Modeling Of Material Behavior Research Articles

Lateral ring compression test applied to a small caliber steel jacket: Identification of a constitutive model

The evolution of threats and scenarios requires continuous performance improvements of ballistic protections for armed forces. From a modeling point of view, it is necessary to use sufficiently precise material behavior models to accurately describe the phenomena observed during the impact of a projectile on a protective equipment. In this context, the goal of this paper is to characterize the behavior of a small caliber steel jacket by combining experimental and numerical approaches. The experimental method is based on the lateral compression of ring specimens directly machined from the thin and small ammunition. Various speeds and temperatures are considered in a quasi-static regime in order to reveal the strain rate and temperature dependencies of the tested material. The Finite Element Updating Method (FEMU) is used. Experimental results are coupled with an inverse optimization method and a finite element numerical model in order to determine the parameters of a constitutive model representative of the jacket material. Predictions of the present model are verified against experimental results and a parametric study as well as a discussion on the identified material parameters are proposed. The results indicate that the strain hardening parameter can be neglected and the behavior of the thin steel jacket can be described by a modeling without strain hardening sensitivity.

Anisotropic modeling of material behavior for additively manufactured parts made by material extrusion

Anisotropic modeling of material behavior for additively manufactured parts made by material extrusion

A data-based derivation of the internal stress in the discrete-continuum transition regime of dislocation based plasticity

Effectively homogenizing microstructure heterogeneity within the coarse-graining volume is a long-lasting challenge in crystal plasticity theories. In this paper, we propose a data-based homogenization method that utilizes discrete dislocation dynamic simulations to derive the nearfield correction stress (back stress) for continuum models. This stress accounts for the effective stress field induced by microstructure heterogeneity under the length scale of a coarse-graining volume, providing a physically based homogenization approach. To bridge the gap between discrete and continuous regimes, we introduce two versions of the nearfield correction stress, as well as a criterion based on microstructure and numerical parameters to determine the discrete and continuous transition. Moreover, by analyzing the mathematical connections with the work-conjugated gradient plasticity theory, we further provide a physical explanation for the observed material length scale in the thermodynamically consistent back stress term. This work presents a novel methodology for effectively addressing microstructure heterogeneity and advancing the understanding and modeling of material behavior bridging different length scales.

BARIK: an extended Hoek–Brown-based anisotropic constitutive model for fractured crystalline rock

Abstract. The disposal of heat-generating radioactive waste in deep geologic formations is a global concern. Numerical methods play a key role in understanding and assessing the disposal scenarios of radioactive waste in deep geological repositories. However, the complexities of the thermal, hydrological, mechanical, chemical, and biological processes associated with the disposal of radioactive waste in porous and fractured materials constitute significant challenges. One of the most challenging issues in this field is the complex material behavior of fractured crystalline rock. The presence of fractures makes the rock anisotropic, nonlinear, and dependent on loading paths. Additionally, the Biot coefficient cannot be considered constant throughout the critical and subcritical fracture development regions. These factors make the development of an accurate constitutive model for fractured crystalline hard rock a critical component of any deep geological disposal project. Furthermore, to demonstrate the integrity of the containment-providing rock zone in crystalline host rock, the qualitative integrity criteria must be quantified so that numerical simulation can be performed with concrete numerical values. Part of this assessment for a crystalline host rock is a dilatancy criterion, which is currently based on the Hoek–Brown constitutive model. BARIK is the German acronym for the research project on which this paper is based. This contribution provides an overview of the development and verification of the BARIK constitutive model, an extended Hoek–Brown model for fractured crystalline hard rock that takes into account up to three fracture systems. The model enables the consideration of the matrix and joint behavior of the rock separately, with each component having unique strength characteristics and failure criteria. These criteria are formulated such that suitable consideration of the strength-reducing properties of the respective fracture systems during barrier integrity verification is possible. The BARIK model has been implemented into two computer codes, FLAC3D and MFront for OpenGeoSys, allowing for the identification and evaluation of any inaccuracies that may arise from the use of different codes. The model enables isotropic–elastic, orthotropic–elastic, isotropic–elasto-plastic, and orthotropic–elasto-plastic calculations of the matrix, making it a valuable tool for the site selection process and for the construction and long-term safety of underground repositories. Furthermore, this poster presentation will show how the constitutive model was evaluated in relation to the dilatancy criterion and how the BARIK constitutive model's suitability for conducting an integrity assessment was validated. In conclusion, the development of BARIK is a significant step forward in the understanding and modeling of the complex material behavior of fractured crystalline hard rock. This contribution will provide insights into the development and verification of this model for the safe disposal of radioactive waste.

