Xiaoyu Zhang, Zeang Zhao, Shengyu Duan, H. Lei, Daining Fang
This work investigates the effect of material dispersion on the tensile strength of brittle diamond lattice structure. In actual lattice structures fabricated by additive manufacturing, the dispersion of strength comes from microscale defect, geometric deviation and manufacture-induced anisotropy. The weakening of ultimate failure strength due to material dispersion cannot be predicted by most existing theoretical models, because they assume homogeneous and determinate mechanical properties of the lattice structure. In this paper, we employ diamond lattice structure made from brittle material as a typical example, and its tensile behavior is numerically investigated by incorporating the Gaussian distribution of strut strength. Inspired by the simulation results, a stochastic theoretical model is developed to predict the deformation and failure of diamond lattice structure with material dispersion. This model captures the fact that weaker struts break first even if the whole structure can still bear load. With the continuous increase of stress, these broken struts accumulate into continuous cracks, and ultimate failure occurs when the energy release rate of the initiated crack surpasses the intrinsic fracture toughness of the lattice structure. This research supplements stochastic feature into classical theories, and improves the understanding of potential strengthening and toughening designs for lattice structures.
{"title":"The tensile strength of brittle diamond lattice structure with material dispersion","authors":"Xiaoyu Zhang, Zeang Zhao, Shengyu Duan, H. Lei, Daining Fang","doi":"10.1115/1.4065195","DOIUrl":"https://doi.org/10.1115/1.4065195","url":null,"abstract":"\u0000 This work investigates the effect of material dispersion on the tensile strength of brittle diamond lattice structure. In actual lattice structures fabricated by additive manufacturing, the dispersion of strength comes from microscale defect, geometric deviation and manufacture-induced anisotropy. The weakening of ultimate failure strength due to material dispersion cannot be predicted by most existing theoretical models, because they assume homogeneous and determinate mechanical properties of the lattice structure. In this paper, we employ diamond lattice structure made from brittle material as a typical example, and its tensile behavior is numerically investigated by incorporating the Gaussian distribution of strut strength. Inspired by the simulation results, a stochastic theoretical model is developed to predict the deformation and failure of diamond lattice structure with material dispersion. This model captures the fact that weaker struts break first even if the whole structure can still bear load. With the continuous increase of stress, these broken struts accumulate into continuous cracks, and ultimate failure occurs when the energy release rate of the initiated crack surpasses the intrinsic fracture toughness of the lattice structure. This research supplements stochastic feature into classical theories, and improves the understanding of potential strengthening and toughening designs for lattice structures.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"67 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140376283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop a nonlinear mixed finite element method for flexoelectric semiconductors and analyze the mechanically-tuned redistributions of free carriers and electric currents through flexoelectric polarization in typical structures. We first present a macroscopic theory for flexoelectric semiconductors by combining flexoelectricity and nonlinear drift-diffusion theory. To use C0 continuous elements, we derive an incremental constrained weak form by introducing Langrage multipliers, in which the kinematic constraints between the displacement and its gradient are guaranteed. Based on the weak form, we established a mixed C0 continuous 9-node quadrilateral finite element as well as an iterative process for solving nonlinear boundary-value problems. The accuracy and convergence of the proposed element are validated by comparing linear finite element method results against analytical solutions for the bending of a beam. Finally, the nonlinear element method is applied to more complex problems, such as a circular ring, a plate with a hole and an isosceles trapezoid. Results indicate that mechanical loads and doping levels have distinct influences on electric properties.
