Pub Date : 2025-02-25DOI: 10.1016/j.euromechsol.2025.105613
Michele Benzi , Daniele La Pegna , Paolo Maria Mariano
We consider the dynamics of bodies with ‘active’ microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the constitutive choices adopted for the microstructural actions associated with the considered phase field. The occurrence of non-normality requires to look at the pseudospectrum of the considered matrix, namely the set of all possible eigenvalues of matrices in a -neighborhood of the matrix itself, because the eigenvalues of non-normal matrices can be very sensitive to small perturbations and therefore the spectral analysis alone would not be sufficient to distinguish with certainty between stable and unstable behavior. We develop the relevant analyses in the case of quasicrystals for which the values of some constitutive parameters are not known or are uncertain from an experimental point of view, a circumstance suggesting parametric analyses. We find circumstances in which the pseudospectra obtained by means of the so-called structured perturbations predict instability when, instead, the spectral analysis indicates stability.
{"title":"Spectra and pseudospectra in the evaluation of material stability in phase field schemes","authors":"Michele Benzi , Daniele La Pegna , Paolo Maria Mariano","doi":"10.1016/j.euromechsol.2025.105613","DOIUrl":"10.1016/j.euromechsol.2025.105613","url":null,"abstract":"<div><div>We consider the dynamics of bodies with ‘active’ microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the constitutive choices adopted for the microstructural actions associated with the considered phase field. The occurrence of non-normality requires to look at the pseudospectrum of the considered matrix, namely the set of all possible eigenvalues of matrices in a <span><math><mi>ɛ</mi></math></span>-neighborhood of the matrix itself, because the eigenvalues of non-normal matrices can be very sensitive to small perturbations and therefore the spectral analysis alone would not be sufficient to distinguish with certainty between stable and unstable behavior. We develop the relevant analyses in the case of quasicrystals for which the values of some constitutive parameters are not known or are uncertain from an experimental point of view, a circumstance suggesting parametric analyses. We find circumstances in which the pseudospectra obtained by means of the so-called structured perturbations predict instability when, instead, the spectral analysis indicates stability.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105613"},"PeriodicalIF":4.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143518941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-25DOI: 10.1016/j.euromechsol.2025.105612
Anna Gorgogianni , Tanguy Ramanantsoavina , Chloé Arson
The representation of material microstructure in most existing analytical homogenization models is condensed into a set of well-known “classical” microstructure descriptors, such as the volume fraction and morphology of the individual phases of a composite. This study considers an enriched set of micro descriptors, containing both those “classical” descriptors as well as “non-classical” descriptors which quantify the spatial correlations of any two given micro material points inside a random heterogeneous material. We focus on 2D composites consisting of a matrix with embedded inhomogeneities (or inclusions) of random spatial arrangement. Both phases are treated as homogeneous, linearly elastic and isotropic. Starting from a rich database of reference microstructures, new datasets of perturbed microstructures are created, by inducing changes emulating the physical processes of inclusion nucleation and growth. All microstructures are characterized using the enriched set of micro descriptors, while their apparent stiffness tensor is computed numerically with the finite element (FE) method. A sensitivity analysis between the changes of the micro descriptors and corresponding changes of the apparent stiffness tensor reveals that the “non-classical” descriptors are consistently highly important to the macroscopic behavior. This suggests that enhanced homogenization models, made dependent on the identified pertinent “non-classical” micro descriptors, could be of higher predictive capability than existing approaches.
