Because of their simplicity, efficiency and ability for parallelism, FFT-based methods are very attractive in the context of numerical periodic homogenization, especially when compared to standard FE codes used in the same context. They allow applying to a unit-cell a uniform average strain with a periodic strain fluctuation that is an unknown quantity. Solving the problem allows to evaluate the complete stress-strain fields. The present work proposes to extend the use of the method from uniform loadings (i.e. uniform applied strain) to strain gradient loadings (i.e. strain fields with a uniform strain gradient) while keeping the algorithm as simple as possible. The identification of a subset of strain gradient loadings allows for a minimally invasive modification of the iterative algorithm so that the implementation is straightforward. In spite of a reduced subset of 9 independent loadings among the 18 available, the second part of the paper demonstrates that it is enough for considering the homogenization of beams and plates. A first application validates the approach and compares it to another FFT-based method dedicated to the homogenization of plates. The second application concerns the homogenization of beams, for the first time considered (to author's knowledge) with an FFT-based solver. The method applies to different beam cross-sections and the proposition of using composite voxels drastically improves the numerical solution when the beam cross-section is not conform with the spatial discretization, especially for torsion loading. As a result, the massively parallel AMITEX_FFTP code has been slightly modified and now offers a new functionality, allowing the users to prescribe torsions and flexions to beam or plate heterogeneous unit-cells.
{"title":"A simple extension of FFT-based methods to strain gradient loadings - Application to the homogenization of beams and plates with linear and non-linear behaviors","authors":"L. Gélébart","doi":"10.46298/jtcam.6790","DOIUrl":"https://doi.org/10.46298/jtcam.6790","url":null,"abstract":"Because of their simplicity, efficiency and ability for parallelism, FFT-based methods are very attractive in the context of numerical periodic homogenization, especially when compared to standard FE codes used in the same context. They allow applying to a unit-cell a uniform average strain with a periodic strain fluctuation that is an unknown quantity. Solving the problem allows to evaluate the complete stress-strain fields. The present work proposes to extend the use of the method from uniform loadings (i.e. uniform applied strain) to strain gradient loadings (i.e. strain fields with a uniform strain gradient) while keeping the algorithm as simple as possible. The identification of a subset of strain gradient loadings allows for a minimally invasive modification of the iterative algorithm so that the implementation is straightforward. In spite of a reduced subset of 9 independent loadings among the 18 available, the second part of the paper demonstrates that it is enough for considering the homogenization of beams and plates. A first application validates the approach and compares it to another FFT-based method dedicated to the homogenization of plates. The second application concerns the homogenization of beams, for the first time considered (to author's knowledge) with an FFT-based solver. The method applies to different beam cross-sections and the proposition of using composite voxels drastically improves the numerical solution when the beam cross-section is not conform with the spatial discretization, especially for torsion loading. As a result, the massively parallel AMITEX_FFTP code has been slightly modified and now offers a new functionality, allowing the users to prescribe torsions and flexions to beam or plate heterogeneous unit-cells.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115221456","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 work, a fast explicit method, easy to implement numerically, is proposed in order to compute the effective behavior and the distribution of stresses in a general N-phase laminate made of parallel, planar and perfectly bonded interfaces. The solutions are exact for a homogeneous far-field loading and work for an arbitrary number of phases, a general linear anisotropic elasticity, as well as different uniform thermal and plastic strains in the phases. A simple direct analytical formula is also derived to compute the stress in a given phase once the effective behavior of the laminate is known. Moreover, the correctness of the proposed method is checked by comparisons with finite element simulation results on a same boundary value problem, showing excellent agreements. An application of the method is performed for a near-β titanium alloy with elongated grains, by comparing the level of internal stresses for different elastic loadings within a N-phase laminate made of 100,000 orientations and a 2-phase laminate of equal volume fraction with maximal elastic contrast. Interestingly, the maximum von Mises stress of the 2-phase laminate is always the lowest, which is explained by a volume fraction effect. Finally, comparisons with elastic self-consistent models considering oblate spheroidal grains of different aspect ratios are performed.
