Pub Date : 2025-01-10DOI: 10.1016/j.ijsolstr.2025.113224
T. Parent , P. Morenon , P. Nougayrede , P. Taforel , F. Dubois , S. Morel
The preservation of a historic masonry monument with structural pathologies requires the implementation of a multidisciplinary diagnostic approach including a mechanical assessment of the structure. To this end, a wide variety of models (such as Continuum Homogeneous Models (CHM), Block-Based Models (BBM) and geometry-based models (GBM)) are available in the literature to simulate the mechanical behavior of this type of structure. In this article, three different models (two BBM and one CHM) are used simultaneously to assess the structural behavior of a choir span of Notre-Dame de Paris Cathedral in Paris, with an aim to assist architects with diagnosis and repair operations within a time frame of approximately one year. The same set of assumptions (loading, geometry, mechanical parameters) was applied to all three models. Using these models simultaneously allowed the research team to build an optimized structural assessment based on constant interaction between the different modeling approaches. This enabled the team to leverage the strengths of each method, ensuring a high degree of confidence in the final results. The comparison of models also revealed potential improvements that could be made to each model, with the goal of reducing calculation times and/or enhancing the consistency of results, particularly in terms of failure mechanisms and behavior laws.
{"title":"On the benefits of the use of complementary numerical models for the structural analysis of a historic masonry monument: Application to a sexpartite vault of Notre-Dame de Paris cathedral","authors":"T. Parent , P. Morenon , P. Nougayrede , P. Taforel , F. Dubois , S. Morel","doi":"10.1016/j.ijsolstr.2025.113224","DOIUrl":"10.1016/j.ijsolstr.2025.113224","url":null,"abstract":"<div><div>The preservation of a historic masonry monument with structural pathologies requires the implementation of a multidisciplinary diagnostic approach including a mechanical assessment of the structure. To this end, a wide variety of models (such as Continuum Homogeneous Models (CHM), Block-Based Models (BBM) and geometry-based models (GBM)) are available in the literature to simulate the mechanical behavior of this type of structure. In this article, three different models (two BBM and one CHM) are used simultaneously to assess the structural behavior of a choir span of Notre-Dame de Paris Cathedral in Paris, with an aim to assist architects with diagnosis and repair operations within a time frame of approximately one year. The same set of assumptions (loading, geometry, mechanical parameters) was applied to all three models. Using these models simultaneously allowed the research team to build an optimized structural assessment based on constant interaction between the different modeling approaches. This enabled the team to leverage the strengths of each method, ensuring a high degree of confidence in the final results. The comparison of models also revealed potential improvements that could be made to each model, with the goal of reducing calculation times and/or enhancing the consistency of results, particularly in terms of failure mechanisms and behavior laws.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113224"},"PeriodicalIF":3.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153317","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}
Pub Date : 2025-01-09DOI: 10.1016/j.ijsolstr.2025.113226
Yuanxin Li , Jianwei Zhang , Yunlong Zhang , Minghao Zhao , Chunsheng Lu , Ming Liu
Scratch testing is widely used for its convenience and promise but lacks analytical or semi-analytical solutions for determining the mechanical properties of materials. In this paper, by investigating the scratch-induced strain field, we propose a semi-analytical solution for the forward prediction of scratch responses and inverse characterization of plastic parameters of metallic materials. The solution is verified through finite element simulation and experimental data from eight different metallic materials. The results indicate that the method is precise, with an average error of 5.25% in the forward prediction of scratch forces and 7.48% in the inverse characterization of plastic parameters. This work provides a solid theoretical foundation for using scratch tests to assess material plasticity.