{"title":"A nonlinear mixed finite element method for the analysis of flexoelectric semiconductors","authors":"Qiufeng Yang, Xudong Li, Zhaowei Liu, Feng Jin, Yilin Qu","doi":"10.1115/1.4065161","DOIUrl":"https://doi.org/10.1115/1.4065161","url":null,"abstract":"\u0000 In this paper, we develop a nonlinear mixed finite element method for flexoelectric semiconductors and analyze the mechanically-tuned redistributions of free carriers and electric currents through flexoelectric polarization in typical structures. We first present a macroscopic theory for flexoelectric semiconductors by combining flexoelectricity and nonlinear drift-diffusion theory. To use C0 continuous elements, we derive an incremental constrained weak form by introducing Langrage multipliers, in which the kinematic constraints between the displacement and its gradient are guaranteed. Based on the weak form, we established a mixed C0 continuous 9-node quadrilateral finite element as well as an iterative process for solving nonlinear boundary-value problems. The accuracy and convergence of the proposed element are validated by comparing linear finite element method results against analytical solutions for the bending of a beam. Finally, the nonlinear element method is applied to more complex problems, such as a circular ring, a plate with a hole and an isosceles trapezoid. Results indicate that mechanical loads and doping levels have distinct influences on electric properties.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"114 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, thin-walled tubes were circumferentially strengthened by plasticity ball burnishing of critical locations determined from buckling mode analysis. Axial crush test results revealed that the surface treated (ST) tubes increased localized yield strength, attained superior crashworthiness performance, and triggered predictable deformation modes according to the buckling modes of the tubes. Numerical analysis was performed and successfully validated with experiment at 90% prediction accuracy. The treated tube ST-4 with 12th buckling mode outperformed a conventional tube with an increase in specific energy absorption (SEA) and crush force efficiency (CFE) by up to 70%, while sustaining a low increase in initial peak force (IPF). Furthermore, the tube demonstrated greater rate of energy dissipation compared to tubes with conventional surface treated patterns at the same level of surface treated area. The crashworthiness performance improved as the surface treated area ratio increased. A theoretical model was developed for the surface treated tube based on fundamental deformation kinematics, predicting mean crushing force and total energy absorption with an acceptable accuracy. The findings strongly suggest that the proposed surface enhanced tubes have a great potential to be used as energy absorbing structures in crashworthiness applications.
{"title":"A synergistic approach combining surface enhancement and buckling modes for improved axial crushing performance of thin-walled tubes","authors":"Shahrukh Alam, Mohammad Uddin, Colin Hall","doi":"10.1115/1.4065162","DOIUrl":"https://doi.org/10.1115/1.4065162","url":null,"abstract":"\u0000 In this study, thin-walled tubes were circumferentially strengthened by plasticity ball burnishing of critical locations determined from buckling mode analysis. Axial crush test results revealed that the surface treated (ST) tubes increased localized yield strength, attained superior crashworthiness performance, and triggered predictable deformation modes according to the buckling modes of the tubes. Numerical analysis was performed and successfully validated with experiment at 90% prediction accuracy. The treated tube ST-4 with 12th buckling mode outperformed a conventional tube with an increase in specific energy absorption (SEA) and crush force efficiency (CFE) by up to 70%, while sustaining a low increase in initial peak force (IPF). Furthermore, the tube demonstrated greater rate of energy dissipation compared to tubes with conventional surface treated patterns at the same level of surface treated area. The crashworthiness performance improved as the surface treated area ratio increased. A theoretical model was developed for the surface treated tube based on fundamental deformation kinematics, predicting mean crushing force and total energy absorption with an acceptable accuracy. The findings strongly suggest that the proposed surface enhanced tubes have a great potential to be used as energy absorbing structures in crashworthiness applications.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"105 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate finite plane deformations of an elliptic rigid inclusion embedded in a soft matrix which is made of a particular class of harmonic-type hyperelastic materials. The inclusion is assumed to be perfectly bonded to the matrix which is subjected to a constant remote in-plane loading. Utilizing the Cauchy integral techniques associated with conformal mappings, we derive closed-form solutions for the full-field deformation, Piola stress and Cauchy stress in the entire matrix. Numerical examples are presented to illustrate the current solutions in comparison with those established from linear elasticity theory. We find that in terms of the Cauchy stress around the inclusion, the maximum normal stress component always appears at the endpoints of the major axis of the inclusion irrespective of the magnitude of the remote loading, while the maximum hoop stress component occurs not exactly at the above-mentioned endpoints when the remote loading exceeds a certain value. In particular, we identify an exact explicit formula for determining the relative rotation of the inclusion during deformation induced by a remote uniaxial loading of arbitrarily-given magnitude and direction.