A new texture descriptor for data-driven constitutive modeling of anisotropic plasticity

Constitutive modeling of anisotropic plastic material behavior traditionally follows a deductive scheme, relying on empirical observations that are cast into analytic equations, the so-called phenomenological yield functions. Recently, data-driven constitutive modeling has emerged as an alternative to phenomenological models as it offers a more general way to describe the material behavior with no or fewer assumptions. In data-driven constitutive modeling, methods of statistical learning are applied to infer the yield function directly from a data set generated by experiments or numerical simulations. Currently these data sets solely consist of stresses and strains, considering the microstructure only implicitly. Similar to the phenomenological approach, this limits the generality of the inferred material model, as it is only valid for the specific material employed in the virtual or physical experiments. In this work, we present a new generic descriptor for crystallographic texture that allows an explicit consideration of the microstructure in data-driven constitutive modeling. This descriptor compromises between generality and complexity and is based on an approximately equidistant discretization of the orientation space. We prove its ability to capture the structure–property relationships between a variety of cubic–orthorhombic textures and their anisotropic plastic behavior expressed by the yield function Yld2004-18p. Three different machine learning models trained with the descriptor can predict yield loci as well as r-values of unseen microstructures with sufficient accuracy. The descriptor allows an explicit consideration of crystallographic texture, providing a pathway to microstructure-sensitive data-driven constitutive modeling.

The Study Influence Analysis of the Mathematical Model Choice for Describing Polymer Behavior.

The article considered the three types of description of the material behavior model: elastic, elastic-plastic, and viscoelastic. The problem is considered in the framework of deformable solid mechanics. The paper considers the possibility of describing modern polymeric and composite materials used as antifriction sliding layers in the viscoelasticity framework. A numerical procedure for finding the coefficients to describe the viscoelastic material behavior using the Prony model has been implemented. Numerical results and experimental data are compared. The model problem of spherical indenter penetration into polymer half-space is realized. The influence of the system discretization on the numerical solution is analyzed. The influence of the polymer behavior description in static and dynamic problem formulations is analyzed.

The effect analysis of the finite element approximation order on the protective polymer layer contact deformation

Problems implementation using the finite element method (FEM) is primarily associated with the proper selection of approximation order of the shape functions, material behavior models, the coupling nature analysis and the implementation techniques choice. The choice of numerical solution parameters affects the computational procedures. The paper solves problem of the FEM parameters selection and its realization methods in order to achieve a reasonable balance between the counting time and the solution quality. Simplex elements have shape functions with linear dependences on the coordinates. The FEM implementation with the use of simplex elements has proven itself during the last decades. However, one can note the description inaccuracy of curvilinear boundaries of research objects, which can introduce additional inaccuracies in the problem numerical solution. Second-order elements will allow describing curvilinear boundaries, but require a large expenditure of computational power especially for nonlinear mechanics problems. The development of numerical application software packages allows us to evaluate the influence of the FEM approximation degree on the problem solution with the use of grid methods and computer resources at the present time. The paper found that an increase in the numerical solution error is observed at the point of initial steel - polymer contact. The study considers the elements of order 1 and 2 to analyze the influence of the FEM approximation order on the problem numerical solution. The study is carried out within the framework of the classical Hertz problem. In addition the paper investigate obtained solutions for modeling different characters of contact surface coupling for the problem of contact between a spherical die and a steel half-space through a protective polymer coating 4 mm to 12 mm thick. The study reveal that the elements order has the least influence on the problem solution at ideal contact and the greatest one at frictional contact.

