Pub Date : 2024-02-14DOI: 10.1177/10812865231223921
S Syed Ansari, Amit Acharya, Alankar Alankar
A continuum grain boundary model is developed, which uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a one-dimensional (1D) grain array. The model uses a continuum representation of the misorientation in terms of spatial gradients of the orientation as a fundamental field. The grain boundary energy density employed is non-convex in this orientation gradient, based on physical grounds. Simple gradient descent dynamics of the energy are utilized for idealized microstructure evolution, which requires higher-order regularization of the energy density for the model to be well set; the regularization is physically justified. Microstructure evolution is presented using two plausible energy density functions, both defined from the same experimental data: a “smooth” and a “cusp” energy density. Results of grain boundary equilibria and microstructure evolution representing grain reorientation in 1D are presented. The different shapes of the energy density functions representing a common data set are shown to result in different overall microstructural evolution of the system. Mathematically, the constructed energy functional formally is of the Aviles–Giga/Cross–Newell type but with unequal well depths, resulting in a difference in the structural feature of solutions that can be identified with grain boundaries, as well as in the approach to equilibria from identical initial conditions. This study also investigates the metastability of grain boundaries. It supports the general thermodynamics belief that they persist for extended periods before eventually vanishing due to the lowest energy configuration favored by fluctuations over infinite time.
{"title":"An experimentally informed continuum grain boundary model","authors":"S Syed Ansari, Amit Acharya, Alankar Alankar","doi":"10.1177/10812865231223921","DOIUrl":"https://doi.org/10.1177/10812865231223921","url":null,"abstract":"A continuum grain boundary model is developed, which uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a one-dimensional (1D) grain array. The model uses a continuum representation of the misorientation in terms of spatial gradients of the orientation as a fundamental field. The grain boundary energy density employed is non-convex in this orientation gradient, based on physical grounds. Simple gradient descent dynamics of the energy are utilized for idealized microstructure evolution, which requires higher-order regularization of the energy density for the model to be well set; the regularization is physically justified. Microstructure evolution is presented using two plausible energy density functions, both defined from the same experimental data: a “smooth” and a “cusp” energy density. Results of grain boundary equilibria and microstructure evolution representing grain reorientation in 1D are presented. The different shapes of the energy density functions representing a common data set are shown to result in different overall microstructural evolution of the system. Mathematically, the constructed energy functional formally is of the Aviles–Giga/Cross–Newell type but with unequal well depths, resulting in a difference in the structural feature of solutions that can be identified with grain boundaries, as well as in the approach to equilibria from identical initial conditions. This study also investigates the metastability of grain boundaries. It supports the general thermodynamics belief that they persist for extended periods before eventually vanishing due to the lowest energy configuration favored by fluctuations over infinite time.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"195 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-25DOI: 10.1177/10812865231217096
Oscar Cosserat, Camille Laurent-Gengoux, Vladimir Salnikov
We recall the question of geometric integrators in the context of Poisson geometry and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and compared to traditional methods.
{"title":"Numerical methods in Poisson geometry and their application to mechanics","authors":"Oscar Cosserat, Camille Laurent-Gengoux, Vladimir Salnikov","doi":"10.1177/10812865231217096","DOIUrl":"https://doi.org/10.1177/10812865231217096","url":null,"abstract":"We recall the question of geometric integrators in the context of Poisson geometry and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and compared to traditional methods.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139952619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-08DOI: 10.1177/10812865231209412
Giuseppe Bevilacqua, Gaetano Napoli, S. Turzi
We study the delamination induced by the growth of a thin adhesive sheet from a cylindrical, rigid substrate. Neglecting the deformations along the axis of the cylinder, we treat the sheet as a one-dimensional flexible and compressible ring, which adheres to the substrate by capillary adhesion. Using the calculus of variations, we obtain the equilibrium equations and in particular arrive at a transversality condition involving in a non-trivial way the curvature of the substrate, the extensibility of the ring and capillary adhesion. By numerically solving the equilibrium equations, we show that delamination by growth occurs through a discontinuous transition from the fully adherent solution to the partially delaminated one. The shape of the delaminated part can take the form either of a ruck, with a small slope, or a fold, with a large slope. Furthermore, in the weak adhesion regime, complete delamination may occur. We construct the phase diagram between the different solutions in the parameter space. In the quasi-incompressible limit, numerical results are also supported by asymptotic calculations both in the strong and weak adhesion regimes.