{"title":"Elliptic rigid inclusion in soft materials of harmonic type","authors":"Kui Miao, Ming Dai, Cun-fa Gao","doi":"10.1115/1.4065160","DOIUrl":"https://doi.org/10.1115/1.4065160","url":null,"abstract":"\u0000 We investigate finite plane deformations of an elliptic rigid inclusion embedded in a soft matrix which is made of a particular class of harmonic-type hyperelastic materials. The inclusion is assumed to be perfectly bonded to the matrix which is subjected to a constant remote in-plane loading. Utilizing the Cauchy integral techniques associated with conformal mappings, we derive closed-form solutions for the full-field deformation, Piola stress and Cauchy stress in the entire matrix. Numerical examples are presented to illustrate the current solutions in comparison with those established from linear elasticity theory. We find that in terms of the Cauchy stress around the inclusion, the maximum normal stress component always appears at the endpoints of the major axis of the inclusion irrespective of the magnitude of the remote loading, while the maximum hoop stress component occurs not exactly at the above-mentioned endpoints when the remote loading exceeds a certain value. In particular, we identify an exact explicit formula for determining the relative rotation of the inclusion during deformation induced by a remote uniaxial loading of arbitrarily-given magnitude and direction.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":" 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140384632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the concurrent three-dimensional deformations of fiber-reinforced composite sheets subjected to out-of-plane bending moments via a continuum model, where we invoke the Neo-Hookean strain energy model for the matrix material of fiber-reinforced composite, and assimilate the strain energy of fiber reinforcements into the matrix material model by accounting for stretching, bending, and twisting kinematics of the fibers through the computations of the first-order and second-order gradient of deformation. Emphasis is placed on deriving the Euler equation and boundary conditions of bending moment within the framework of the variational principle and configuring composite surfaces using differential geometry. Significant attention has been given to illustrating the concurrent three-dimensional deformation of fiber composite, meshwork deformation, and fiber kinematics. The simulation results reveal that for a square fiber composite subjected to the out-of-plane bending moment, the maximum in-plane deformation of matrix material occurs along the diagonal direction of the domain while the center of the domain experiences weak in-plane deformation. Notably, the matrix material performs isotropic/anisotropic properties depending on the domain size/shape. In particular, the simulated unit fiber deformations reasonably validate the overall deformation of the network, underscoring that the deformations of the embedded fiber units govern the overall mechanical performance of the fiber meshwork. More importantly, the continuum model qualitatively provides reasonable predictions on the damage patterns of construction materials by demonstrating the kinematics of matrix material and meshwork deformation.
{"title":"The mechanics of elastomeric sheet reinforced with bidirectional fiber mesh subjected to flexure on boundaries","authors":"Wenhao Yao, Tahmid Rakin Siddiqui, Chun-IL Kim","doi":"10.1115/1.4065108","DOIUrl":"https://doi.org/10.1115/1.4065108","url":null,"abstract":"\u0000 We investigate the concurrent three-dimensional deformations of fiber-reinforced composite sheets subjected to out-of-plane bending moments via a continuum model, where we invoke the Neo-Hookean strain energy model for the matrix material of fiber-reinforced composite, and assimilate the strain energy of fiber reinforcements into the matrix material model by accounting for stretching, bending, and twisting kinematics of the fibers through the computations of the first-order and second-order gradient of deformation. Emphasis is placed on deriving the Euler equation and boundary conditions of bending moment within the framework of the variational principle and configuring composite surfaces using differential geometry. Significant attention has been given to illustrating the concurrent three-dimensional deformation of fiber composite, meshwork deformation, and fiber kinematics. The simulation results reveal that for a square fiber composite subjected to the out-of-plane bending moment, the maximum in-plane deformation of matrix material occurs along the diagonal direction of the domain while the center of the domain experiences weak in-plane deformation. Notably, the matrix material performs isotropic/anisotropic properties depending on the domain size/shape. In particular, the simulated unit fiber deformations reasonably validate the overall deformation of the network, underscoring that the deformations of the embedded fiber units govern the overall mechanical performance of the fiber meshwork. More importantly, the continuum model qualitatively provides reasonable predictions on the damage patterns of construction materials by demonstrating the kinematics of matrix material and meshwork deformation.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"14 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140234412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nary Savoeurn, Chettapong Janya-anurak, V. Uthaisangsuk
In this work, dynamic mode decomposition (DMD) was applied as an algorithm for determining the natural frequency and damping ratio of viscoelastic lattice structures. The algorithm has been developed based on the Hankel alternative view of Koopman and DMD (HAVOK-DMD). In general, the Hankel matrix is based on time-delay embedding, which is meant for the hidden variable in a time series data. Vibration properties of a system could be then estimated from the eigenvalues of approximated Koopman operator. Results of the proposed algorithm was firstly validated with those of the traditional discrete Fourier transform (DFT) approach and half power bandwidth (HPBW) by using analytical dataset of multi-modal spring-mass-damper system. Afterwards, the algorithm was further used to analyze dynamic responses of viscoelastic lattice structures, in which data from both experimental and numerical finite element (FE) model were considered. It was found that the DMD based algorithm could accurately estimate the natural frequencies and damping ratios of the examined structures. In particular, it is beneficial to any dataset with limited amounts of data, whereby experiments or data gathering processes are expensive.