{"title":"A semi-analytical solution for determining plastic parameters of metallic materials from scratch tests","authors":"Yuanxin Li , Jianwei Zhang , Yunlong Zhang , Minghao Zhao , Chunsheng Lu , Ming Liu","doi":"10.1016/j.ijsolstr.2025.113226","DOIUrl":"10.1016/j.ijsolstr.2025.113226","url":null,"abstract":"<div><div>Scratch testing is widely used for its convenience and promise but lacks analytical or semi-analytical solutions for determining the mechanical properties of materials. In this paper, by investigating the scratch-induced strain field, we propose a semi-analytical solution for the forward prediction of scratch responses and inverse characterization of plastic parameters of metallic materials. The solution is verified through finite element simulation and experimental data from eight different metallic materials. The results indicate that the method is precise, with an average error of 5.25% in the forward prediction of scratch forces and 7.48% in the inverse characterization of plastic parameters. This work provides a solid theoretical foundation for using scratch tests to assess material plasticity.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113226"},"PeriodicalIF":3.4,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153311","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}
Biaxial tensile tests of a 6000 series aluminum alloy sheet were performed using cruciform specimens and tubular specimens fabricated by bending and welding sheet samples. The contours of plastic work and the direction of the plastic strain rate were measured along nine linear stress paths. The test sample exhibited differential hardening because the shape of the work contours gradually changed with increased plastic strain. The direction of the plastic strain rate measured for every stress path was almost constant regardless of the amount of plastic strain and coincided with the direction normal to the work contour associated with a 0.2% plastic strain. Based on these observations, two material models were developed. One was an associated flow rule (AFR) model, in which the material is assumed to follow the AFR with respect to the measured work contours with differential hardening. The other was a non-associated flow rule (NAFR) model, in which the yield function was determined as approximating the work contours with differential hardening and the plastic potential function was chosen to be the work contour associated with a 0.2% plastic strain. A hydraulic bulge forming experiment and simulations with finite element AFR and NAFR models were performed to check the effect of the material models on the accuracy of the forming simulation. The thickness strain at the apex of the test piece internal pressure curve and thickness strain initial radial coordinate curve were measured and compared with the finite element simulation results based on both material models. The results revealed that the predictive accuracy of the NAFR model is superior to that of the AFR model for the aluminum alloy sheet used in this study.
{"title":"Experimental validation of non-associated flow rule and hydraulic bulge forming simulation for a 6000 series aluminum alloy sheet","authors":"Tomoyuki Hakoyama , Chiharu Sekiguchi Hakoyama , Toshihiko Kuwabara","doi":"10.1016/j.ijsolstr.2025.113218","DOIUrl":"10.1016/j.ijsolstr.2025.113218","url":null,"abstract":"<div><div>Biaxial tensile tests of a 6000 series aluminum alloy sheet were performed using cruciform specimens and tubular specimens fabricated by bending and welding sheet samples. The contours of plastic work and the direction of the plastic strain rate were measured along nine linear stress paths. The test sample exhibited differential hardening because the shape of the work contours gradually changed with increased plastic strain. The direction of the plastic strain rate measured for every stress path was almost constant regardless of the amount of plastic strain and coincided with the direction normal to the work contour associated with a 0.2% plastic strain. Based on these observations, two material models were developed. One was an associated flow rule (AFR) model, in which the material is assumed to follow the AFR with respect to the measured work contours with differential hardening. The other was a non-associated flow rule (NAFR) model, in which the yield function was determined as approximating the work contours with differential hardening and the plastic potential function was chosen to be the work contour associated with a 0.2% plastic strain. A hydraulic bulge forming experiment and simulations with finite element AFR and NAFR models were performed to check the effect of the material models on the accuracy of the forming simulation. The thickness strain at the apex of the test piece <span><math><mo>-</mo></math></span> internal pressure curve and thickness strain <span><math><mo>-</mo></math></span> initial radial coordinate curve were measured and compared with the finite element simulation results based on both material models. The results revealed that the predictive accuracy of the NAFR model is superior to that of the AFR model for the aluminum alloy sheet used in this study.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"311 ","pages":"Article 113218"},"PeriodicalIF":3.4,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167704","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}