{"title":"Growth-induced delamination of an elastic film adhered to a cylinder","authors":"Giuseppe Bevilacqua, Gaetano Napoli, S. Turzi","doi":"10.1177/10812865231209412","DOIUrl":"https://doi.org/10.1177/10812865231209412","url":null,"abstract":"We study the delamination induced by the growth of a thin adhesive sheet from a cylindrical, rigid substrate. Neglecting the deformations along the axis of the cylinder, we treat the sheet as a one-dimensional flexible and compressible ring, which adheres to the substrate by capillary adhesion. Using the calculus of variations, we obtain the equilibrium equations and in particular arrive at a transversality condition involving in a non-trivial way the curvature of the substrate, the extensibility of the ring and capillary adhesion. By numerically solving the equilibrium equations, we show that delamination by growth occurs through a discontinuous transition from the fully adherent solution to the partially delaminated one. The shape of the delaminated part can take the form either of a ruck, with a small slope, or a fold, with a large slope. Furthermore, in the weak adhesion regime, complete delamination may occur. We construct the phase diagram between the different solutions in the parameter space. In the quasi-incompressible limit, numerical results are also supported by asymptotic calculations both in the strong and weak adhesion regimes.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"34 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139446521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-06DOI: 10.1177/10812865231203154
Derek E Moulton, H. Oliveri
In this paper, we propose a mechanical model for a game of tug of war (rope pulling). We focus on a game opposing two players, modelling each player’s body as a structure composed of straight rods that can be actuated in three different ways to generate a pulling force. We first examine the static problem of two opponents being in a deadlock configuration of mechanical equilibrium; here we show that this situation is essentially governed by the ratio of masses of the players, with the heavier player having a strong advantage. We then turn to the dynamic problem and model the response of the system to an abrupt change in activation by one of the players. In this case, the system exhibits a nontrivial response; in particular, we compare a sudden pulling and a sudden “letting up,” and demonstrate the existence of regimes in which the lighter player can momentarily take the advantage.
{"title":"The mathematics and mechanics of tug of war","authors":"Derek E Moulton, H. Oliveri","doi":"10.1177/10812865231203154","DOIUrl":"https://doi.org/10.1177/10812865231203154","url":null,"abstract":"In this paper, we propose a mechanical model for a game of tug of war (rope pulling). We focus on a game opposing two players, modelling each player’s body as a structure composed of straight rods that can be actuated in three different ways to generate a pulling force. We first examine the static problem of two opponents being in a deadlock configuration of mechanical equilibrium; here we show that this situation is essentially governed by the ratio of masses of the players, with the heavier player having a strong advantage. We then turn to the dynamic problem and model the response of the system to an abrupt change in activation by one of the players. In this case, the system exhibits a nontrivial response; in particular, we compare a sudden pulling and a sudden “letting up,” and demonstrate the existence of regimes in which the lighter player can momentarily take the advantage.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"4 12","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139380453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-06DOI: 10.1177/10812865231206544
Jan Hinrichsen, Lea Feiler, Nina Reiter, Lars Bräuer, M. Schicht, Friedrich Paulsen, S. Budday
The mechanical properties of human brain tissue remain far from being fully understood. One aspect that has gained more attention recently is their regional dependency, as the brain’s microstructure varies significantly from one region to another. Understanding the correlation between tissue components and the mechanical behavior is an important step toward better understanding how human brain tissue properties change in space and time and to develop highly spatially resolved constitutive models for large-scale brain simulations. Here, we analyze the correlation between human brain tissue components quantified through enzyme-linked immunosorbent assays (ELISA) and material parameters obtained through an inverse parameter identification scheme based on a hyperelastic Ogden model and multimodal mechanical testing data for eight regions of the brain. We use neural networks as a metamodel to save computational costs. The networks are trained on finite element simulation outputs and are able to replace the simulations in the initial optimization step. We identified strong dependencies between mechanical properties and Iba1 associated with microglia cells, collagen VI, GFAP associated with astrocytes, and collagen IV. These results advance our understanding of microstructure-mechanics relations in human brain tissue and will contribute to the development of highly spatially resolved microstructure-informed constitutive models.
