{"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}
Mirna Teresita Armendáriz Hernández , Alberto Díaz Díaz , Axel Fernando Domínguez Alvarado , Carlos Humberto Rubio Rascón
{"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}
Yifeng Chen , David A. Hills , John E. Huber , Lifeng Ma
{"title":"Analysis of a prismatic elastic contact of finite length","authors":"Yifeng Chen , David A. Hills , John E. Huber , Lifeng Ma","doi":"10.1016/j.euromechsol.2025.105609","DOIUrl":"10.1016/j.euromechsol.2025.105609","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105609"},"PeriodicalIF":4.4,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437489","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}
{"title":"Prediction of complex modulus for asphalt concrete based on micromechanics considering interaction among randomly oriented aggregates","authors":"Yadong Guo","doi":"10.1016/j.euromechsol.2025.105604","DOIUrl":"10.1016/j.euromechsol.2025.105604","url":null,"abstract":"<div><div>Complex modulus is one fundamental mechanical property of viscoelastic composites. In some existing methods on the prediction of complex modulus, inhomogeneities were usually assumed to be spherical and symmetric, and some complicated calculations were often performed to deal with the inverse Laplace transform. Most importantly, the effect of interaction among randomly oriented inhomogeneities on the complex modulus of composites has not been studied carefully. In this study, to address these challenges, aggregates in asphalt concrete are modeled as asymmetric ellipsoids. To account for the impact of aggregate interactions on the complex modulus, the orientation interaction model (OIM) is employed in conjunction with the elastic-viscoelastic correspondence principle. Based on OIM, the Laplace transform of the composite relaxation modulus is derived from the component characteristics. Then, according to the relationship between relaxation modulus and complex modulus for viscoelastic materials, the complex modulus of composites is obtained directly from the Laplace transform of the composite relaxation modulus, so the inverse Laplace transform is avoided. Model predictions agree well with test data, and it is found the aggregate geometry has a considerable influence on the composite property. The proposed model also captures the decrease of the composite dynamic Poisson's ratio with the increase of loading frequencies. The effects of component volume contents and the Poisson's ratio of the matrix on the composite dynamic modulus are analyzed, and model predictions are consistent with experimental observations.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"112 ","pages":"Article 105604"},"PeriodicalIF":4.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437490","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}
{"title":"Advanced finite element approaches for the 2D analysis of multilayered composite and sandwich beams","authors":"Matteo Sorrenti , Francesc Turon , Fermin Otero , Xavier Martinez , Marco Gherlone","doi":"10.1016/j.euromechsol.2025.105606","DOIUrl":"10.1016/j.euromechsol.2025.105606","url":null,"abstract":"<div><div>This work presents a new critical overview and a numerical assessment of some advanced Finite Element (FE) approaches for the analysis of multilayered composite and sandwich beams. Firstly, the fundamental hypotheses behind the Timoshenko Beam Theory (TBT) and the Refined Zigzag Theory (RZT) are addressed, and corresponding low-order simple and efficient <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> two-noded beam elements are recalled for 2D cylindrical bending problems. Additionally, two novel advanced FE techniques are employed for 2D bending analysis, i.e. the Multi-Scale (MS) analysis and the Beam-Like Reduced Order Model (BLROM). The proposed FE models are used to investigate the static cylindrical bending response of multilayered composite and sandwich beams under different boundary conditions. The results demonstrate the superior predictive capabilities of the RZT, MS and BLROM models compared to the TBT one. Furthermore, despite having the same kinematics as the TBT, the MS and BLROM models guarantee enhancements in axial strain and transverse shear stress distributions. In addition, the RZT confirms its superior accuracy in predicting both transverse displacements and strains across the laminate thickness. Depending on their accuracy, the RZT, MS and BLROM models are computationally more advantageous than other expensive high-fidelity FE approaches and excellent candidates for the 2D static analysis of multilayered beams.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105606"},"PeriodicalIF":4.4,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419871","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}