Pub Date : 2025-01-07DOI: 10.1016/j.ijsolstr.2024.113198
Adair R. Aguiar, Lucas A. Rocha
<div><div>The theory of classical linear elasticity predicts self-intersection in the neighborhood of interior points of anisotropic solids, crack tips, and corners. This physically unrealistic behavior is characterized by the violation of the local injectivity condition, according to which, the determinant of the deformation gradient, <span><math><mrow><mi>J</mi><mo>≜</mo><mo>det</mo><mi>F</mi></mrow></math></span>, must be positive. One way to impose this condition in elasticity consists of minimizing the total potential energy subjected to the condition <span><math><mrow><mi>J</mi><mo>≥</mo><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span>, where <span><math><mi>ɛ</mi></math></span> is a small positive parameter.</div><div>We present a minimization theory constrained by <span><math><mrow><mi>J</mi><mo>≥</mo><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span> for hyperelastic solids undergoing finite deformations and derive necessary conditions for a deformation field to be a minimizer, which include both continuity of traction and dissipation-free conditions across a surface of discontinuity. We then apply this theory in the analysis of equilibrium of an annular disk made of an orthotropic St Venant-Kirchhoff material. This material is a natural constitutive extension of its classical linear counterpart. The disk is fixed on its inner surface and compressed by a constant pressure on its outer surface.</div><div>The disk problem is formulated as both a boundary value problem (disk BVP) and a minimization problem (disk MP), which are solved in the context of both the classical and the constrained (<span><math><mrow><mi>J</mi><mo>≥</mo><mi>ɛ</mi></mrow></math></span>) nonlinear theories. These formulations yield non-smooth solutions for large enough pressure, which pose numerical difficulties. To address these difficulties, we use a phase-plane technique to construct a trajectory of solution for the disk BVP and the finite element method together with nonlinear programming tools to find a minimizer for the disk MP.</div><div>In the classical nonlinear theory, we find that there is a critical pressure <span><math><mover><mrow><mi>p</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>, which tends to zero as the inner radius of the disk tends to zero, above which a solution of either the disk BVP or the disk MP becomes non-smooth and predicts <span><math><mrow><mi>J</mi><mo>≤</mo><mn>0</mn></mrow></math></span>. In addition, <span><math><mover><mrow><mi>p</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> is smaller than its counterpart predicted by the classical linear theory and, therefore, serves as an upper bound below which the linear theory is valid.</div><div>In the constrained nonlinear theory, the solutions of both the disk BVP and the disk MP agree very well and satisfy all the necessary conditions for an admissible minimizer, including the injectivity condition. Analytical and numerical results show that, for an annular
{"title":"A minimization theory in finite elasticity to prevent self-intersection","authors":"Adair R. Aguiar, Lucas A. Rocha","doi":"10.1016/j.ijsolstr.2024.113198","DOIUrl":"10.1016/j.ijsolstr.2024.113198","url":null,"abstract":"<div><div>The theory of classical linear elasticity predicts self-intersection in the neighborhood of interior points of anisotropic solids, crack tips, and corners. This physically unrealistic behavior is characterized by the violation of the local injectivity condition, according to which, the determinant of the deformation gradient, <span><math><mrow><mi>J</mi><mo>≜</mo><mo>det</mo><mi>F</mi></mrow></math></span>, must be positive. One way to impose this condition in elasticity consists of minimizing the total potential energy subjected to the condition <span><math><mrow><mi>J</mi><mo>≥</mo><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span>, where <span><math><mi>ɛ</mi></math></span> is a small positive parameter.</div><div>We present a minimization theory constrained by <span><math><mrow><mi>J</mi><mo>≥</mo><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span> for hyperelastic solids undergoing finite deformations and derive necessary conditions for a deformation field to be a minimizer, which include both continuity of traction and dissipation-free conditions across a surface of discontinuity. We then apply this theory in the analysis of equilibrium of an annular disk made of an orthotropic St Venant-Kirchhoff material. This material is a natural constitutive extension of its classical linear counterpart. The disk is fixed on its inner surface and compressed by a constant pressure on its outer surface.</div><div>The disk problem is formulated as both a boundary value problem (disk BVP) and a minimization problem (disk MP), which are solved in the context of both the classical and the constrained (<span><math><mrow><mi>J</mi><mo>≥</mo><mi>ɛ</mi></mrow></math></span>) nonlinear theories. These formulations yield non-smooth solutions for large enough pressure, which pose numerical difficulties. To address these difficulties, we use a phase-plane technique to construct a trajectory of solution for the disk BVP and the finite element method together with nonlinear programming tools to find a minimizer for the disk MP.