人类脑组织的机械特性远未被完全了解。最近越来越受关注的一个方面是它们的区域依赖性，因为大脑的微观结构在不同区域之间存在显著差异。了解组织成分与力学行为之间的相关性是更好地理解人类脑组织特性在空间和时间上如何变化的重要一步，也是为大规模脑模拟开发高空间分辨率构成模型的重要一步。在这里，我们分析了通过酶联免疫吸附试验（ELISA）量化的人脑组织成分与通过基于超弹性奥格登模型的反参数识别方案获得的材料参数之间的相关性，以及大脑八个区域的多模态力学测试数据。我们使用神经网络作为元模型，以节省计算成本。神经网络根据有限元模拟输出进行训练，能够在初始优化步骤中取代模拟输出。我们发现机械性能与小胶质细胞相关的 Iba1、胶原蛋白 VI、星形胶质细胞相关的 GFAP 和胶原蛋白 IV 之间存在很强的依赖关系。这些结果加深了我们对人类脑组织微观结构-力学关系的理解，并将有助于开发高度空间分辨的微观结构信息构成模型。
{"title":"Identifying composition-mechanics relations in human brain tissue based on neural-network-enhanced inverse parameter identification","authors":"Jan Hinrichsen, Lea Feiler, Nina Reiter, Lars Bräuer, M. Schicht, Friedrich Paulsen, S. Budday","doi":"10.1177/10812865231206544","DOIUrl":"https://doi.org/10.1177/10812865231206544","url":null,"abstract":"The mechanical properties of human brain tissue remain far from being fully understood. One aspect that has gained more attention recently is their regional dependency, as the brain’s microstructure varies significantly from one region to another. Understanding the correlation between tissue components and the mechanical behavior is an important step toward better understanding how human brain tissue properties change in space and time and to develop highly spatially resolved constitutive models for large-scale brain simulations. Here, we analyze the correlation between human brain tissue components quantified through enzyme-linked immunosorbent assays (ELISA) and material parameters obtained through an inverse parameter identification scheme based on a hyperelastic Ogden model and multimodal mechanical testing data for eight regions of the brain. We use neural networks as a metamodel to save computational costs. The networks are trained on finite element simulation outputs and are able to replace the simulations in the initial optimization step. We identified strong dependencies between mechanical properties and Iba1 associated with microglia cells, collagen VI, GFAP associated with astrocytes, and collagen IV. These results advance our understanding of microstructure-mechanics relations in human brain tissue and will contribute to the development of highly spatially resolved microstructure-informed constitutive models.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"11 24","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139380181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-04DOI: 10.1177/10812865231213321
KP Soldatos
{"title":"Author’s response to Shariff et al. [1]: Basic errors in couple-stress hyperelasticity articles","authors":"KP Soldatos","doi":"10.1177/10812865231213321","DOIUrl":"https://doi.org/10.1177/10812865231213321","url":null,"abstract":"","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"49 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139386596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-04DOI: 10.1177/10812865231213311
M. Shariff, R. Bustamante, J. Merodio
We highlight the basic errors found in a related set of couple-stress hyperelasticity articles and evince some statements are incorrect, which suggest that the results obtained in these set of articles are questionable.
{"title":"Basic errors in couple-stress hyperelasticity articles","authors":"M. Shariff, R. Bustamante, J. Merodio","doi":"10.1177/10812865231213311","DOIUrl":"https://doi.org/10.1177/10812865231213311","url":null,"abstract":"We highlight the basic errors found in a related set of couple-stress hyperelasticity articles and evince some statements are incorrect, which suggest that the results obtained in these set of articles are questionable.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"51 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139385079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-03DOI: 10.1177/10812865231214262
Heiko Topol, Alejandro Font, Andrey Melnikov, Jesús Lacalle, M. Stoffel, J. Merodio
We consider the bifurcation and post-bifurcation of an extended and inflated circular cylindrical membrane under limited extensibility of its constituents. First, for illustration of the limited extensibility effect, a membrane made of the (isotropic) Gent model is briefly analyzed. Second, the membrane is considered to be made of an isotropic ground substance reinforced with fibers symmetrically arranged in two helically distributed families which are mechanically equivalent. The mechanical behavior of the fibers in a similar way to the (isotropic) Gent model is taken to reflect fiber limited extensibility. In particular, the materials under consideration are NH models augmented with two functions called reinforcing models, each one accounting for unidirectional reinforcement. For a specific material, since both families are mechanically equivalent, the reinforcing models are equal. The nature of the anisotropy considered, i.e., the reinforcing model, can depend only on the stretch in the fiber direction or can depend on the fiber stretch and also can have an influence on the shear response of the material (i.e., it also captures shearing in the fiber direction). The limitation associated with the material anisotropic deformability as well as the arrangement of the material constituents is discussed with respect to the initiation of bulging and necking for the membrane. The subsequent consequences for configurations in equilibrium during post-bifurcation are also studied in detail and a variety of results are given in terms of the limited extensibility (deformability) of the fibers as well as their mechanical response and arrangement (fiber winding angle).
