducted. Comparative analyses with several recently proposed yield criteria, especially Poly6-18p, highlighted the efficiency of the proposed constitutive framework. Furthermore, this study explores intrinsic shear constraints, particularly the absence of through-thickness strains under in-plane shear stress. Additionally, it offers an enhanced description of plastic anisotropy in shear yield stress within the general framework, providing valuable insights into the complexities of SHDD.

Exploring the Dynamic Behavior of a Tapered Stenosed Artery: An Investigation into Its Unsteady Model

In this communication, blood flow is considered in a two-phase model of the tapered stenosed artery. Non-Newtonian and Newtonian models are considered in inner and outer regions, respectively. The transverse magnetic field is applied externally on the presumed pulsatile flow of blood to examine the nature of blood flow. It is anticipated that, in the inner region, blood follows the Jeffrey fluid model, and in the outer region, it follows the Bingham Plastic fluid model. The mathematical model of this system is formulated, a non-dimensionalization technique is used, and a numerical solution is obtained using the Finite difference method, one of the most suitable numerical methods for the formulated problem. The expressions for the primary/fundamental characteristics in determining the effect of blood flow are developed to explore the consequence of hematocrit, time component, tapering angle, and magnetic field. Scilab software is employed for mathematical simulations, revealing that flow characteristics within a stenosed artery undergo significant alterations, while the presence of a magnetic field aids in partially regulating the flow characteristics.

Comparison of the Torsional Strength of Material Samples Made Using Selected Rapid Prototyping Methods

In recent years, there has been a marked increase in the use of rapid prototyping techniques that support industrial processes. The analysis of studies on strength tests of parts manufactured using additive techniques from model materials and hybrid composites usually includes tests of material and strength parameters based on uniaxial tension, bending, and compression tests. For elements manufactured from polymeric materials using traditional methods (e.g. injection moulding), data obtained from these tests are sufficient to determine the strength of the material and to apply the results in the product design process. In the case of the layered extrusion method, due to the model construction process, strength data based on standard samples do not have a direct transposition on the strength of machine parts operating under various load ranges, especially torsional loads. The publication presents the results of tests on the torsional strength of cylindrical samples with splines produced by layered extrusion, vacuum casting technology, and hybrid technology, which combines both technologies. The test samples were made using a Prusa i3 MK3 3D printer and the plasticised plastic modelling (fused filament fabrication, FFF) method, while PolyJet technology was used to create a reference model. The findings indicate that hybrid technology, in which a thin-walled mould is filled with a chemically hardened polymer, achieves the desired strength for the manufactured parts while maintaining dimensional accuracy and shape. The research results show that producing rotating elements using the hybrid technology reduces the sample core’s ability to undergo plastic deformation due to the adhesion between the materials and the occurrence of notches resulting from the model production process using the layered extrusion method.