Saeedeh Qaderi , Michele Bacciocchi , Nicholas Fantuzzi
{"title":"C0 FEM approximation for the thermal buckling analysis of thin plates: Lagrange Multiplier and Penalty Methods","authors":"Saeedeh Qaderi , Michele Bacciocchi , Nicholas Fantuzzi","doi":"10.1016/j.euromechsol.2025.105605","DOIUrl":"10.1016/j.euromechsol.2025.105605","url":null,"abstract":"<div><div>A <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> FEM approximation for the thermal buckling of laminated thin plates employing the Lagrange Multiplier Method (LMM) and Penalty Method (PM) has been assessed. Such methods enforce internal constraints without requiring more complex formulations in a classical finite element implementation. Specifically, the thin plate assumption is applied in a first-order plate theory, eliminating the need for Hermite interpolation functions and complex meshing. Constraints are included in the formulation via energy functions. Applying the two methods enables the interpolation of displacement parameters using Lagrange shape functions with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> continuity. This approach simplifies implementation and enhances computational efficiency. In terms of model size, the Penalty Method (PM) does not introduce additional degrees of freedom (DOF). In contrast, the Lagrange Multiplier Method (LMM) increases the system’s DOF due to the inclusion of Lagrange multipliers. For the case of LMM, the regularization method has been utilized to solve the saddle point problem. A parametric study has been carried out for the critical buckling temperatures of laminated thin plates. To verify the effectiveness of the proposed method, results were compared with known analytical solutions and other conventional approaches, demonstrating strong agreement. Comparing the two methods shows that both LMM and PM simplify implementing numerical algorithms for optimal solutions in computational environments.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105605"},"PeriodicalIF":4.4,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419860","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}
{"title":"Static analysis of functionally graded and laminated composite beams using various higher-order shear deformation theories: A study with mixed finite element models","authors":"Abdullah Müsevitoğlu , Atilla Özütok , J.N. Reddy","doi":"10.1016/j.euromechsol.2025.105596","DOIUrl":"10.1016/j.euromechsol.2025.105596","url":null,"abstract":"<div><div>Technological advancements continuously increase the demand for advanced materials. Laminated composites and Functionally Graded Materials (FGMs) are preferred for their high strength and lightweight properties. This study examines the static behavior of laminated composite and functionally graded beams. The field equations are formulated using the principle of virtual displacements. A functional is derived using a generalized higher-order shear deformation theory that incorporates several existing beam theories as special cases. A mixed finite element model of this theory is developed, treating displacement, force, and moment as nodal degrees of freedom. Various beam problems with different thickness functions and boundary conditions are analyzed. A comparison of the present model’s numerical results with those in the literature shows that the present solutions for both laminated composite and functionally graded beams are accurate. Additionally, a detailed study of the stiffness coefficients of functionally graded beams is conducted.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105596"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429694","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}
Murat Akpınar , Uğur Kafkas , Büşra Uzun , Mustafa Özgür Yaylı
{"title":"On the torsional vibration of a porous nanorod with arbitrary boundary conditions considering nonlocal lam strain gradient theory","authors":"Murat Akpınar , Uğur Kafkas , Büşra Uzun , Mustafa Özgür Yaylı","doi":"10.1016/j.euromechsol.2025.105610","DOIUrl":"10.1016/j.euromechsol.2025.105610","url":null,"abstract":"<div><div>Porous materials are an important type of advanced materials due to their excellent properties, with one of the most notable being their lightweight nature. It is also important to accurately understand the mechanical response of nanorods, one of the components of nano-electro-mechanical systems. Therefore, a porous material is considered for the nanorod and elastic boundary conditions are considered, which presents a more realistic model. In order to provide a general eigenvalue solution based on these boundary conditions, an approach based on Fourier sine series and Stokes’ transform is