{"title":"Stress partitioning and effective behavior of N-phase laminates in anisotropic elasticity from a fast explicit method","authors":"T. Richeton","doi":"10.46298/jtcam.8506","DOIUrl":"https://doi.org/10.46298/jtcam.8506","url":null,"abstract":"In this work, a fast explicit method, easy to implement numerically, is proposed in order to compute the effective behavior and the distribution of stresses in a general N-phase laminate made of parallel, planar and perfectly bonded interfaces. The solutions are exact for a homogeneous far-field loading and work for an arbitrary number of phases, a general linear anisotropic elasticity, as well as different uniform thermal and plastic strains in the phases. A simple direct analytical formula is also derived to compute the stress in a given phase once the effective behavior of the laminate is known. Moreover, the correctness of the proposed method is checked by comparisons with finite element simulation results on a same boundary value problem, showing excellent agreements. An application of the method is performed for a near-β titanium alloy with elongated grains, by comparing the level of internal stresses for different elastic loadings within a N-phase laminate made of 100,000 orientations and a 2-phase laminate of equal volume fraction with maximal elastic contrast. Interestingly, the maximum von Mises stress of the 2-phase laminate is always the lowest, which is explained by a volume fraction effect. Finally, comparisons with elastic self-consistent models considering oblate spheroidal grains of different aspect ratios are performed.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129452152","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}
The objective of this paper is to present an energy damage criterion for cohesive zone models (CZM) within the framework of the non-linear thermodynamics of irreversible processes (TIP). An isotropic elastic damageable material is considered for isothermal transformations. Damage is then the only irreversible effect accompanying the deformation process and this mechanism is supposed to be fully dissipative. Once a separation law and a damage state variable have been chosen, the paper shows that the damage criterion can be automatically derived from the energy balance. From this observation, a CZM is derived for a given choice of traction-separation law and damage state variable and the quality of its numerical predictions is analyzed using an experimental benchmark bending test extracted from literature. Finally, damage, elastic and dissipated energy fields around the crack path are shown during this rupture test.
{"title":"A damage criterion based on energy balance for isotropic cohesive zone model","authors":"A. Chrysochoos, L. Daridon, M. Renouf","doi":"10.46298/jtcam.7056","DOIUrl":"https://doi.org/10.46298/jtcam.7056","url":null,"abstract":"The objective of this paper is to present an energy damage criterion for cohesive zone models (CZM) within the framework of the non-linear thermodynamics of irreversible processes (TIP). An isotropic elastic damageable material is considered for isothermal transformations. Damage is then the only irreversible effect accompanying the deformation process and this mechanism is supposed to be fully dissipative. Once a separation law and a damage state variable have been chosen, the paper shows that the damage criterion can be automatically derived from the energy balance. From this observation, a CZM is derived for a given choice of traction-separation law and damage state variable and the quality of its numerical predictions is analyzed using an experimental benchmark bending test extracted from literature. Finally, damage, elastic and dissipated energy fields around the crack path are shown during this rupture test.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128526612","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}
Computational homogenization allows to let the macroscopic constitutive behavior of materials emerge from microscale simulations without loss of generality with respect to microstructure and microscale constitutive response. Although computationally demanding, computational homogenization works very well for the hardening response of materials where the macroscopic stress and strain fields are smooth. However, in case of softening materials, when localization of deformation takes place, special care is needed to ensure objectivity of the method. In this paper, a generic multiscale computational homogenization approach for modeling onset and propagation of cracks in heterogeneous materials that is capable of considering various microscale mechanisms is presented. The common acoustic tensor bifurcation criterion is reinforced by an additional condition to help detect the localization mode more robustly. After the onset of macroscale localization, a key scale transition parameter is needed to translate the macroscopic displacement jump to an averaged strain over the micromodel domain. Then the macroscale crack is governed by a homogenized traction-separation relation evaluated from the underlying micromodel in which micro-failure accumulates. The scale transition parameter is studied for a range of different scenarios and endowed with a geometrical interpretation. Various numerical tests have been performed to confirm the objectivity and validity of the framework. The framework is generic in the sense that no assumptions on the microscale constitutive or kinematic representation of material failure are made in the scale transition. The framework is also highly compatible with the first order computational homogenization, which minimizes the additional complexity of adding macroscopic crack growth to the computational implementation.
