Extreme Mechanics Letters最新文献

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Orientation-dependent deformation and failure of micropillar shape memory ceramics: A 3D phase-field study 微柱形状记忆陶瓷的定向变形和失效:三维相场研究
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-11 DOI: 10.1016/j.eml.2024.102245
Amirreza Lotfolahpour, Mohsen Asle Zaeem
{"title":"Orientation-dependent deformation and failure of micropillar shape memory ceramics: A 3D phase-field study","authors":"Amirreza Lotfolahpour,&nbsp;Mohsen Asle Zaeem","doi":"10.1016/j.eml.2024.102245","DOIUrl":"10.1016/j.eml.2024.102245","url":null,"abstract":"<div><div>Some microscopic samples of zirconia-based shape memory ceramics (SMCs) have shown full martensitic phase transformation (MPT) over multiple loading cycles without cracking. However, the occurrence of MPT is strongly influenced by grain orientation. Depending on the specific grain orientation relative to the loading direction, alternative mechanisms such as plastic slip and fracture may emerge. This study introduces a phase-field (PF) based framework that integrates a PF-MPT model, a PF fracture model, and a crystal viscoplasticity model to investigate the effects of grain orientation on MPT, plastic slip, and fracture mechanisms in SMC micropillars. Single crystal micropillars are created to distinguish the orientations that facilitate each mechanism. A wide range of grain orientations are found to predominantly exhibit MPT. Micropillars with grain orientations close to the (100) and (001) directions primarily experience fracture, with minimal plastic slip. Additionally, samples oriented along the (110) direction show a significant amount of plastic slip. A pole figure is constructed to elucidate the interplay between MPT, cracking, and plastic slip under compressive loading conditions. This research provides valuable insights into the intricate behavior of SMCs under different loading scenarios, crucial for optimizing their performance in practical applications.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"73 ","pages":"Article 102245"},"PeriodicalIF":4.3,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hopping potential wells and gait switching in a fish-like robot with a bistable tail 双稳态尾巴鱼形机器人的跳跃势阱和步态切换
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-11 DOI: 10.1016/j.eml.2024.102239
Prashanth Chivkula, Colin Rodwell, Phanindra Tallapragada
{"title":"Hopping potential wells and gait switching in a fish-like robot with a bistable tail","authors":"Prashanth Chivkula,&nbsp;Colin Rodwell,&nbsp;Phanindra Tallapragada","doi":"10.1016/j.eml.2024.102239","DOIUrl":"10.1016/j.eml.2024.102239","url":null,"abstract":"<div><div>Fish outperform current underwater robots in speed, agility, and efficiency of locomotion, in part due to their flexible appendages that are capable of rich combinations of modes of motion. In fish-like robots, actuating many different modes of oscillation of tails or fins can become a challenge. This paper presents a highly underactuated (with a single actuator) fish-like robot with a bistable tail that features a double-well elastic potential. Oscillations of such a tail depend on the frequency and amplitude of excitation, and tuning the frequency–amplitude can produce controllable oscillations in different modes leading to different gaits of the robot. This robot design is inspired by recent work on underactuated flexible swimming robots driven by a single rotor. The oscillations of the rotor can propel and steer the robot, but saturation of the rotor makes performing long turns challenging. This paper demonstrates that by adding geometric bistability to the flexible tail, turns can be performed by controllably exciting single-well oscillations in the tail, while exciting double-well oscillations of the tail produces average straight-line motion. The findings of this paper go beyond the application to a narrow class of fish-like robots. More broadly we have demonstrated the use of periodic excitation to produce bistable response that generate different gaits including a steering gait. The mechanics demonstrated here show the feasibility of applications to other mobile soft robots.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102239"},"PeriodicalIF":4.3,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
HyperCAN: Hypernetwork-driven deep parameterized constitutive models for metamaterials HyperCAN:超网络驱动的超材料深度参数化构成模型
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-11 DOI: 10.1016/j.eml.2024.102243
Li Zheng , Dennis M. Kochmann , Siddhant Kumar