{"title":"On the inflation, bulging/necking bifurcation and post-bifurcation of a cylindrical membrane under limited extensibility of its constituents","authors":"Heiko Topol, Alejandro Font, Andrey Melnikov, Jesús Lacalle, M. Stoffel, J. Merodio","doi":"10.1177/10812865231214262","DOIUrl":"https://doi.org/10.1177/10812865231214262","url":null,"abstract":"We consider the bifurcation and post-bifurcation of an extended and inflated circular cylindrical membrane under limited extensibility of its constituents. First, for illustration of the limited extensibility effect, a membrane made of the (isotropic) Gent model is briefly analyzed. Second, the membrane is considered to be made of an isotropic ground substance reinforced with fibers symmetrically arranged in two helically distributed families which are mechanically equivalent. The mechanical behavior of the fibers in a similar way to the (isotropic) Gent model is taken to reflect fiber limited extensibility. In particular, the materials under consideration are NH models augmented with two functions called reinforcing models, each one accounting for unidirectional reinforcement. For a specific material, since both families are mechanically equivalent, the reinforcing models are equal. The nature of the anisotropy considered, i.e., the reinforcing model, can depend only on the stretch in the fiber direction or can depend on the fiber stretch and also can have an influence on the shear response of the material (i.e., it also captures shearing in the fiber direction). The limitation associated with the material anisotropic deformability as well as the arrangement of the material constituents is discussed with respect to the initiation of bulging and necking for the membrane. The subsequent consequences for configurations in equilibrium during post-bifurcation are also studied in detail and a variety of results are given in terms of the limited extensibility (deformability) of the fibers as well as their mechanical response and arrangement (fiber winding angle).","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"142 18","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139387469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-01-02DOI: 10.1177/10812865231217640
M. Shirani, Mircea Bîrsan, D. Steigmann
The quasiconvexity inequality associated with energy minimizers is derived in the context of a nonlinear Cosserat elasticity theory for fiber-reinforced elastic solids in which the intrinsic flexural and torsional elasticities of the fibers are taken into account explicitly. The derivation accounts for non-standard kinematic constraints, associated with the materiality of the embedded fibers, connecting the deformation gradient and the Cosserat rotation field.
{"title":"Quasiconvexity in a model of fiber-reinforced solids based on Cosserat elasticity theory","authors":"M. Shirani, Mircea Bîrsan, D. Steigmann","doi":"10.1177/10812865231217640","DOIUrl":"https://doi.org/10.1177/10812865231217640","url":null,"abstract":"The quasiconvexity inequality associated with energy minimizers is derived in the context of a nonlinear Cosserat elasticity theory for fiber-reinforced elastic solids in which the intrinsic flexural and torsional elasticities of the fibers are taken into account explicitly. The derivation accounts for non-standard kinematic constraints, associated with the materiality of the embedded fibers, connecting the deformation gradient and the Cosserat rotation field.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"142 24","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139452956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2023-12-18DOI: 10.1177/10812865231208016
Davide Ambrosi, L. Deorsola, Stefano Turzi, Marta Zoppello
This paper investigates the role of mechanics in the morphogenesis of the annulus of the mitral valve. We represent the annulus in its embryonic stage as an elastic ring and we perform a mechanical simulation of the development process applying a distributed torque on the rod: because of the mechanical action of the other growing cardiac chambers on the atrio-ventricular region, it departs from a planar circular shape. The numerical integration of the mathematical rod model subject to a bending load yields a shape very near to the one reported in the medical literature as anatomical reference for healthy patients. To make the comparison quantitative, we illustrate a numerical approach to match two curves in 3D defining their distance in a proper mathematical way. Such a methodology is first applied to compare the annular shape resulting from the mechanical model with an anatomical reference “master” shape and it is then applied to set to clinical data extracted from MRI for a cohort of healthy patients. The good agreement among anatomical master description, numerical mechanical model, and clinical data supports our speculation about a possible role of mechanics in determining the shape of the mitral valve.
{"title":"The shape of the mitral annulus: A hypothesis of mechanical morphogenesis","authors":"Davide Ambrosi, L. Deorsola, Stefano Turzi, Marta Zoppello","doi":"10.1177/10812865231208016","DOIUrl":"https://doi.org/10.1177/10812865231208016","url":null,"abstract":"This paper investigates the role of mechanics in the morphogenesis of the annulus of the mitral valve. We represent the annulus in its embryonic stage as an elastic ring and we perform a mechanical simulation of the development process applying a distributed torque on the rod: because of the mechanical action of the other growing cardiac chambers on the atrio-ventricular region, it departs from a planar circular shape. The numerical integration of the mathematical rod model subject to a bending load yields a shape very near to the one reported in the medical literature as anatomical reference for healthy patients. To make the comparison quantitative, we illustrate a numerical approach to match two curves in 3D defining their distance in a proper mathematical way. Such a methodology is first applied to compare the annular shape resulting from the mechanical model with an anatomical reference “master” shape and it is then applied to set to clinical data extracted from MRI for a cohort of healthy patients. The good agreement among anatomical master description, numerical mechanical model, and clinical data supports our speculation about a possible role of mechanics in determining the shape of the mitral valve.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":" 17","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138994827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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