{"title":"A computational homogenization framework with enhanced localization criterion for macroscopic cohesive failure in heterogeneous materials","authors":"Luoyilang Ke, F. P. van der Meer","doi":"10.46298/jtcam.7707","DOIUrl":"https://doi.org/10.46298/jtcam.7707","url":null,"abstract":"Computational homogenization allows to let the macroscopic constitutive behavior of materials emerge from microscale simulations without loss of generality with respect to microstructure and microscale constitutive response. Although computationally demanding, computational homogenization works very well for the hardening response of materials where the macroscopic stress and strain fields are smooth. However, in case of softening materials, when localization of deformation takes place, special care is needed to ensure objectivity of the method. In this paper, a generic multiscale computational homogenization approach for modeling onset and propagation of cracks in heterogeneous materials that is capable of considering various microscale mechanisms is presented. The common acoustic tensor bifurcation criterion is reinforced by an additional condition to help detect the localization mode more robustly. After the onset of macroscale localization, a key scale transition parameter is needed to translate the macroscopic displacement jump to an averaged strain over the micromodel domain. Then the macroscale crack is governed by a homogenized traction-separation relation evaluated from the underlying micromodel in which micro-failure accumulates. The scale transition parameter is studied for a range of different scenarios and endowed with a geometrical interpretation. Various numerical tests have been performed to confirm the objectivity and validity of the framework. The framework is generic in the sense that no assumptions on the microscale constitutive or kinematic representation of material failure are made in the scale transition. The framework is also highly compatible with the first order computational homogenization, which minimizes the additional complexity of adding macroscopic crack growth to the computational implementation.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115033913","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}
Up-to-date, back pain is among the most prevalent health issues and generally takes its origins from lesions of the annulus fibrosus (AF). While the AF ex vivo mechanical properties are increasingly well understood, in vivo data are still missing. In particular, very few studies have precisely measured the residual strains within the AF and thus the in vivo deformation state of the AF is still miss-interpreted and miss-evaluated. In this work, we propose an original and robust method for the AF residual strains quantification via digital image correlation technics. Ten pig annulus fibrosus were extracted from adjacent vertebrae followed by a radial incision to release the residual strains. The operations were filmed and then analyzed by a custom digital image correlation software in order to quantify the circumferential, radial and shear residual deformations. Our results show that residual strains are of the same order of magnitude than the in vivo one. The average circumferential strains are in tension on the outer periphery ([3.32; 5.94]%) and in compression on the inner periphery ([−6.4; −1.69]%). The mean radial residual strains are essentially in compression ([−10.4; 2.29]%). Locally, radial and circumferential residual strains can reach really large values up to 40% of compression. The mean shear strains remain very small (−0.04% ± 2.88%). This study also shows that circumferential and radial residual strains evolve linearly along the radius and non-linearly along the angle. We propose a simple model to predict their spatial variations. Our results and methods will allow the quantification of more realistic in vivo strains and stresses within the human intervertebral disc.
{"title":"Residual strains estimation in the annulus fibrosus through digital image correlation","authors":"G. Dusfour, D. Ambard, P. Canãdas, S. Lefloch","doi":"10.46298/jtcam.6971","DOIUrl":"https://doi.org/10.46298/jtcam.6971","url":null,"abstract":"Up-to-date, back pain is among the most prevalent health issues and generally takes its origins from lesions of the annulus fibrosus (AF). While the AF ex vivo mechanical properties are increasingly well understood, in vivo data are still missing. In particular, very few studies have precisely measured the residual strains within the AF and thus the in vivo deformation state of the AF is still miss-interpreted and miss-evaluated. In this work, we propose an original and robust method for the AF residual strains quantification via digital image correlation technics. Ten pig annulus fibrosus were extracted from adjacent vertebrae followed by a radial incision to release the residual strains. The operations were filmed and then analyzed by a custom digital image correlation software in order to quantify the circumferential, radial and shear residual deformations. Our results show that residual strains are of the same order of magnitude than the in vivo one. The average circumferential strains are in tension on the outer periphery ([3.32; 5.94]%) and in compression on the inner periphery ([−6.4; −1.69]%). The mean radial residual strains are essentially in compression ([−10.4; 2.29]%). Locally, radial and circumferential residual strains can reach really large values up to 40% of compression. The mean shear strains remain very small (−0.04% ± 2.88%). This study also shows that circumferential and radial residual strains evolve linearly along the radius and non-linearly along the angle. We propose a simple model to predict their spatial variations. Our results and methods will allow the quantification of more realistic in vivo strains and stresses within the human intervertebral disc.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125148759","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}
L. Laiarinandrasana, Clément Bertaux, N. Amouroux, Cristian Ovalle Rodas
With the goal of ensuring the security of passengers for automotive industry, the present work addresses the ductile fracture process of plasticized PVC. Dedicated clamped single edge notch bending (SENB) specimens were used to characterize the mechanisms of crack initiation and propagation for the studied material. The exploitation of the experimental database associated with finite element simulation of the crack propagation allowed, on the one hand, the calibration factor η p of this specific SENB specimen to be established, as a function of the crack depth ratio. On the other hand, the fracture toughness of the studied plasticized PVC was estimated to be 10.8 kJ/m 2 , value which was close to that reported in the literature for modified PVC. By using this fracture toughness value, a methodology aiming at the prediction of ductile crack initiation of the PVC skin integrated into a real dashboard (full scale test) was proposed.