{"title":"HyperCAN: Hypernetwork-driven deep parameterized constitutive models for metamaterials","authors":"Li Zheng ,&nbsp;Dennis M. Kochmann ,&nbsp;Siddhant Kumar","doi":"10.1016/j.eml.2024.102243","DOIUrl":"10.1016/j.eml.2024.102243","url":null,"abstract":"<div><div>We introduce HyperCAN, a machine learning framework that utilizes <u>hyper</u>networks to construct adaptable <u>c</u>onstitutive <u>a</u>rtificial <u>n</u>eural networks for a wide range of beam-based metamaterials exhibiting diverse mechanical behavior under finite deformations. HyperCAN integrates an input convex neural network that models the nonlinear stress–strain map of a truss lattice, while ensuring adherence to fundamental mechanics principles, along with a hypernetwork that dynamically adjusts the parameters of the convex network as a function of the lattice topology and geometry. This unified framework demonstrates robust generalization in predicting the mechanical behavior of previously unseen metamaterial designs and loading scenarios well beyond the training domain. We show how HyperCAN can be integrated into multiscale simulations to accurately capture the highly nonlinear responses of large-scale truss metamaterials, closely matching fully resolved simulations while significantly reducing computational costs. This offers new efficient opportunities for the multiscale design and optimization of truss metamaterials.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102243"},"PeriodicalIF":4.3,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Electrothermally actuated network metamaterials with reconfigurable bending deformation modes 具有可重构弯曲变形模式的电热致动网络超材料
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-10 DOI: 10.1016/j.eml.2024.102241
Kai Zhang , Jinyu Ji , Xiao Kang , Xiaogang Guo
{"title":"Electrothermally actuated network metamaterials with reconfigurable bending deformation modes","authors":"Kai Zhang ,&nbsp;Jinyu Ji ,&nbsp;Xiao Kang ,&nbsp;Xiaogang Guo","doi":"10.1016/j.eml.2024.102241","DOIUrl":"10.1016/j.eml.2024.102241","url":null,"abstract":"<div><div>Reconfigurable metamaterials with specific deformation modes show great promise in applications such as multifunctional antenna, stretchable electronic device, and reconfigurable soft robot, due to their ability to achieve multiple operational states within a single system. Previous researches on active metamaterials with bending deformation responses revealed two main issues: (1) achieving reconfigurable deformation within the same metamaterial is challenging due to the reliance on uniform external field actuation; and (2) there is a lack of in-depth studies on the microstructure-property relationships for the bending deformation responses of network metamaterials due to the lack of theoretical analysis. To address these issues, this study presents a mechanical design strategy for an electrothermally actuated network metamaterials to realize reconfigurable bending deformation. A theoretical model describing the electrothermally actuated bending deformation responses is developed through a three-level analysis, which offers a comprehensive understanding of the parameter-property relationships and accurately describes the bending deformation behaviors. The validity of these mechanical models is confirmed through finite element analyses (FEAs) and experimental results. These mechanical models provide analytical solutions for crucial mechanical quantities, including the electrothermally actuated bending angles and effective strains for bending deformation responses. The bending behaviors of the reconfigurable metamaterials under electrothermal actuation can be adjusted by the key nondimensional geometric parameters and the actuation strategies. Additionally, experimental results and FE calculations demonstrate that multiple bending responses can be realized within a single metamaterial by different actuation strategies. This study offers comprehensive guideline from theoretical predictions, FE calculations, and experimental demonstrations for future researched of reconfigurable metamaterials to realize required deformation behaviors.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102241"},"PeriodicalIF":4.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Directional soft jumper by harnessing asymmetric snapping of a semi-open shell 利用半开放式外壳的非对称扣合,打造定向软质毛衣
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-09 DOI: 10.1016/j.eml.2024.102242
Min Li , Huikai Zhang , Wei Fang , Jian Wu , Xi-Qiao Feng
{"title":"Directional soft jumper by harnessing asymmetric snapping of a semi-open shell","authors":"Min Li ,&nbsp;Huikai Zhang ,&nbsp;Wei Fang ,&nbsp;Jian Wu ,&nbsp;Xi-Qiao Feng","doi":"10.1016/j.eml.2024.102242","DOIUrl":"10.1016/j.eml.2024.102242","url":null,"abstract":"<div><div>Precise control of the jumping direction and trajectory of soft robotics poses a challenge due to their large deformation and low stiffness. In this paper, we propose a pneumatic soft actuator consisting of an inward semi-spherical shell with a pre-existing T-shaped incision, which exhibits asymmetric snapping-through buckling under an increasing internal pressure. During the dynamic snapping, the shell deforms rapidly, resulting in an asymmetric, inclined impact with the ground. The impact force drives the soft actuator to jump in a controllable direction, and the adopted semi-open pneumatic system greatly improves the efficient utilization of air ejection energy. This design not only enhances the jumping performance, but also allows the control of the trajectory through adjusting the air pressure. Our experiments demonstrate that the actuator can achieve various jumping functions, for examples, to jump over obstacles of varying heights and depths, to execute rapid and continuous locomotion, and even to escape from a deep bottle. This work offers a paradigmatic idea for designing highly maneuverable and controllable soft robots.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102242"},"PeriodicalIF":4.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The strength of an adhesive contact in the presence of interfacial defects 存在界面缺陷时的粘合接触强度