Three-dimensional simulation of granular materials by discrete element method (DEM) by considering the fracture effect of particles

Coarse-grained materials, such as sand and gravel, exhibit a significant dependence on particle failure rate, which greatly influences their engineering behavior. This research focuses on the three-dimensional modeling of grain material behavior using the discrete element method (DEM) with PFC3D software and FISH programming language. The specific objective is to model the particle breakage phenomenon and its impact on resistance behavior and deformation. To accurately represent the non-spherical shape of the particles, an interconnected sphere approach was employed. The modeling of grain failure was achieved by establishing a failure criterion that considers two critical conditions: the heterogeneity of contact forces and stress within the particle. The proposed model and criteria were validated through comparison with triaxial experimental results obtained from the Purulia dam gravel. The results demonstrate that the developed model successfully captures the essential aspects of particle failure and its influence on the behavior of the granular environment. The simulations accurately represent the resistance behavior and deformation characteristics observed in the triaxial experiments. This validates the effectiveness of the proposed model in simulating the significant effects of particle failure on the behavior of coarse-grained materials. The findings of this study contribute to a deeper understanding of the complex behavior of coarse-grained materials, particularly in terms of their response to particle failure. The developed DEM model, incorporating the particle breakage phenomenon, provides a valuable tool for accurately predicting and analyzing the behavior of granular materials in various engineering applications.

A microscale constitutive model for thin stainless steel sheets considering size effect

This research is focused on the modeling of the deformation behavior of thin austenitic stainless steel sheets to consider size effect in microscale. First, the material with two different thicknesses is heat treated to obtain different grain sizes, and then they are characterized by the uniaxial tensile tests. The experimental results show that flow stress decreases with the reduction of the sheet thickness and the increase of the grain size. The decline of the flow stress curve is associated with the decrease of the strength coefficient and increase of the hardening exponent as the plastic deformation is scaled down to the microscale. To better model the behavior of the material in the microscale, a new constitutive model is proposed based on the Swift equation to take into account the geometry and grain size effect. This model is also defined in the finite element model of the uniaxial tensile test. It is found that the flow stress curve predicted by the proposed constitutive model shifts down by the decrease of the number of grains across the thickness, which are consistent with the experimental results. In addition, the finite element model with the proposed constitutive model predicts accurately the deformation load in the uniaxial tensile tests. It can be concluded that the proposed constitutive model can provide a good description of the flow stress by considering the interactive effect of specimen and grain sizes and can be used in the modeling of material behavior in microforming processes.

Constitutive Modeling with Single and Dual Internal Variables.

Phenomenological constitutive models with internal variables have been applied for a wide range of material behavior. The developed models can be classified as related to the single internal variable formalism based on the thermodynamic approach by Coleman and Gurtin. The extension of this theory to so-called dual internal variables opens up new avenues for the constitutive modeling of macroscopic material behavior. This paper reveals the distinction between constitutive modeling with single and dual internal variables using examples of heat conduction in rigid solids, linear thermoelasticity, and viscous fluids. A thermodynamically consistent framework for treating internal variables with as little a priori knowledge as possible is presented. This framework is based on the exploitation of the Clausius-Duhem inequality. Since the considered internal variables are "observable but not controllable", only the Onsagerian procedure with the use of the extra entropy flux is appropriate for the derivation of evolution equations for internal variables. The key distinctions between single and dual internal variables are that the evolution equations are parabolic in the case of a single internal variable and hyperbolic if dual internal variables are employed.

Model-free damage prediction of brittle materials based on particle swarm optimization coupled with a probabilistic fission method

This study aims to develop a model-free damage prediction algorithm to predict directly local mesoscopic elasticity modulus and damage distribution of brittle materials based on only the monitored global structural response such as force–displacement curve, which can overcome complex theoretical modeling material behavior. The algorithm is established based on the modification of particle swarm optimization algorithm by establishing a probabilistic fission method, which can consider the physical mechanism that damage is correlatedpositivelywiththe stress level in the optimization process. A representative numerical example of a Brazilian disk test is implemented to verify the algorithm. The damage prediction result is compared with the result obtained from the traditional particle swarm optimization algorithm and the corresponding experimental result. As can be seen from the comparison results, the ability and effectiveness of the algorithm are supported. Furthermore, the effect of different divisions of representativevolumeelementsin the algorithm is analyzed to support the conclusion that fine division of representativevolumeelementscan obtain refined prediction results, but it can significantly increase the prediction error and computation time. The recommended size of representativevolumeelementis about 2 mm for the numerical case in this study.