{"title":"Determination of dynamic characteristics of lattice structure using dynamic mode decomposition","authors":"Nary Savoeurn, Chettapong Janya-anurak, V. Uthaisangsuk","doi":"10.1115/1.4065055","DOIUrl":"https://doi.org/10.1115/1.4065055","url":null,"abstract":"\u0000 In this work, dynamic mode decomposition (DMD) was applied as an algorithm for determining the natural frequency and damping ratio of viscoelastic lattice structures. The algorithm has been developed based on the Hankel alternative view of Koopman and DMD (HAVOK-DMD). In general, the Hankel matrix is based on time-delay embedding, which is meant for the hidden variable in a time series data. Vibration properties of a system could be then estimated from the eigenvalues of approximated Koopman operator. Results of the proposed algorithm was firstly validated with those of the traditional discrete Fourier transform (DFT) approach and half power bandwidth (HPBW) by using analytical dataset of multi-modal spring-mass-damper system. Afterwards, the algorithm was further used to analyze dynamic responses of viscoelastic lattice structures, in which data from both experimental and numerical finite element (FE) model were considered. It was found that the DMD based algorithm could accurately estimate the natural frequencies and damping ratios of the examined structures. In particular, it is beneficial to any dataset with limited amounts of data, whereby experiments or data gathering processes are expensive.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"6 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140247726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work presents closed-form methods to solve the Continuous-Time Algebraic Riccati Equation (CARE) for second-order systems. The standard CARE solution requires the computation of certain eigenvectors, which becomes expensive and erroneous as the size of the system increases. We mitigate these issues by developing closedform solutions to CARE expressed in terms of physically meaningful mass, damping, and stiffness matrices. We present two methods – one that requires the modal transformation of mass and stiffness matrices, and another that does not require this modal transformation. We show using hundreds of high-dimensional second-order systems that the proposed methods achieve similar or better accuracy compared to the state-of-the-art, while significantly reducing the computation time. We further substantiate our methods by illustrating their advantages when applied to engineering problems such as vibration control.
本研究提出了解决二阶系统连续时间代数里卡提方程（CARE）的闭式方法。标准的 CARE 解法需要计算某些特征向量，随着系统规模的增大，这种方法变得昂贵且错误百出。我们通过开发以物理意义上的质量、阻尼和刚度矩阵表示的 CARE 闭式解来缓解这些问题。我们提出了两种方法--一种需要对质量和刚度矩阵进行模态变换，另一种则不需要这种模态变换。我们使用数百个高维二阶系统证明，与最先进的方法相比，我们提出的方法达到了相似或更高的精度，同时大大减少了计算时间。我们进一步证明了我们的方法在应用于振动控制等工程问题时的优势。
{"title":"Closed-Form Solutions to Continuous-Time Algebraic Riccati Equation for Second-Order Systems","authors":"Vishvendra Rustagi, Cornel Sultan","doi":"10.1115/1.4065057","DOIUrl":"https://doi.org/10.1115/1.4065057","url":null,"abstract":"\u0000 This work presents closed-form methods to solve the Continuous-Time Algebraic Riccati Equation (CARE) for second-order systems. The standard CARE solution requires the computation of certain eigenvectors, which becomes expensive and erroneous as the size of the system increases. We mitigate these issues by developing closedform solutions to CARE expressed in terms of physically meaningful mass, damping, and stiffness matrices. We present two methods – one that requires the modal transformation of mass and stiffness matrices, and another that does not require this modal transformation. We show using hundreds of high-dimensional second-order systems that the proposed methods achieve similar or better accuracy compared to the state-of-the-art, while significantly reducing the computation time. We further substantiate our methods by illustrating their advantages when applied to engineering problems such as vibration control.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140245260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a theoretical basis and a systematic process for resolving all inertia forces along generalized coordinates from the overall energy equation of a dynamical system. The theory is developed for natural systems with scleronomic constraints, where the potential energy is independent of generalized velocities. The process involves expansion of the energy equation, and specifically a special expansion of the kinetic energy term, from which the inertia forces emerge. The expansion uses fundamental kinematic identities of the phase space. It is also guided by insights drawn from the structure of the Hamiltonian function. The resulting equation has the structure of the D'Alembert's equation but involving generalized coordinates, from which the Lagrange's equations of motion are obtained. The expansion process elucidates how certain inertia forces manifest in the energy equation as composite terms that must be accurately resolved along different generalized coordinates. The process uses only the system energy equation, and neither the Hamiltonian nor the Lagrangian function are required. Extension of this theory to non-autonomous and nonholonomic systems is an area of future research.