{"title":"Error propagation from microstructure changes to apparent stiffness in 2D biphase matrix-inclusion composites","authors":"Anna Gorgogianni , Tanguy Ramanantsoavina , Chloé Arson","doi":"10.1016/j.euromechsol.2025.105612","DOIUrl":"10.1016/j.euromechsol.2025.105612","url":null,"abstract":"<div><div>The representation of material microstructure in most existing analytical homogenization models is condensed into a set of well-known “classical” microstructure descriptors, such as the volume fraction and morphology of the individual phases of a composite. This study considers an enriched set of micro descriptors, containing both those “classical” descriptors as well as “non-classical” descriptors which quantify the spatial correlations of any two given micro material points inside a random heterogeneous material. We focus on 2D composites consisting of a matrix with embedded inhomogeneities (or inclusions) of random spatial arrangement. Both phases are treated as homogeneous, linearly elastic and isotropic. Starting from a rich database of reference microstructures, new datasets of perturbed microstructures are created, by inducing changes emulating the physical processes of inclusion nucleation and growth. All microstructures are characterized using the enriched set of micro descriptors, while their apparent stiffness tensor is computed numerically with the finite element (FE) method. A sensitivity analysis between the changes of the micro descriptors and corresponding changes of the apparent stiffness tensor reveals that the “non-classical” descriptors are consistently highly important to the macroscopic behavior. This suggests that enhanced homogenization models, made dependent on the identified pertinent “non-classical” micro descriptors, could be of higher predictive capability than existing approaches.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105612"},"PeriodicalIF":4.4,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Continuous damage models are increasingly used in numerical simulations to design structures, but their local formulations are sensitive to mesh size and present localization of strains in an infinitely thin region. To overcome these problems non-local damage models and related regularization methods, have been developed introducing a characteristic/internal length, thus avoiding pathological mesh dependence. Those methods make the damage evolution depends on the mechanical quantities at the current material point (local) and its neighborhood (non-local).
Existing approaches to calibrate the internal length use global quantities in the calibration process, although local data is now becoming accessible (e.g., using digital image correlation). In this study, we investigate the use of full-field displacement measurements an propose a new methodology for calibrating a non-local damage model based on local field measurements and we apply it to calibrate the Eikonal Non-local Gradient (ENL-G) approach from the measured strain and damage field. After detailing the calibration procedure, we then apply it on a simple ideal case. We illustrate, and analyze the robustness of the calibration procedure with respect to the choice of evolution law and measurement noise of the proposed calibration method. To confront the procedure to a more realistic case, we employed a 2D beam-particle model. This discrete model is first identified with respect to the size and shape effect based on one of the comprehensive experimental data sets available in the literature, including four shapes with three sizes each. Then, it is used to generate a “reference” evolution of the damage and strain fields in beams of different sizes subjected to uniaxial tension.
The parameters of the discrete model used have been calibrated to represent the scale and size effects, giving a very good representation of the experiments. We also illustrate the evolution of non-local interactions in the Eikonal approach using Green functions. Finally, the application of the calibration procedure shows that it is possible to determine the internal length of the non-local problem studied as well as the damage evolution law and its parameters. The outcomes of this study contribute to shed light on a new methodology to identify non-local damage models based on full-field measurements, and call for experimental size effect campaign with displacement field.
{"title":"Calibration of non-local damage models from full-field measurements: Application to discrete element fields","authors":"Louis Védrine , Flavien Loiseau , Cécile Oliver-Leblond , Rodrigue Desmorat","doi":"10.1016/j.euromechsol.2025.105611","DOIUrl":"10.1016/j.euromechsol.2025.105611","url":null,"abstract":"<div><div>Continuous damage models are increasingly used in numerical simulations to design structures, but their local formulations are sensitive to mesh size and present localization of strains in an infinitely thin region. To overcome these problems non-local damage models and related regularization methods, have been developed introducing a characteristic/internal length, thus avoiding pathological mesh dependence. Those methods make the damage evolution depends on the mechanical quantities at the current material point (local) and its neighborhood (non-local).</div><div>Existing approaches to calibrate the internal length use global quantities in the calibration process, although local data is now becoming accessible (<em>e.g.