Probabilistic impact fragility analysis of bridges under Barge collision and local scour

Vessel collision is a common cause of structural failure to bridges crossing navigable waterways. Although numerous efforts focus on the safety evaluation of bridge structures under vessel impact, very few jointly consider a more threatening situation that involves a scoured bridge colliding with a vessel (e.g., a barge). In this work, an impact fragility analysis (IFA) process is proposed to understand a bridge's failure probability under the combined hazards. To achieve high-fidelity modeling of material behavior during the collision process, scaled pier-foundation models subjected to pendulum impacts are experimentally studied. Nonlinear material models and an explicit dynamic simulation procedure are verified, which are further adopted to develop a high-resolution finite-element model for a full-scale three-span bridge. The resulting impact-fragility models conditional upon impact velocities at different scour depths reveal essential insights into the failure modes of the bridge. The findings include that: (1) scour has a minor effect on the probability of slight and moderate damage at various impact velocities; (2) at a high impact velocity (when higher than an impact fragility velocity threshold), scour can significantly increase the probability of major damage and collapse; (3) barge-tonnage has a significant influence on the threshold value reflecting the significant scour effects.

Modeling of welding residual stress in a dissimilar metal butt-welded joint between P92 ferritic steel and SUS304 austenitic stainless steel

In this study, a butt-welded joint between P92 ferritic steel and SUS304 austenitic stainless steel was fabricated with a nickel-based filler material. Based on Sysweld software, three-dimensional thermal-metallurgical-mechanical coupled finite element analyses were performed to investigate the hardness and welding residual stress in the welded joint. In the material behavior model, various factors influencing the formation and distribution of hardness and welding residual stress were carefully considered, including the austenitic transformation, martensitic transformation, and the tempering of martensite in P92 steel; the isotropic strain hardening, annealing effect, and melting effect of all materials; and the differential thermal expansion between dissimilar metals. The neutron diffraction method and hole-drilling strain gauge method were applied to measure the profiles of residual stress of the welded joint, respectively. Hardness mapping was performed on a weld cross-section specimen. The predicted results of welding residual stress and hardness are in good agreement with the measurements, respectively. The peak residual stresses in longitudinal and transverse directions are above 600 MPa in P92 steel. There are high tensile residual stress and significant cold work near the weld root in SUS304 stainless steel. The solid-state phase transformation induces compressive longitudinal residual stress in the heat-affected zone, high tensile transverse residual stress near the weld toe in P92 steel, and a significant stress gradient. The tempering effect can reduce the hardness and tensile residual stress in the heat-affected zone of P92 steel. The formation mechanism of welding-induced residual stress was illustrated based on the Satoh test. The effects of peak temperature, internal restraint, and differential thermal expansion are found to be decisive for the formation of residual stress. Large tensile residual stress can be generated with internal restraints, which promote the stress increase and lead to material yielding. A restraint factor was proposed for the quantitative assessment of stress evolution.

EXPERIMENTAL AND NUMERICAL STUDY OF THE INFLUENCE OF MANUFACTURING PARAMETERS ON THE INTERLAYER BEHAVIOR OF 3D PRINTING MATERIALS WITH AND WITHOUT REINFORCEMENT FIBERS

This work carries out an in-depth analysis of the influence of the manufacturing parameters on the behavior of a material with better mechanical properties than the usual ones, PLA and ABS, such as PETG (Polyethylene terephthalate with glycol), and the carbon fiber reinforced version. This study performs the experi-mental characterization on interlaminar fracture of this material, with the aim of acquiring a better knowledge of it, but also generates a model of material behavior that takes into account the effects on the properties of the printing profile, in other words, of the selected manufacturing parameters. In order to achieve such objective, a finite element numerical model has been developed, using cohesive elements to simulate the contact zones between layers. Also, failure and degradation modes of the material would be enclosed in the model behavior. A bilinear behavior model is used to simulate the response of the interlaminar zones. The properties of the model, as well as its subsequent adjustment, are supported from the results obtained in the experimental phase. As a final result of the work, the authors propose a series of graphs that allow the selection of these properties to be used in the model, depending on the manufacturing parameters selected for a future application. Keywords: FDM; PETG; DCB test; cohesive modeling