</div><div>In the classical nonlinear theory, we find that there is a critical pressure <span><math><mover><mrow><mi>p</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>, which tends to zero as the inner radius of the disk tends to zero, above which a solution of either the disk BVP or the disk MP becomes non-smooth and predicts <span><math><mrow><mi>J</mi><mo>≤</mo><mn>0</mn></mrow></math></span>. In addition, <span><math><mover><mrow><mi>p</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> is smaller than its counterpart predicted by the classical linear theory and, therefore, serves as an upper bound below which the linear theory is valid.</div><div>In the constrained nonlinear theory, the solutions of both the disk BVP and the disk MP agree very well and satisfy all the necessary conditions for an admissible minimizer, including the injectivity condition. Analytical and numerical results show that, for an annular","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113198"},"PeriodicalIF":3.4,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153313","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}
Pub Date : 2025-01-07DOI: 10.1016/j.ijsolstr.2025.113219
Yaoze Zhuang , Deqing Yang , Qing Li , Xiaoming Geng
The vibro-acoustic spectrum characteristics for underwater thin-walled structures continue to attract attention. This study presents a load-bearing, wide-bandgap metastructure for modifying vibro-acoustic spectrum characteristics of a cylindrical shell. Initially, methods for calculating and evaluating the load-bearing capacity and bandgap characteristics of unit cells are established. Subsequently, an annular metastructure is configured in a cylindrical coordinate, broadening the bandgap and the range of radiated noise suppression through compound unit cells. Finally, by localized mass and reinforcement, the enhancement of macroscopic structural load-bearing capacity and the modified spectrum characteristics are achieved. This study provides a cylindrical shell in which internal vibration transmits through the flange to the shell and then generates radiated noise. The sound power of the assembly which is equipped with either the original support or the metastructures was obtained through experiments and simulations. The experimental study demonstrated a 3.1 dB noise reduction across a broad frequency range from 824 Hz to 1500 Hz, with over 50 % of the frequency characteristics significantly altered. Furthermore, the metastructure achieved a weight reduction of 2.16 kg compared with the original configuration. This study not only achieves the evaluation of the load-bearing capacity of the microscopic unit cell but also realizes the amplitude suppression and spectrum modification of radiated noise for underwater cylindrical shells.
{"title":"Modified vibro-acoustic spectrum characteristics for underwater cylindrical shells with mechanical metastructures","authors":"Yaoze Zhuang , Deqing Yang , Qing Li , Xiaoming Geng","doi":"10.1016/j.ijsolstr.2025.113219","DOIUrl":"10.1016/j.ijsolstr.2025.113219","url":null,"abstract":"<div><div>The vibro-acoustic spectrum characteristics for underwater thin-walled structures continue to attract attention. This study presents a load-bearing, wide-bandgap metastructure for modifying vibro-acoustic spectrum characteristics of a cylindrical shell. Initially, methods for calculating and evaluating the load-bearing capacity and bandgap characteristics of unit cells are established. Subsequently, an annular metastructure is configured in a cylindrical coordinate, broadening the bandgap and the range of radiated noise suppression through compound unit cells. Finally, by localized mass and reinforcement, the enhancement of macroscopic structural load-bearing capacity and the modified spectrum characteristics are achieved. This study provides a cylindrical shell in which internal vibration transmits through the flange to the shell and then generates radiated noise. The sound power of the assembly which is equipped with either the original support or the metastructures was obtained through experiments and simulations. The experimental study demonstrated a 3.1 dB noise reduction across a broad frequency range from 824 Hz to 1500 Hz, with over 50 % of the frequency characteristics significantly altered. Furthermore, the metastructure achieved a weight reduction of 2.16 kg compared with the original configuration. This study not only achieves the evaluation of the load-bearing capacity of the microscopic unit cell but also realizes the amplitude suppression and spectrum modification of radiated noise for underwater cylindrical shells.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113219"},"PeriodicalIF":3.4,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153316","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}
Pub Date : 2025-01-04DOI: 10.1016/j.ijsolstr.2024.113208
Annalisa Tresoldi , Jason Shore , Alfonso Pagani , Guglielmo Aglietti