</em>, using digital image correlation). In this study, we investigate the use of full-field displacement measurements an propose a new methodology for calibrating a non-local damage model based on local field measurements and we apply it to calibrate the Eikonal Non-local Gradient (ENL-G) approach from the measured strain and damage field. After detailing the calibration procedure, we then apply it on a simple ideal case. We illustrate, and analyze the robustness of the calibration procedure with respect to the choice of evolution law and measurement noise of the proposed calibration method. To confront the procedure to a more realistic case, we employed a 2D beam-particle model. This discrete model is first identified with respect to the size and shape effect based on one of the comprehensive experimental data sets available in the literature, including four shapes with three sizes each. Then, it is used to generate a “reference” evolution of the damage and strain fields in beams of different sizes subjected to uniaxial tension.</div><div>The parameters of the discrete model used have been calibrated to represent the scale and size effects, giving a very good representation of the experiments. We also illustrate the evolution of non-local interactions in the Eikonal approach using Green functions. Finally, the application of the calibration procedure shows that it is possible to determine the internal length of the non-local problem studied as well as the damage evolution law and its parameters. The outcomes of this study contribute to shed light on a new methodology to identify non-local damage models based on full-field measurements, and call for experimental size effect campaign with displacement field.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105611"},"PeriodicalIF":4.4,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-20DOI: 10.1016/j.euromechsol.2025.105618
K.V. Spiliopoulos, I.A. Kapogiannis
{"title":"Corrigendum to ‘Fast and robust RSDM shakedown solutions of structures under cyclic variation of loads and imposed displacements’ [Eur. J. Mech. / A Solids 95 (2022) 1–19/104657]","authors":"K.V. Spiliopoulos, I.A. Kapogiannis","doi":"10.1016/j.euromechsol.2025.105618","DOIUrl":"10.1016/j.euromechsol.2025.105618","url":null,"abstract":"","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105618"},"PeriodicalIF":4.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-19DOI: 10.1016/j.euromechsol.2025.105615
B. Mandolesi, C. Iandiorio, V.G. Belardi, F. Vivio
Metamaterials are increasingly gaining attention due to their ability to exhibit exceptional properties through architectural design. Among these, spinodal topologies, inspired by minimal surface structures, represent a novel class derived from the spinodal decomposition process occurring in certain metal alloys. In metamaterials research, the spinodal decomposition process is typically approximated using statistical methods, such as the superposition of Gaussian random fields, which are only valid during the initial stages of the phenomenon. In this study, we advance the exploration of metamaterials inspired by spinodal decomposition by addressing the full nonlinear dynamic evolution governed by the Cahn-Hilliard partial differential equation (PDE). While solving this nonlinear PDE at the natural scales of spinodal decomposition usually demands ad hoc algorithms, our approach focuses on scales orders of magnitude larger—those relevant to the production of metamaterials. This scale adjustment allows us to employ a straightforward finite difference algorithm, which is computationally efficient and well-suited to the structural scales of interest. To design metamaterials with tailored elastic properties, we solve the Cahn-Hilliard equation in its dimensionless form, governed by two key dimensionless parameters. The solution fields generated are then transformed into CAD models via a dedicated algorithm, enabling subsequent finite element analysis (FEA) to extract the homogenized elastic properties of the resulting structures. Our analysis investigates how variations in the two dimensionless parameters influence the anisotropic elastic properties of the metamaterial unit-cell. By constructing response surfaces for these properties, we enable a reverse homogenization approach, allowing to design materials with targeted mechanical characteristics. This capability offering precise control over the elastic behavior of metamaterials, of interest in the field of material design. Finally, numerical and experimental validations demonstrate the accuracy of the proposed homogenization framework in predicting displacement fields, even for the complex topologies of spinodal decomposition-inspired metamaterial.
{"title":"Spinodal decomposition-inspired metamaterial: Tailored homogenized elastic properties via the dimensionless Cahn-Hilliard equation","authors":"B. Mandolesi, C. Iandiorio, V.G. Belardi, F. Vivio","doi":"10.1016/j.euromechsol.2025.105615","DOIUrl":"10.1016/j.euromechsol.2025.105615","url":null,"abstract":"<div><div>Metamaterials are increasingly gaining attention due to their ability to exhibit exceptional properties through architectural design. Among these, spinodal topologies, inspired by minimal surface structures, represent a novel class derived from the spinodal decomposition process occurring in certain metal alloys. In metamaterials research, the spinodal decomposition process is typically approximated using statistical methods, such as the superposition of Gaussian random fields, which are only valid during the initial stages of the phenomenon. In this study, we advance the exploration of metamaterials inspired by spinodal decomposition by addressing the full nonlinear dynamic evolution governed by the Cahn-Hilliard partial differential equation (PDE). While solving this nonlinear PDE at the natural scales of spinodal decomposition usually demands <em>ad hoc</em> algorithms, our approach focuses on scales orders of magnitude larger—those relevant to the production of metamaterials. This scale adjustment allows us to employ a straightforward finite difference algorithm, which is computationally efficient and well-suited to the