{"title":"Ductile crack initiation and growth on a plasticized Polyvinylchloride during air bag deployment","authors":"L. Laiarinandrasana, Clément Bertaux, N. Amouroux, Cristian Ovalle Rodas","doi":"10.46298/jtcam.7401","DOIUrl":"https://doi.org/10.46298/jtcam.7401","url":null,"abstract":"With the goal of ensuring the security of passengers for automotive industry, the present work addresses the ductile fracture process of plasticized PVC. Dedicated clamped single edge notch bending (SENB) specimens were used to characterize the mechanisms of crack initiation and propagation for the studied material. The exploitation of the experimental database associated with finite element simulation of the crack propagation allowed, on the one hand, the calibration factor η p of this specific SENB specimen to be established, as a function of the crack depth ratio. On the other hand, the fracture toughness of the studied plasticized PVC was estimated to be 10.8 kJ/m 2 , value which was close to that reported in the literature for modified PVC. By using this fracture toughness value, a methodology aiming at the prediction of ductile crack initiation of the PVC skin integrated into a real dashboard (full scale test) was proposed.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115411312","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}
S. Neukirch, M. Yavari, N. Challamel, Olivier Thomas
International audience We compare different models describing the buckling, post-buckling and vibrations of elastic beams in the plane. Focus is put on the first buckled equilibrium solution and the first two vibration modes around it. In the incipient post-buckling regime, the classic Woinowsky-Krieger model is known to grasp the behavior of the system. It is based on the von Kármán approximation, a 2nd order expansion in the strains of the buckled beam. But as the curvature of the beam becomes larger, the Woinowsky-Krieger model starts to show limitations and we introduce a 3rd order model, derived from the geometrically-exact Kirchhoff model. We discuss and quantify the shortcomings of the Woinowsky-Krieger model and the contributions of the 3rd order terms in the new model, and we compare them both to the Kirchhoff model. Different ways to nondi-mensionalize the models are compared and we believe that, although this study is performed for specific boundary conditions, the present results have a general scope and can be used as abacuses to estimate the validity range of the simplified models.
{"title":"Comparison of the Von Kármán and Kirchhoff models for the post-buckling and vibrations of elastic beams","authors":"S. Neukirch, M. Yavari, N. Challamel, Olivier Thomas","doi":"10.46298/JTCAM.6828","DOIUrl":"https://doi.org/10.46298/JTCAM.6828","url":null,"abstract":"International audience\u0000 \u0000 We compare different models describing the buckling, post-buckling and vibrations of elastic beams in the plane. Focus is put on the first buckled equilibrium solution and the first two vibration modes around it. In the incipient post-buckling regime, the classic Woinowsky-Krieger model is known to grasp the behavior of the system. It is based on the von Kármán approximation, a 2nd order expansion in the strains of the buckled beam. But as the curvature of the beam becomes larger, the Woinowsky-Krieger model starts to show limitations and we introduce a 3rd order model, derived from the geometrically-exact Kirchhoff model. We discuss and quantify the shortcomings of the Woinowsky-Krieger model and the contributions of the 3rd order terms in the new model, and we compare them both to the Kirchhoff model. Different ways to nondi-mensionalize the models are compared and we believe that, although this study is performed for specific boundary conditions, the present results have a general scope and can be used as abacuses to estimate the validity range of the simplified models.\u0000","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126345825","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}
International audience Dynamic crack propagation in elastomer membranes is investigated; the focus is laid on cracks reaching the speed of shear waves in the material. The specific experimental setup developed to measure crack speed is presented in details. The protocol consists in (1) stretching an elastomer membrane under planar tension loading conditions, then (2) initiating a small crack on one side of the membrane. The crack speed is measured all along the crack path in both reference and actual configurations, including both acceleration and deceleration phases, i.e. non steady-state crack propagation phases. The influence of the prescribed stretch ratio on crack speed is analysed in the light of both these new experiments and the few previously published studies. Conclusions previously drawn for steady-state crack growth are extended to non steady-state conditions: stretch perpendicular to the crack path governs crack speed in intersonic crack propagation regime, and the role of the stretch in crack direction is minor.