The Deployable Rolled-up Composite Antenna - Synthetic Aperture Radar (DERCA-SAR) concept design is proposed for a 12U CubeSat low-power remote sensing application. A SAR reflectarray system is considered to be implemented on a High-Strain Composite (HSC) structure with a shallow “tape-measure” inspired shape. The stiffness required in the deployed state is provided by the cross-sectional curvature of the shell, which will be rigidly maintained at the root during stowage. To provide a low-mass solution for this application, the DERCA-SAR technology considers flattening and coiling the shell tip until it reaches the clamped root and deploys by releasing the elastic strain energy stored in the coiled configuration. In this paper, two analytical models are developed to describe the deployment dynamics of this structure and predict the deployment velocity that may impact the antenna performance. Given an initial coil radius , which is much smaller than the natural radius to fit a nanosatellite platform, the deployment occurs in two stages that have been revealed through experiments. The first blossoming phase is described as an expanding and uncoiling process based on the Lagrangian approach. The second and more chaotic phase of the deployment is modelled using a Hencky-type model that discretises the shell’s structure in a multi-pendulum system connected by elastic rotational hinges/springs. In this model, the shell’s stiffness is made to locally change based on the characteristic tape springs’ moment–rotation relationship and the implementation of a stiffness function. The analytical results are then compared to experimental data derived from deployment testing on samples of the shells with different material properties. The predictions from the two models capture the significant trends of the data well, and predict the maximum speed with an error of 10 %.
{"title":"Deployment dynamics of a high strain deployable rolled-up composite SAR antenna","authors":"Annalisa Tresoldi , Jason Shore , Alfonso Pagani , Guglielmo Aglietti","doi":"10.1016/j.ijsolstr.2024.113208","DOIUrl":"10.1016/j.ijsolstr.2024.113208","url":null,"abstract":"<div><div>The Deployable Rolled-up Composite Antenna - Synthetic Aperture Radar (DERCA-SAR) concept design is proposed for a 12U CubeSat low-power remote sensing application. A SAR reflectarray system is considered to be implemented on a High-Strain Composite (HSC) structure with a shallow “tape-measure” inspired shape. The stiffness required in the deployed state is provided by the cross-sectional curvature of the shell, which will be rigidly maintained at the root during stowage. To provide a low-mass solution for this application, the DERCA-SAR technology considers flattening and coiling the shell tip until it reaches the clamped root and deploys by releasing the elastic strain energy stored in the coiled configuration. In this paper, two analytical models are developed to describe the deployment dynamics of this structure and predict the deployment velocity that may impact the antenna performance. Given an initial coil radius <span><math><mi>r</mi></math></span>, which is much smaller than the natural radius <span><math><mi>R</mi></math></span> to fit a nanosatellite platform, the deployment occurs in two stages that have been revealed through experiments. The first blossoming phase is described as an expanding and uncoiling process based on the Lagrangian approach. The second and more chaotic phase of the deployment is modelled using a Hencky-type model that discretises the shell’s structure in a multi-pendulum system connected by elastic rotational hinges/springs. In this model, the shell’s stiffness is made to locally change based on the characteristic tape springs’ moment–rotation relationship and the implementation of a stiffness function. The analytical results are then compared to experimental data derived from deployment testing on samples of the shells with different material properties. The predictions from the two models capture the significant trends of the data well, and predict the maximum speed with an error of <span><math><mo><</mo></math></span> 10<!--> <!-->%.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113208"},"PeriodicalIF":3.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153314","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}
Pub Date : 2025-01-04DOI: 10.1016/j.ijsolstr.2025.113216
Shuyang Yu, Xueying Hu, Zilin Liang
The existences of cracks affect the strength and fracture morphologies of rock masses. However, there are few discussions on factors such as fissure apertures and quantities. Based on this background, sand 3D printing is used to prepare rock-like samples. Crack propagation experiments are carried out on fissured samples with different fissure apertures and fissure numbers. DIC technology is utilized to obtain the full-field strain distributions on specimen surfaces. Meanwhile, a meshless numerical method is developed to simulate rock damage evolutions. Results show that: Three crack types can be seen, wing cracks, shear cracks as well as main cracks. Wing crack extensions on two prefabricated fissures outer sides are along the loading direction, while inner side wing cracks overlap with two prefabricated fissures to form a “fusiformis-shaped part”. The propagation of shear cracks after wing cracks indicates final specimen failure. Main cracks exist in the circumstances with large fissure apertures. As fissure apertures increase, wing cracks initiating points deviate from tips, and the appearance of inner wing cracks in double fissure specimens precedes outer wing cracks. Stress–strain curves of the specimen experience five stages: 1) compressive stage; 2) elastic stage; 3) stress drop stage; 4) crack propagation stage and 5) failure stage. Finally, formation mechanisms of wing cracks, shear cracks, “fusiformis-shaped parts” as well as the mechanical influences of fissure apertures on the specimens are discussed.