structural scales of interest. To design metamaterials with tailored elastic properties, we solve the Cahn-Hilliard equation in its dimensionless form, governed by two key dimensionless parameters. The solution fields generated are then transformed into CAD models via a dedicated algorithm, enabling subsequent finite element analysis (FEA) to extract the homogenized elastic properties of the resulting structures. Our analysis investigates how variations in the two dimensionless parameters influence the anisotropic elastic properties of the metamaterial unit-cell. By constructing response surfaces for these properties, we enable a reverse homogenization approach, allowing to design materials with targeted mechanical characteristics. This capability offering precise control over the elastic behavior of metamaterials, of interest in the field of material design. Finally, numerical and experimental validations demonstrate the accuracy of the proposed homogenization framework in predicting displacement fields, even for the complex topologies of spinodal decomposition-inspired metamaterial.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105615"},"PeriodicalIF":4.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-18DOI: 10.1016/j.euromechsol.2025.105614
Oliver Jorg, Livio Baccelli, Gualtiero Fantoni
This paper introduces a novel two-phase gripper that exploits a flexible be-haviour during actuation and is rigid during grasping and handling. It uses form closure but keeps the footprint at the minimum, thus allowing complex insertions in limited spaces. The main advantages of the gripper are its capability of grasping fragile objects with different shapes, sizes and weights, its low footprint and simple architecture (low number of degrees of freedom), as well as the easy actuation. The gripper has been designed as the end effector of a robot for cores manipulation in casting moulds in steel industry. Indeed, in foundry the casting operation takes place pouring steel in a mould where fragile sand cores plugs are delicately and precisely placed. The gripper is based on a rigid flexible beam, that is flexible in one direction and becomes rigid in the opposite one, so it bends and curves with almost no force in a direction but behaves like a beam in the other one. When approaching it exploits the flexibility to wrap the core, then, thanks to an engagement and by exploiting the weight of the object, it acts as a rigid beam. The paper illustrates how the gripper is conceived and modelled, and a prototype developed, tested and evaluated. The prototype showed a very good adaptability to different object shapes and sizes.
{"title":"Exploiting flexi-rigid behaviour for complex insertion in limited spaces: Towards a flexi-gripper for heavy objects","authors":"Oliver Jorg, Livio Baccelli, Gualtiero Fantoni","doi":"10.1016/j.euromechsol.2025.105614","DOIUrl":"10.1016/j.euromechsol.2025.105614","url":null,"abstract":"<div><div>This paper introduces a novel two-phase gripper that exploits a flexible be-haviour during actuation and is rigid during grasping and handling. It uses form closure but keeps the footprint at the minimum, thus allowing complex insertions in limited spaces. The main advantages of the gripper are its capability of grasping fragile objects with different shapes, sizes and weights, its low footprint and simple architecture (low number of degrees of freedom), as well as the easy actuation. The gripper has been designed as the end effector of a robot for cores manipulation in casting moulds in steel industry. Indeed, in foundry the casting operation takes place pouring steel in a mould where fragile sand cores plugs are delicately and precisely placed. The gripper is based on a rigid flexible beam, that is flexible in one direction and becomes rigid in the opposite one, so it bends and curves with almost no force in a direction but behaves like a beam in the other one. When approaching it exploits the flexibility to wrap the core, then, thanks to an engagement and by exploiting the weight of the object, it acts as a rigid beam. The paper illustrates how the gripper is conceived and modelled, and a prototype developed, tested and evaluated. The prototype showed a very good adaptability to different object shapes and sizes.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105614"},"PeriodicalIF":4.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Compliant mechanisms are widely applied in fast-tool-servo machining and micro/nano-positioning devices. However, for multi-degree-of-freedom mechanisms, designing them is a multi-objective, multi-constraint problem where multiple factors need to be considered, such as large stroke, nanometer-level positioning accuracy, and static failure. Currently, traditional design methods may not be able to comprehensively address these factors. To solve these problems, this study proposes a topology optimization-based design method to develop a compliant mechanism with fully decoupled kinematics and two degrees of freedom, where a hexagonal element mesh with Wachspress shape functions is utilized. Besides, a coupling constraint formulation is designed to avoid the motion coupling in the input end and output end of the compliant mechanism and enhance positioning accuracy. Furthermore, a normalized p-norm stress method is used to restrict the compliant mechanism's maximum stress, which aims to prevent static failure and enhance its reliability. Finally, a dual-axial compliant mechanism with decoupled kinematics, as the numerical example, is designed by the proposed topology optimization method, and its performance specifications are verified by the finite element simulation, which demonstrates the effectiveness and superiority of the proposed topology optimization method on the design of the compliant mechanism.