{"title":"Non steady-state intersonic cracks in elastomer membranes under large static strain","authors":"T. Corre, M. Coret, E. Verron, B. Leblé","doi":"10.46298/JTCAM.6906","DOIUrl":"https://doi.org/10.46298/JTCAM.6906","url":null,"abstract":"International audience\u0000 \u0000 Dynamic crack propagation in elastomer membranes is investigated; the focus is laid on cracks reaching the speed of shear waves in the material. The specific experimental setup developed to measure crack speed is presented in details. The protocol consists in (1) stretching an elastomer membrane under planar tension loading conditions, then (2) initiating a small crack on one side of the membrane. The crack speed is measured all along the crack path in both reference and actual configurations, including both acceleration and deceleration phases, i.e. non steady-state crack propagation phases. The influence of the prescribed stretch ratio on crack speed is analysed in the light of both these new experiments and the few previously published studies. Conclusions previously drawn for steady-state crack growth are extended to non steady-state conditions: stretch perpendicular to the crack path governs crack speed in intersonic crack propagation regime, and the role of the stretch in crack direction is minor.\u0000","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114069461","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}
A. Harish, V. Nandurdikar, Shubham Deshpande, S. Andress
Tensegrity structures have been extensively studied over the last years due to their potential applications in modern engineering like metamaterials, deployable structures, planetary lander modules, etc. Many of the form-finding methods proposed continue to produce structures with one or more soft/swinging modes. These modes have been vividly highlighted and outlined as the grounds for these structures to be unsuitable as engineering structures. This work proposes a relationship between the number of rods and strings to satisfy the full-rank convexity criterion as a part of the form-finding process. Using the proposed form-finding process for the famous three-rod tensegrity, the work proposes an alternative three-rod ten-string that is stable. The work demonstrates that the stable tensegrities suitable for engineering are feasible and can be designed.
{"title":"Mathematics of stable tensegrity structures","authors":"A. Harish, V. Nandurdikar, Shubham Deshpande, S. Andress","doi":"10.46298/jtcam.7337","DOIUrl":"https://doi.org/10.46298/jtcam.7337","url":null,"abstract":"Tensegrity structures have been extensively studied over the last years due\u0000to their potential applications in modern engineering like metamaterials,\u0000deployable structures, planetary lander modules, etc. Many of the form-finding\u0000methods proposed continue to produce structures with one or more soft/swinging\u0000modes. These modes have been vividly highlighted and outlined as the grounds\u0000for these structures to be unsuitable as engineering structures. This work\u0000proposes a relationship between the number of rods and strings to satisfy the\u0000full-rank convexity criterion as a part of the form-finding process. Using the\u0000proposed form-finding process for the famous three-rod tensegrity, the work\u0000proposes an alternative three-rod ten-string that is stable. The work\u0000demonstrates that the stable tensegrities suitable for engineering are feasible\u0000and can be designed.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133101239","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}
A polycrystalline plasticity model, which incorporates the contribution of deformation twinning, is proposed. For this purpose, each material point is treated as a composite material consisting of a parent constituent and multiple twin variants. In the constitutive equations, the twin volume fractions and their spatial gradients are treated as external state variables to account for the contribution of twin boundaries to free energy. The set of constitutive relations is implemented in a spectral solver, which allows solving the differential equations resulting from equilibrium and compatibility conditions. The proposed model is then used to investigate the behavior of a AZ31 magnesium alloy. For the investigated loading conditions, the mechanical behavior is controlled by the joint contribution of basal slip and tensile twinning. Also, according to the numerical results, the development of crystallographic texture, morphological texture and internal stresses is consistent with the experimental observations of the literature.
{"title":"A non-local model for the description of twinning in polycrystalline\u0000 materials in the context of infinitesimal strains: application to a magnesium\u0000 alloy","authors":"C. Mareau, H. Abdolvand","doi":"10.46298/jtcam.7562","DOIUrl":"https://doi.org/10.46298/jtcam.7562","url":null,"abstract":"A polycrystalline plasticity model, which incorporates the contribution of\u0000deformation twinning, is proposed. For this purpose, each material point is\u0000treated as a composite material consisting of a parent constituent and multiple\u0000twin variants. In the constitutive equations, the twin volume fractions and\u0000their spatial gradients are treated as external state variables to account for\u0000the contribution of twin boundaries to free energy. The set of constitutive\u0000relations is implemented in a spectral solver, which allows solving the\u0000differential equations resulting from equilibrium and compatibility conditions.\u0000The proposed model is then used to investigate the behavior of a AZ31 magnesium\u0000alloy. For the investigated loading conditions, the mechanical behavior is\u0000controlled by the joint contribution of basal slip and tensile twinning. Also,\u0000according to the numerical results, the development of crystallographic\u0000texture, morphological texture and internal stresses is consistent with the\u0000experimental observations of the literature.","PeriodicalId":115014,"journal":{"name":"Journal of Theoretical, Computational and Applied Mechanics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114958497","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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