considered. The main novelty of this eigenvalue solution, which calculates the torsional frequencies of the porous nanorod, lies in its ability to analyze both rigid and deformable boundary conditions. Although the analysis of other types of rods under arbitrary boundary conditions has been performed in the literature, the torsional vibration of porous nanorods based on nonlocal Lam strain gradient theory presented in this work is the first. To summarize the key findings of the study, it can be said that an increase in the nonlocal parameter and the porosity parameter which affects the shear modulus, cause a decrease in the torsional vibrations of the porous nanorod. On the other hand, an increase in the material length scale parameters, the spring stiffnesses at the ends and the porosity parameter, which causes the alters the mass density, results in an increase in the vibration frequencies.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105610"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429695","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}
Reijo Kouhia , Niels Saabye Ottosen , Matti Ristinmaa , Arturo Rubio Ruiz , Sami Holopainen , Timo Saksala
{"title":"Modelling of anisotropic high-cycle fatigue of metals","authors":"Reijo Kouhia , Niels Saabye Ottosen , Matti Ristinmaa , Arturo Rubio Ruiz , Sami Holopainen , Timo Saksala","doi":"10.1016/j.euromechsol.2025.105601","DOIUrl":"10.1016/j.euromechsol.2025.105601","url":null,"abstract":"<div><div>A continuum approach for anisotropic high-cycle fatigue modelling for metals is described. The approach is based on the idea of an endurance surface moving in the stress space where the movement is described by a back-stress tensor. The movement of the endurance surface is governed by an evolution equation. Thereby, the back stress tensor memorizes the load history so that fatigue damage accumulation can be easily calculated under arbitrary complex loading conditions without cycle counting techniques. Orthotropy and transverse isotropy are treated using the invariant theory. Anisotropic forms for both endurance function and evolution equations for the back stress and damage, are considered. It is also shown that for proportional loading and infinite life time this approach leads to generalizations of Sines criterion to orthotropy and transverse isotropy. Identification of the model parameters is carried out for metallic materials with the experimental results available in the literature.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105601"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419859","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}
Jian Li , Jia Chen , Yuxuan Liu , Wei Jiang , Qianhua Kan
{"title":"Constitutive modeling for the creep-ratcheting interaction of 0Cr18Ni10Ti stainless steel at high temperature","authors":"Jian Li , Jia Chen , Yuxuan Liu , Wei Jiang , Qianhua Kan","doi":"10.1016/j.euromechsol.2025.105602","DOIUrl":"10.1016/j.euromechsol.2025.105602","url":null,"abstract":"<div><div>The 0Cr18Ni10Ti stainless steel serves as a crucial component in the construction of reactor piping, which is subjected to complex cyclic loadings at high temperatures. Hence, undertaking both experimental observation and computational modeling to explore the cyclic deformation behavior of this material is of significant importance. Cyclic experimental investigations of 0Cr18Ni10Ti stainless steel with various holding waveforms and holding times were conducted at 623 K. The results reveal that the holding variables influence on the cyclic responses, presenting a creep-ratcheting interaction. A nonlinear static recovery factor is integrated into the kinematic hardening equation within a unified visco-plastic (UVP) framework to assess the effects of these holding variables on creep-ratcheting interaction. Additionally, a nonlinear static recovery factor associated with isotropic resistance is incorporated into the isotropic hardening equation to account for the stress relaxation during holding intervals. The derived results demonstrate that this modified UVP constitutive model can reasonably simulate the creep-ratcheting interaction of 0Cr18Ni10Ti stainless steel at 623 K. Particularly, it accurately captures the stress amplitude evolution observed during sustained peak strain and the ratcheting strain accumulation while maintaining peak stress. The proposed model provides a fundamental basis for evaluating the cyclic deformation responses of 0Cr18Ni10Ti stainless steel, as used within nuclear reactor environments.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"111 ","pages":"Article 105602"},"PeriodicalIF":4.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419858","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}