{"title":"Exploring the elliptic fissure cracking mechanisms from the perspective of sand 3D printing technology and Meshfree numerical strategy","authors":"Shuyang Yu, Xueying Hu, Zilin Liang","doi":"10.1016/j.ijsolstr.2025.113216","DOIUrl":"10.1016/j.ijsolstr.2025.113216","url":null,"abstract":"<div><div>The existences of cracks affect the strength and fracture morphologies of rock masses. However, there are few discussions on factors such as fissure apertures and quantities. Based on this background, sand 3D printing is used to prepare rock-like samples. Crack propagation experiments are carried out on fissured samples with different fissure apertures and fissure numbers. DIC technology is utilized to obtain the full-field strain distributions on specimen surfaces. Meanwhile, a meshless numerical method is developed to simulate rock damage evolutions. Results show that: Three crack types can be seen, wing cracks, shear cracks as well as main cracks. Wing crack extensions on two prefabricated fissures outer sides are along the loading direction, while inner side wing cracks overlap with two prefabricated fissures to form a “fusiformis-shaped part”. The propagation of shear cracks after wing cracks indicates final specimen failure. Main cracks exist in the circumstances with large fissure apertures. As fissure apertures increase, wing cracks initiating points deviate from tips, and the appearance of inner wing cracks in double fissure specimens precedes outer wing cracks. Stress–strain curves of the specimen experience five stages: 1) compressive stage; 2) elastic stage; 3) stress drop stage; 4) crack propagation stage and 5) failure stage. Finally, formation mechanisms of wing cracks, shear cracks, “fusiformis-shaped parts” as well as the mechanical influences of fissure apertures on the specimens are discussed.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113216"},"PeriodicalIF":3.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153318","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}
Pub Date : 2025-01-04DOI: 10.1016/j.ijsolstr.2025.113215
Yuran Jin , Qing Peng , Xiaoming Liu
The woodpile structure shows exceptional cushioning and vibration reduction under impact. The impact, such as the case of a sphere impacting on stacked beams (a beam chain), has been studied using the discrete element method (DEM) in the literature, which shows that the DEM approach is limited to low-frequency vibrations, mostly up to the third harmonic mode triggered by the impact. However, many impact contacts, similar to step loads, will induce high-order modal vibrations (excited eigenmodes beyond the fifth modes). Present work encompasses the higher vibrational modes under such impact. With Timoshenko beams considering shear effect, the dynamics of sphere-woodpile impact is studied by coupling the superposition method for higher modes and the Hertz law for nonlinear contact. Result reveals the high mode vibration greatly reduces the contact force on the stacked beam, thus slender beam can expedite the dissipation of impact energy. Also, the higher-order vibrations enhance the speed of wave propagating within the beam chain and amplify attenuation effects. These insights offer a guidance for the design of impact-resistant structures and advanced shock absorbers.