{"title":"Resolving Absorbed Work and Generalized Inertia Forces from System Energy Equation - A Hamiltonian and Phase-Space Kinematics Approach","authors":"Tuhin Das","doi":"10.1115/1.4065056","DOIUrl":"https://doi.org/10.1115/1.4065056","url":null,"abstract":"\u0000 This paper develops a theoretical basis and a systematic process for resolving all inertia forces along generalized coordinates from the overall energy equation of a dynamical system. The theory is developed for natural systems with scleronomic constraints, where the potential energy is independent of generalized velocities. The process involves expansion of the energy equation, and specifically a special expansion of the kinetic energy term, from which the inertia forces emerge. The expansion uses fundamental kinematic identities of the phase space. It is also guided by insights drawn from the structure of the Hamiltonian function. The resulting equation has the structure of the D'Alembert's equation but involving generalized coordinates, from which the Lagrange's equations of motion are obtained. The expansion process elucidates how certain inertia forces manifest in the energy equation as composite terms that must be accurately resolved along different generalized coordinates. The process uses only the system energy equation, and neither the Hamiltonian nor the Lagrangian function are required. Extension of this theory to non-autonomous and nonholonomic systems is an area of future research.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140246154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper illustrates how particle size affects the initial yield stress of particle-reinforced composites. A formulation in a closed form is presented to demonstrate the size effect of yielding of the composites. This paper also demonstrates that there is an upper bound and a lower bound for the size-dependent yield stress with the change of particle size. This means that decreasing particle size increases its yield stress up to an upper bound. Similarly, increasing particle size decrease its yield stress up to a lower bound. In this paper the asymptotic homogenization method is used in framework of the Cosserat elasticity. A virtual “unreinforced matrix” is introduced as a reference configuration. As a numerical example, the size effect of yielding of SiCp/Al is predicted.
{"title":"Size Effect of Yielding of Particle-Reinforced Composites","authors":"Ruo Jing Zhang, Yan Liu","doi":"10.1115/1.4065007","DOIUrl":"https://doi.org/10.1115/1.4065007","url":null,"abstract":"\u0000 This paper illustrates how particle size affects the initial yield stress of particle-reinforced composites. A formulation in a closed form is presented to demonstrate the size effect of yielding of the composites. This paper also demonstrates that there is an upper bound and a lower bound for the size-dependent yield stress with the change of particle size. This means that decreasing particle size increases its yield stress up to an upper bound. Similarly, increasing particle size decrease its yield stress up to a lower bound. In this paper the asymptotic homogenization method is used in framework of the Cosserat elasticity. A virtual “unreinforced matrix” is introduced as a reference configuration. As a numerical example, the size effect of yielding of SiCp/Al is predicted.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"44 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140259247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zheng Zhang, Fuhua Ye, Yuhang Dong, Fan Zhang, Zhichao Fan
Arch and serpentine structures are two fundamental structural forms with significant applications in various fields. When subjected to compressive loading at both ends, these structures undergo flexural-torsional post-buckling, resulting in complex deformation modes that are challenging to describe using basic functions, posing significant challenges in finding analytical solutions. In this study, we propose a novel approach to address this issue. By representing the lateral displacement with a trigonometric series expansion and utilizing the equilibrium equation, the angular displacement is expressed in terms of special functions known as Mathieu functions. Furthermore, the energy method is employed to obtain analytical solutions for the flexural-torsional post-buckling deformation components. The theoretical findings are validated through experiments and finite element analysis (FEA). Based on theoretical results, explicit analytical expressions for the maximum principal strain and the bending-torsion ratio of the structures are derived, offering valuable insights for the design of arch and serpentine structures in practical applications.
{"title":"Post-Buckling Analysis of Arch and Serpentine Structures under End-to-End Compression","authors":"Zheng Zhang, Fuhua Ye, Yuhang Dong, Fan Zhang, Zhichao Fan","doi":"10.1115/1.4064962","DOIUrl":"https://doi.org/10.1115/1.4064962","url":null,"abstract":"\u0000 Arch and serpentine structures are two fundamental structural forms with significant applications in various fields. When subjected to compressive loading at both ends, these structures undergo flexural-torsional post-buckling, resulting in complex deformation modes that are challenging to describe using basic functions, posing significant challenges in finding analytical solutions. In this study, we propose a novel approach to address this issue. By representing the lateral displacement with a trigonometric series expansion and utilizing the equilibrium equation, the angular displacement is expressed in terms of special functions known as Mathieu functions. Furthermore, the energy method is employed to obtain analytical solutions for the flexural-torsional post-buckling deformation components. The theoretical findings are validated through experiments and finite element analysis (FEA). Based on theoretical results, explicit analytical expressions for the maximum principal strain and the bending-torsion ratio of the structures are derived, offering valuable insights for the design of arch and serpentine structures in practical applications.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"16 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140418867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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