{"title":"Hexagonal element-based topology optimization of dual-axial compliant mechanisms with decoupled kinematics","authors":"Dongpo Zhao , Haofeng Xu , Hanheng Du , Zhiwei Zhu","doi":"10.1016/j.euromechsol.2025.105617","DOIUrl":"10.1016/j.euromechsol.2025.105617","url":null,"abstract":"<div><div>Compliant mechanisms are widely applied in fast-tool-servo machining and micro/nano-positioning devices. However, for multi-degree-of-freedom mechanisms, designing them is a multi-objective, multi-constraint problem where multiple factors need to be considered, such as large stroke, nanometer-level positioning accuracy, and static failure. Currently, traditional design methods may not be able to comprehensively address these factors. To solve these problems, this study proposes a topology optimization-based design method to develop a compliant mechanism with fully decoupled kinematics and two degrees of freedom, where a hexagonal element mesh with Wachspress shape functions is utilized. Besides, a coupling constraint formulation is designed to avoid the motion coupling in the input end and output end of the compliant mechanism and enhance positioning accuracy. Furthermore, a normalized p-norm stress method is used to restrict the compliant mechanism's maximum stress, which aims to prevent static failure and enhance its reliability. Finally, a dual-axial compliant mechanism with decoupled kinematics, as the numerical example, is designed by the proposed topology optimization method, and its performance specifications are verified by the finite element simulation, which demonstrates the effectiveness and superiority of the proposed topology optimization method on the design of the compliant mechanism.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105617"},"PeriodicalIF":4.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The frontal crumple zone of a vehicle, particularly the crash box, plays a crucial role in absorbing impact energy during collisions to mitigate passenger injuries. This study presents a novel approach to improve vehicle crashworthiness by incorporating an Förstner Random Dots (FRD) cellular structure as a filler component within a conventional square-hollow tube crash box. The finite element model of the crash box is employed to investigate the crashworthiness performance using nonlinear explicit dynamics analysis via LS-DYNA. Additionally, the functionally graded thickness (FGT) technique is applied in the design of the Triply Periodic Minimal Surface (TPMS)-filled crash box to reduce the initial peak crash force (IPF). The TPMS-filled crash box demonstrates superior energy-absorbing capabilities compared to conventional designs. To achieve the highest crashworthiness with a lightweight design, multi-objective particle swarm optimization is utilized to determine the optimal grading exponents of the outer and filler structures. The optimization process aims to maximize specific energy absorption and mean crushing force simultaneously. Pareto fronts of non-dominated solutions are generated, and optimal solutions are identified using multi-criteria decision-making with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Results suggest an optimal crash box design featuring a thickness gradient along its height, with a thinner profile from top to middle to facilitate progressive deformation and thicker sections at the bottom to prevent buckling. The optimized FGT model significantly reduces the IPF and controls the deformation behavior of the crash box, leading to progressive failure, especially under oblique impact scenarios, compared to the uniform thickness model.
{"title":"Optimization of novel functionally graded FRD-filled crash box for enhanced crashworthiness","authors":"Sorrawit Lophisarn , Phittayut Bunsri , Pattaramon Jongpradist , Suphanut Kongwat","doi":"10.1016/j.euromechsol.2025.105616","DOIUrl":"10.1016/j.euromechsol.2025.105616","url":null,"abstract":"<div><div>The frontal crumple zone of a vehicle, particularly the crash box, plays a crucial role in absorbing impact energy during collisions to mitigate passenger injuries. This study presents a novel approach to improve vehicle crashworthiness by incorporating an Förstner Random Dots (FRD) cellular structure as a filler component within a conventional square-hollow tube crash box. The finite element model of the crash box is employed to investigate the crashworthiness performance using nonlinear explicit dynamics analysis via LS-DYNA. Additionally, the functionally graded thickness (FGT) technique is applied in the design of the Triply Periodic Minimal Surface (TPMS)-filled crash box to reduce the initial peak crash force (IPF). The TPMS-filled crash box demonstrates superior energy-absorbing capabilities compared to conventional designs. To achieve the highest crashworthiness with a lightweight design, multi-objective particle swarm optimization is utilized to determine the optimal grading exponents of the outer and filler structures. The optimization process aims to maximize specific energy absorption and mean crushing force simultaneously. Pareto fronts of non-dominated solutions are generated, and optimal solutions are identified using multi-criteria decision-making with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Results suggest an optimal crash box design featuring a thickness gradient along its height, with a thinner profile from top to middle to facilitate progressive deformation and thicker sections at the bottom to prevent buckling. The optimized FGT model significantly reduces the IPF and controls the deformation behavior of the crash box, leading to progressive failure, especially under oblique impact scenarios, compared to the uniform thickness model.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105616"},"PeriodicalIF":4.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1016/j.euromechsol.2025.105607