{"title":"Impact attenuation of sphere on woodpile","authors":"Yuran Jin , Qing Peng , Xiaoming Liu","doi":"10.1016/j.ijsolstr.2025.113215","DOIUrl":"10.1016/j.ijsolstr.2025.113215","url":null,"abstract":"<div><div>The woodpile structure shows exceptional cushioning and vibration reduction under impact. The impact, such as the case of a sphere impacting on stacked beams (a beam chain), has been studied using the discrete element method (DEM) in the literature, which shows that the DEM approach is limited to low-frequency vibrations, mostly up to the third harmonic mode triggered by the impact. However, many impact contacts, similar to step loads, will induce high-order modal vibrations (excited eigenmodes beyond the fifth modes). Present work encompasses the higher vibrational modes under such impact. With Timoshenko beams considering shear effect, the dynamics of sphere-woodpile impact is studied by coupling the superposition method for higher modes and the Hertz law for nonlinear contact. Result reveals the high mode vibration greatly reduces the contact force on the stacked beam, thus slender beam can expedite the dissipation of impact energy. Also, the higher-order vibrations enhance the speed of wave propagating within the beam chain and amplify attenuation effects. These insights offer a guidance for the design of impact-resistant structures and advanced shock absorbers.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113215"},"PeriodicalIF":3.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153364","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}
Pub Date : 2025-01-03DOI: 10.1016/j.ijsolstr.2024.113211
Youxue Ban, Changwen Mi
This paper investigates the axisymmetric nanocontact of a gradient nanostructure, comprising an exponentially graded coating and a homogeneous half-space, under a rigid spherical indenter. The Steigmann–Ogden surface elastic theory is utilized to model the surface effects at the upper surface of the coating and the interface effects at the coating–substrate boundary. We derive nonclassical boundary conditions and, in conjunction with the displacement continuity across the interface, construct the integral equation describing the nanocontact using the Hankel integral transform. Along with the force equilibrium condition, this equation is discretized and collocated with Gauss–Chebyshev quadratures. An iterative algorithm is developed to solve the resulting algebraic system for contact pressure and radius of the contact circle. Validation against existing literature confirms the accuracy and reliability of the proposed solution method and numerical algorithm. Extensive parametric studies reveal the significant influence of surface and interface effects, the inhomogeneity index of the graded coating, and the indenter radius on nanocontact behavior. The surface effects, characterized by a reduction in contact radius, maximum stress, and subsidence, demonstrate a pronounced size dependency. Notably, soft coatings exhibit a more substantial impact, and the reduction of indenter radius or external load further amplifies these effects. The interface effects, though less pronounced than surface effects, also play a crucial role in affecting contact properties, particularly for hard graded coatings. These findings underscore the importance of considering both surface and interface effects in the design and analysis of nanostructured materials.
{"title":"On the axisymmetric nanoindentation of an exponentially graded coating–substrate structure with both surface and interface effects","authors":"Youxue Ban, Changwen Mi","doi":"10.1016/j.ijsolstr.2024.113211","DOIUrl":"10.1016/j.ijsolstr.2024.113211","url":null,"abstract":"<div><div>This paper investigates the axisymmetric nanocontact of a gradient nanostructure, comprising an exponentially graded coating and a homogeneous half-space, under a rigid spherical indenter. The Steigmann–Ogden surface elastic theory is utilized to model the surface effects at the upper surface of the coating and the interface effects at the coating–substrate boundary. We derive nonclassical boundary conditions and, in conjunction with the displacement continuity across the interface, construct the integral equation describing the nanocontact using the Hankel integral transform. Along with the force equilibrium condition, this equation is discretized and collocated with Gauss–Chebyshev quadratures. An iterative algorithm is developed to solve the resulting algebraic system for contact pressure and radius of the contact circle. Validation against existing literature confirms the accuracy and reliability of the proposed solution method and numerical algorithm. Extensive parametric studies reveal the significant influence of surface and interface effects, the inhomogeneity index of the graded coating, and the indenter radius on nanocontact behavior. The surface effects, characterized by a reduction in contact radius, maximum stress, and subsidence, demonstrate a pronounced size dependency. Notably, soft coatings exhibit a more substantial impact, and the reduction of indenter radius or external load further amplifies these effects. The interface effects, though less pronounced than surface effects, also play a crucial role in affecting contact properties, particularly for hard graded coatings. These findings underscore the importance of considering both surface and interface effects in the design and analysis of nanostructured materials.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113211"},"PeriodicalIF":3.4,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153368","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}