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-05 DOI: 10.1016/j.eml.2024.102238
Coby K. Jones , Jamie L. Hale , Helen K. Minsky , Jamie A. Booth
{"title":"The strength of an adhesive contact in the presence of interfacial defects","authors":"Coby K. Jones ,&nbsp;Jamie L. Hale ,&nbsp;Helen K. Minsky ,&nbsp;Jamie A. Booth","doi":"10.1016/j.eml.2024.102238","DOIUrl":"10.1016/j.eml.2024.102238","url":null,"abstract":"<div><div>Adhesive contacts which possess a dominant stress concentration, such as at the contact edge in spherical junctions or at the detachment front in a peeling film, are well studied. More complex adhesive junction geometries, such as mushroom-shaped fibrils in bioinspired micropatterned dry adhesives, have exhibited a complex dependence of adhesive strength on the presence of interfacial defects within the contact. This has led to the emergence of statistical variation of the local behavior among micropatterned sub-contacts. In order to examine the interplay between geometry and interfacial defect character in control of the adhesive strength, the model system of a stiff cylindrical probe on an elastic layer is examined. Both experiments (glass on PDMS) and cohesive zone finite element simulations are performed, with analytical asymptotic limits also considered. The thickness of the elastic layer is varied to alter the interfacial stress distribution, with thinner layers having a reduced edge stress concentration at the expense of increased stress at the contact center. The size and position of manufactured interfacial defects is varied. It is observed that for the thickest substrates the edge stress concentration is dominant, with detachment propagating from this region regardless of the presence of an interfacial defect within the contact. Only very large center defects, with radius greater than half of that of the contact influence the adhesive strength. This transition is in agreement with analytical asymptotic limits. As the substrate is made thinner and the stress distribution changes, a strong decay in adhesive strength with increasing center defect radius emerges. For the thinnest substrate the flaw-insensitive upper bound is approached, suggesting that this decay is dominated by a reduction in the contact area. For penny-shaped defects at increasing radial positions, the adhesive strength for the thinnest substrates becomes non-monotonic. This confirms an intricate interplay between the geometry-controlled interfacial stress distribution and the size and position of interfacial defects in adhesive contacts, which will lead to statistical variation in strength when defects form due to surface roughness, fabrication imperfections, or contaminant particles.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102238"},"PeriodicalIF":4.3,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tunable bandgaps in an elastic meta-plate with shape memory alloy springs 带形状记忆合金弹簧的弹性元板中的可调带隙
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-10-03 DOI: 10.1016/j.eml.2024.102240
Bingfei Liu , Ping Chen , Tong Zhu , Yan-Feng Wang
{"title":"Tunable bandgaps in an elastic meta-plate with shape memory alloy springs","authors":"Bingfei Liu ,&nbsp;Ping Chen ,&nbsp;Tong Zhu ,&nbsp;Yan-Feng Wang","doi":"10.1016/j.eml.2024.102240","DOIUrl":"10.1016/j.eml.2024.102240","url":null,"abstract":"<div><div>In this paper, a tunable metamaterial based on shape memory alloy springs is designed, which can achieve bandgap tuning by spring's unique shape memory effect. The variation mechanism of shear modulus and geometrical parameters of shape memory alloy springs is investigated by considering a detailed phase transition mechanism. For any specific temperatures, the energy band structure and frequency response spectrum of the metamaterial are calculated by numerical simulation. And the theoretical prediction models of bandgap boundary frequency and tuning range at different temperatures are established. The experimental test of vibration transmission of metamaterial is finally presented. The results show that (1) By varying the spring's shear modulus and height, the metamaterial exhibits excellent vibration isolation characteristics and bandgap tuning in low-frequency range of 124–226Hz. (2) The bandgap boundaries and tuning ranges can be predicted by the theoretical prediction model, which shows good agreement with both the simulation results and the experimental data. (3) By artificially designing shape memory alloy springs with larger shear modulus and wire radius, smaller helix radius and number of turns, the bandgap moves to higher frequencies. The current work can provide a reference for further engineering applications with the tunable elastic/acoustic metamaterials.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102240"},"PeriodicalIF":4.3,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recent advances in the integration of protein mechanics and machine learning 蛋白质力学与机器学习相结合的最新进展
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-09-20 DOI: 10.1016/j.eml.2024.102236
Yen-Lin Chen , Shu-Wei Chang