Mirna Teresita Armendáriz Hernández , Alberto Díaz Díaz , Axel Fernando Domínguez Alvarado , Carlos Humberto Rubio Rascón
This paper aims to develop the first stress approach model for elastodynamic problems of functionally graded plates. The new model is called SAM-FG7, and like many other plate models, it is an alternative to solid finite elements to avoid high computational cost calculations for thickness ratios ranging from moderately thick to thin. SAM-FG7 stress approximation is intended to improve the stress results of models based on a displacement approach; the approximation is also an enhancement of that of the static shell model SAM-FG applied to plates since it considers two additional generalized forces. In statics, the SAM-FG7 stress field verifies the 3D equilibrium conditions, and the generalized equations are obtained by using the minimum complementary energy principle. For dynamic problems, a consistent derivation of the generalized motion equations is obtained by applying the method proposed by Bouteiller et al. (2022). SAM-FG7 features seven generalized displacements, i.e., two more fields than SAM-FG. Its equations were implemented and solved in COMSOL Multiphysics 6.2 finite element software. To validate the model, eigenfrequencies and modal stresses for a family of square functionally graded plates are calculated and compared with those given by solid finite elements and other models found in the literature. In order to demonstrate the accuracy of the model in more complicated problems, perforated functionally graded plates with transversely isotropic materials are considered; free vibration and frequency response analyses are made. SAM-FG7 predictions accurately approximate solid finite element results.
{"title":"A stress approach model for elastodynamic problems of functionally graded plates","authors":"Mirna Teresita Armendáriz Hernández , Alberto Díaz Díaz , Axel Fernando Domínguez Alvarado , Carlos Humberto Rubio Rascón","doi":"10.1016/j.euromechsol.2025.105607","DOIUrl":"10.1016/j.euromechsol.2025.105607","url":null,"abstract":"<div><div>This paper aims to develop the first stress approach model for elastodynamic problems of functionally graded plates. The new model is called SAM-FG7, and like many other plate models, it is an alternative to solid finite elements to avoid high computational cost calculations for thickness ratios ranging from moderately thick to thin. SAM-FG7 stress approximation is intended to improve the stress results of models based on a displacement approach; the approximation is also an enhancement of that of the static shell model SAM-FG applied to plates since it considers two additional generalized forces. In statics, the SAM-FG7 stress field verifies the 3D equilibrium conditions, and the generalized equations are obtained by using the minimum complementary energy principle. For dynamic problems, a consistent derivation of the generalized motion equations is obtained by applying the method proposed by Bouteiller et al. (2022). SAM-FG7 features seven generalized displacements, i.e., two more fields than SAM-FG. Its equations were implemented and solved in COMSOL Multiphysics 6.2 finite element software. To validate the model, eigenfrequencies and modal stresses for a family of square functionally graded plates are calculated and compared with those given by solid finite elements and other models found in the literature. In order to demonstrate the accuracy of the model in more complicated problems, perforated functionally graded plates with transversely isotropic materials are considered; free vibration and frequency response analyses are made. SAM-FG7 predictions accurately approximate solid finite element results.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105607"},"PeriodicalIF":4.4,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-14DOI: 10.1016/j.euromechsol.2025.105609
Yifeng Chen , David A. Hills , John E. Huber , Lifeng Ma
This paper is concerned with a contact problem which is geometrically two dimensional, but of finite extent in a third dimension. Two different contact models (common edge contact and incomplete contact) are analyzed, using a finite element model to investigate the 3D end effects. The object is to take the 2D plane strain solution in each model as a reference, and to show how it must be modified to allow for the 3D finite extent contact problem with free end faces. It is shown that, for a sufficiently long prismatic contact, the in-plane stress distribution at the mid-plane matches the solution to the 2D plane strain problem. Additionally, the end effect is evaluated using the finite element results to show how it decays with distance from the free end. The decay is exponential and governed by a dominant length-scale of the problem. For a common edge contact, this length-scale is the contact width. However, for a Hertzian contact, the contact width varies in the third dimension and the governing length scale is the radius of curvature, typically much larger than the contact width.
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