Pub Date : 2025-01-02DOI: 10.1016/j.ijsolstr.2024.113214
Xiangsheng Hu , Guowei Zeng , Minsheng Huang , Zhenhuan Li , Yaxin Zhu , Lv Zhao
Nickel-based and Cobalt-based superalloys (NBSA and CBSA) are widely used in hot-end components of aero engines for their excellent mechanical properties and special microstructures with both γ and γ’ phases. The γ’ phase exhibits a yield strength anomaly (YSA, i.e., the yield strength increases with the increase of temperature), which can significantly affect the overall mechanical behavior of superalloys. To investigate the necessary conditions for the generation of YSA in these L12-ordered NBSAs and CBSAs, the commonly used PPV model is improved with special consideration of the potential type I’ superdislocation core structure, and the related parameters and physical properties of superdislocations are achieved by the enhanced SVPN model including the lattice discreteness effect and by the DFT calculations. It is found that there are three possible superdislocation core structures (i.e., type I, type I’ and type II), but the type I’ core structure has the lowest total energy, and thus the formation of type I’ superdislocation configuration is the most energetically favorable at least when external loading is applied. For this, the influence of type I’ superdislocation on the generation of YSA behavior should be given special consideration. In addition, the energetically favorable type I’ configuration also exhibits the lowest predicted Peierls stress. Further, if the classical PPV model without considering the type I’ configuration is employed, it may give a wrong prediction for the YSA behavior of Ni3Al, Ni3Ga, Ni3Si, Ni3Ge and Co3Al0.5W0.5. However, by the present improved PPV model, predictions consistent with the experimental observation can be obtained. Consequently, the consideration of type I’ configuration in the present improved PPV model and the employment of enhanced SVPN model with lattice discreteness effect are necessary and appropriate.
{"title":"Prediction of yield strength anomaly by improved semi-discrete variation Peierls-Nabarro model for L12-ordered alloys Ni3X and Co3X","authors":"Xiangsheng Hu , Guowei Zeng , Minsheng Huang , Zhenhuan Li , Yaxin Zhu , Lv Zhao","doi":"10.1016/j.ijsolstr.2024.113214","DOIUrl":"10.1016/j.ijsolstr.2024.113214","url":null,"abstract":"<div><div>Nickel-based and Cobalt-based superalloys (NBSA and CBSA) are widely used in hot-end components of aero engines for their excellent mechanical properties and special microstructures with both <em>γ</em> and <em>γ’</em> phases. The <em>γ’</em> phase exhibits a yield strength anomaly (YSA, <em>i.e.</em>, the yield strength increases with the increase of temperature), which can significantly affect the overall mechanical behavior of superalloys. To investigate the necessary conditions for the generation of YSA in these L1<sub>2</sub>-ordered NBSAs and CBSAs, the commonly used PPV model is improved with special consideration of the potential type <em>I’</em> superdislocation core structure, and the related parameters and physical properties of superdislocations are achieved by the enhanced SVPN model including the lattice discreteness effect and by the DFT calculations. It is found that there are three possible superdislocation core structures (<em>i.e.</em>, type <em>I</em>, type <em>I’</em> and type <em>II</em>), but the type <em>I’</em> core structure has the lowest total energy, and thus the formation of type <em>I’</em> superdislocation configuration is the most energetically favorable at least when external loading is applied. For this, the influence of type <em>I’</em> superdislocation on the generation of YSA behavior should be given special consideration. In addition, the energetically favorable type <em>I’</em> configuration also exhibits the lowest predicted Peierls stress. Further, if the classical PPV model without considering the type <em>I’</em> configuration is employed, it may give a wrong prediction for the YSA behavior of Ni<sub>3</sub>Al, Ni<sub>3</sub>Ga, Ni<sub>3</sub>Si, Ni<sub>3</sub>Ge and Co<sub>3</sub>Al<sub>0.5</sub>W<sub>0.5</sub>. However, by the present improved PPV model, predictions consistent with the experimental observation can be obtained. Consequently, the consideration of type <em>I’</em> configuration in the present improved PPV model and the employment of enhanced SVPN model with lattice discreteness effect are necessary and appropriate.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"310 ","pages":"Article 113214"},"PeriodicalIF":3.4,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153315","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}
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