{"title":"Recent advances in the integration of protein mechanics and machine learning","authors":"Yen-Lin Chen ,&nbsp;Shu-Wei Chang","doi":"10.1016/j.eml.2024.102236","DOIUrl":"10.1016/j.eml.2024.102236","url":null,"abstract":"<div><div>Mechanics underlies protein properties and behavior. From a theoretical standpoint, it is possible to derive these based on physical rules. This is appealing because they provide insights into physiology and disease, as well as aid in protein engineering; however, the convoluted nature of the biological system and current computational speeds limit its feasibility. Machine learning (ML) architectures are known for their ability to make inferences on complex data, such as the relationship between protein mechanics, properties, and behavior. Substantial efforts have been made to learn such correlations in tasks such as the prediction of structure, stability, natural frequency, mechanical strength, folding rate, solubility, and function. Each of these properties is interconnected through protein mechanics, and it is not surprising that the methods used in these tasks overlap highly in model input and architecture. In this review, we evaluate ML methods for the seven aforementioned prediction tasks to identify current trends in ML research in the field of protein sciences, focusing on the input and model architecture of each method. A short overview of <em>de novo</em> protein design is also provided. Finally, we highlight trends in the application of ML methods in the field of protein science, as well as directions for future improvements.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102236"},"PeriodicalIF":4.3,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Problem-independent machine learning-enhanced structural topology optimization of complex design domains based on isoparametric elements 基于等参数元素的复杂设计域结构拓扑优化--与问题无关的机器学习增强型结构拓扑优化
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-09-20 DOI: 10.1016/j.eml.2024.102237
Linfeng Zhang, Mengcheng Huang, Chang Liu, Zongliang Du, Tianchen Cui, Xu Guo
{"title":"Problem-independent machine learning-enhanced structural topology optimization of complex design domains based on isoparametric elements","authors":"Linfeng Zhang,&nbsp;Mengcheng Huang,&nbsp;Chang Liu,&nbsp;Zongliang Du,&nbsp;Tianchen Cui,&nbsp;Xu Guo","doi":"10.1016/j.eml.2024.102237","DOIUrl":"10.1016/j.eml.2024.102237","url":null,"abstract":"<div><div>Topology optimization requires dozens or even hundreds of iterations, each requiring a complete finite element analysis (FEA). Significant computation cost limits the application of topology optimization in engineering, especially for high-resolution problems containing complex design domains. To address the issue, a Problem-Independent Machine Learning (PIML) model based on isoparametric elements is proposed. Effectively reducing the computational time of FEA, the proposed model enables efficient topology optimization and extends the solvable problem range to complex design domains. The essential idea is leveraging the substructure method and establishing a mapping from element shapes and material distribution within the substructure to its numerical shape functions through machine learning models. Both sample generation and model training are conducted offline, allowing the trained machine learning model to be directly employed during the topology optimization process. Since the shape function of the substructure is problem-independent, it requires no sample regeneration or modification of the proposed machine learning model when changing the geometry or boundary conditions of the optimization problem. Numerical examples demonstrate that the proposed machine learning model boosts the efficiency of topology optimization by one order of magnitude without parallel techniques.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102237"},"PeriodicalIF":4.3,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A hyperelastic beam model for the photo-induced response of nematic liquid crystal elastomers 向列液晶弹性体光诱导响应的超弹性梁模型
IF 4.3 3区 工程技术
Extreme Mechanics Letters Pub Date : 2024-09-19 DOI: 10.1016/j.eml.2024.102233
Farzam Dadgar-Rad , Mohammad Mehdi Mahjoub , Mokarram Hossain
{"title":"A hyperelastic beam model for the photo-induced response of nematic liquid crystal elastomers","authors":"Farzam Dadgar-Rad ,&nbsp;Mohammad Mehdi Mahjoub ,&nbsp;Mokarram Hossain","doi":"10.1016/j.eml.2024.102233","DOIUrl":"10.1016/j.eml.2024.102233","url":null,"abstract":"<div><p>Liquid crystal elastomers (LCEs) are a novel class of materials created by combining polymeric solids with stiff, rod-like molecules known as nematic mesogens. These materials exhibit large, reversible deformations under mechanical, thermal, and optical stimuli. In this work, we develop a nonlinear beam formulation for analyzing the finite elastic deformation of beam-like structures made of LCEs under photo-actuation. This formulation applies to ideal, non-ideal, isotropic genesis, and nematic genesis LCEs. We establish the variational form of the problem based on the principle of virtual work. To solve numerical examples, we also develop a nonlinear finite element formulation based on B-spline functions. Several numerical examples are presented to demonstrate the applicability of the proposed formulation.</p></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"72 ","pages":"Article 102233"},"PeriodicalIF":4.3,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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