Modelagem computacional de vigas de concreto simples e reforçados com fibras de aço sem armadura transversal

Abstract Finite element analysis with nonlinear material behavior modeling can be used to design concrete structures. This study aimed to develop a computational model to represent the shear behavior of concrete beams without transverse reinforcement described in the literature, with or without steel fibers. Two different approaches of finite element analysis were investigated, namely smeared and discrete crack models. The results of the smeared crack model were compared with the results of double-notched push-through tests, and an empirical equation for the shear retention factor of plain concrete was suggested. The computational model using a discrete crack approach with representation of the aggregate interlocking mechanism was compared with the results of push-of test, and an accurate correlation was observed up to the maximum shear stress. It was concluded that the discrete crack approach provided the most accurate representation of the shear behavior of a non-reinforced beam with a shear span-to-depth ratio of 2.17. However, for a non-reinforced beam with a shear span-to-depth ratio of 2.66, the smeared crack approach accurately represents the shear strength and stiffness of the beam. The shear retention factor had little influence on the overall behavior of a steel fiber-reinforced concrete beam. Finally, it was concluded that a variable shear retention factor should be used in the smeared crack approach with fixed crack, as a constant shear retention factor tends to overestimate the shear strength of beams.

Dynamic photoelastic study of flexure hinges produced by additive manufacturing technology

There are many challenges in compliant mechanism redesign for additive manufacturing (AM) technologies, and in order to assess their applicability and propose adequate recommendations, the behavior of compliant elements has to be examined. Plastic materials are often used in AM technologies and are well suited for large volume compliant mechanisms due to their flexibility to strength ratio. However, they also have many disadvantages, notably a low fatigue strength and complex material behavior. Therefore, in this paper a photoelastic observations of corner-filleted flexure hinges manufactured from the transparent acrylic based photopolymer using the Digital Light Processing (DLP) AM technology subjected to the dynamic loading have been conducted in order to assess the fatigue strength and potentials of the photoelastic methods for the material behavior modeling. Three-point flexural tests on rectangular beam samples with the standardized dimensions printed in vertical and in horizontal orientation have been performed and the obtained data has been used for numerical simulations of corner-filleted flexure hinges. The specimens printed in different orientations exhibit significantly different anisotropic properties; the horizontally printed samples exhibit brittle behavior, while the samples printed vertically yields and consequently have much higher deformations, the calculated flexural moduli are also very different. Corner-filleted flexure hinges printed in vertical orientation and subjected to dynamic cantilever beam bending tests at relatively high stress amplitudes proved sufficient for the low dynamic compliant mechanisms applications. The qualitative photoelastic observations have shown that the photoelasticity is applicable in dynamic tests and useful in residual stress determination and stress concentration investigations.

The Numerical Simulation of Thermal Efficiency of Triple Pipe Heat Exchanger Using PCMs (Paraffin and Lauric Acid) System

COMSOL Multiphysics is used to adequately study the numerical modeling of phase change material behavior in a triple heat exchanger. The triple heat exchanger comprises three sides: an interior pipe for water cooling and heating, an annular space between the second and first interior pipes conveying Paraffin, and a third side annular space between the outer pipe and the second pipe holding Lauric acid. The dimensions of the triple heat exchanger are as follows: 30 cm length and side diameters of (0.5 in: 2.5 in: 3.5 in). Overall, the patterns reveal that the CFD and experimental work are in perfect agreement. PCM 2 is more reliable than paraffin. As the flow rate rises, the validity decreases; the maximum validation is obtained at 11 L/min. The results shows that the number of fins enhances efficiency by 5% (from 6 to 4); any number of fins over 6 promotes no more efficiency percentage. The additional fins are considered to produce increased heat transfer resistance, resulting in a significant increase in heat transmission. Copper slightly conducts heat better than aluminum and iron. Aluminum is the best material; its efficiency is equivalent to copper's. The diameter of the pipe has no effect on the percentage of paraffin efficiency. The better the heat resistance with an uniform heat transfer area between the paraffin and lauric acid layers, the broader the diameter of the lauric acid layer. Improving the outer diameter of the heat charge process implies increasing the efficiency percentage. The highest efficiency% is seen at 4.5 in.

Hardening soil model in prediction of plastic deformation zone in soft rock mass of Yakovlevo iron ore deposit

The authors propose a sizing procedure for the zone of plastic deformation (possible failure) in rock mass in the vicinity of stoping using the method of numerical modeling and the Hardening Soil Model (HSM). The relevance of HSM application in the conditions of Yakovlevo deposit is confirmed, among other things, by the dependence of the deformation modulus of rocks in the volumetric stress state on the effective stresses. The subject of research is the Yakovlevo deposit of high-grade iron ore, which holds the largest reserves in the Belgorod Region of the Kursk Magnetic Anomaly. Stoping and mine support operations induce continuous rock falls and caving because of the unreliable prediction of rock mass stability in the vicinity of stoping and due to the low strength of enclosing rock mass. Selection and validation of HSM parameters for iron–mica–martite ore of Yakovlevo deposit included processing of laboratory testing results obtained using equipment of the Saint-Petersburg Mining University. The triaxial tests of ore samples at different values of lateral pressure were computationally reduced to a reference abutment pressure value pref set by the software designer. The numerical experiments and virtual testing of the material behavior model, as well as the justification of the possible failure zone size were implemented in the certified software environment Bentley Systems PLAXIS-3D. Finally, on the basis of the integrated research of different-density ore samples, including laboratory tests and numerical experiments, the rock mass behavior models are constructed and the parameters of plastic deformation zones (possible failure) in the vicinity of a single stone are predicted.The study was supported under the state contract for scientific work in 2021, Grant No. FSRW-2020-0014.

Multi-scale modelling of deformation heterogeneities in explosively welded layered sheets

A multi-scale numerical investigation of local heterogeneities in the strain and stress fields occurring during forming of explosively welded layered metallic sheets is the main goal of the research. Explosive welding is a complex process involving various phenomena occurring in materials during an impact at high velocities and pressures, especially at the interfaces of colliding metals. As a result, the interface of the layered metallic sheets is often highly heterogeneous at the microscale level, what directly affects the sheet behaviour under subsequent forming conditions. To investigate this issue, the mesh-free numerical model of the explosive welding process is used first to recreate the characteristic features of the interface morphology. Various detonation velocities are used to provide diversified morphological features at the interface. Obtained results are then used as input data to develop the concurrent multi-scale finite element model of material behaviour under deformation conditions. The multi-scale modelling concept with explicit representation of the interface region is used. The highly refined heterogeneous FE mesh was generated in the interface region to capture local heterogeneities occurring at the microscale. Particular attention is put on numerical investigation of an influence of interface morphology in the welding zone on the development of the stress localisation that may directly lead to fracture initiation during forming.

Digital Image Correlation and Finite Element Computation to Reveal Mechanical Anisotropy in 3D Printing of Polymers

In this study, we propose to revisit the mechanical anisotropy inferred to printed ABS polymers using fused deposition modelling by combining digital image correlation (DIC), mechanical testing and finite element computation. Tensile specimens are printed using different design orientations and raster angles. Monitoring of deformed samples is performed, and strain fields are derived for each configuration. Finite element modelling of the 3D-printed material behaviour is considered to shed more light on deformation mechanisms. Experimental results show that a heterogeneous strain field develops, leading to more significant strain localisation for samples printed with the main dimension aligned with the building direction. The optimal printing angle allowing the filament to be crossed at -45°/+45° shows the best behaviour with even larger elongation at break compared to the raw material. However, digital image correlation based on optical imaging shows that a limiting scale exists for revealing the effect of filament orientation on strain localisation. Finite element results reveal the nature of the strain localisation as related presence of porosity close to the frame and the development of asymmetrical filling within the printed structure.