Pub Date : 2023-12-16DOI: 10.1177/10812865231213408
Cheng Huang, Ming Dai
The plane deformation of an infinite elastic matrix enclosing a single circular inclusion incorporating stretching and bending resistance for the inclusion–matrix interface is revisited using a refined linearized version of the Steigmann–Ogden model. This refined version of the Steigmann–Ogden model differs from other linearized counterparts in the literature mainly in that the tangential force of the interface defined in this version depends not only on the stretch of the interface but also on the bending moment and initial curvature of the interface (the corresponding bending moment relies on the change in the real curvature of the interface during deformation). Closed-form results are derived for the full elastic field in inclusion–matrix structure induced by an arbitrary uniform in-plane far-field loading. It is identified that with this refined version of the Steigmann–Ogden model a uniform stress distribution could be achieved inside the inclusion for any non-hydrostatic far-field loading when [Formula: see text] (where R is the radius of the inclusion, while [Formula: see text] and [Formula: see text] are the stretching and bending stiffness of the interface). Explicit expressions are also obtained for the effective transverse properties of composite materials containing a large number of unidirectional circular cylindrical inclusions using, respectively, the dilute and Mori–Tanaka homogenization methods. Numerical examples are presented to illustrate the differences between the refined version and two typical counterparts of the Steigmann–Ogden model in evaluating the stress field around a circular nanosized inclusion and the effective properties of the corresponding homogenized composites.
{"title":"Circular inclusion with a refined linearized version of Steigmann–Ogden model","authors":"Cheng Huang, Ming Dai","doi":"10.1177/10812865231213408","DOIUrl":"https://doi.org/10.1177/10812865231213408","url":null,"abstract":"The plane deformation of an infinite elastic matrix enclosing a single circular inclusion incorporating stretching and bending resistance for the inclusion–matrix interface is revisited using a refined linearized version of the Steigmann–Ogden model. This refined version of the Steigmann–Ogden model differs from other linearized counterparts in the literature mainly in that the tangential force of the interface defined in this version depends not only on the stretch of the interface but also on the bending moment and initial curvature of the interface (the corresponding bending moment relies on the change in the real curvature of the interface during deformation). Closed-form results are derived for the full elastic field in inclusion–matrix structure induced by an arbitrary uniform in-plane far-field loading. It is identified that with this refined version of the Steigmann–Ogden model a uniform stress distribution could be achieved inside the inclusion for any non-hydrostatic far-field loading when [Formula: see text] (where R is the radius of the inclusion, while [Formula: see text] and [Formula: see text] are the stretching and bending stiffness of the interface). Explicit expressions are also obtained for the effective transverse properties of composite materials containing a large number of unidirectional circular cylindrical inclusions using, respectively, the dilute and Mori–Tanaka homogenization methods. Numerical examples are presented to illustrate the differences between the refined version and two typical counterparts of the Steigmann–Ogden model in evaluating the stress field around a circular nanosized inclusion and the effective properties of the corresponding homogenized composites.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 4p2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138968074","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 : 2023-12-14DOI: 10.1177/10812865231207401
R. Bustamante, K. Rajagopal, Oscar Orellana
The circumferential shear of a nonlinear isotropic incompressible elastic annulus is studied using the neo-Hookean, Ogden constitutive relations in addition to a new constitutive relation for the Hencky strain in terms of the Cauchy stress. The predictions of the three constitutive relations to the specific boundary value problem are delineated. In view of the predictions being quite distinct between the new constitutive relation studied and that for the Ogden constitutive relation, it would be worthwhile to carry out an experiment to determine the efficacy of the models.
{"title":"Circumferential shear for an incompressible non-Green elastic cylindrical annulus","authors":"R. Bustamante, K. Rajagopal, Oscar Orellana","doi":"10.1177/10812865231207401","DOIUrl":"https://doi.org/10.1177/10812865231207401","url":null,"abstract":"The circumferential shear of a nonlinear isotropic incompressible elastic annulus is studied using the neo-Hookean, Ogden constitutive relations in addition to a new constitutive relation for the Hencky strain in terms of the Cauchy stress. The predictions of the three constitutive relations to the specific boundary value problem are delineated. In view of the predictions being quite distinct between the new constitutive relation studied and that for the Ogden constitutive relation, it would be worthwhile to carry out an experiment to determine the efficacy of the models.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"2017 9","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001703","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 : 2023-12-08DOI: 10.1177/10812865231209975
MA Güler, Y. Alinia, E. Radi
This study investigates the contact mechanics of a thin film laying on an elastic substrate within the context of couple-stress elasticity. It aims to introduce the effects of material internal length scale, which has proven an effective way of modeling structures at micro- to nano-scales, allowing to capture their size-dependent behavior. Specifically, stress analysis for a thin film bonded to a couple-stress elastic half-space is considered under plane strain loading conditions by assuming that both shear stress and couple tractions are exchanged between the thin film and the substrate. The problem is converted to a singular integral equation, which is solved by expanding the shear stress tractions as a Chebyshev series. The results show that the introduction of couple tractions decreases the shear stress tractions and the axial load in the thin film. When the characteristic length is sufficiently small, but still finite, the results for classical elastic behavior are approached.
{"title":"Couple-stress effects in a thin film bonded to a half-space","authors":"MA Güler, Y. Alinia, E. Radi","doi":"10.1177/10812865231209975","DOIUrl":"https://doi.org/10.1177/10812865231209975","url":null,"abstract":"This study investigates the contact mechanics of a thin film laying on an elastic substrate within the context of couple-stress elasticity. It aims to introduce the effects of material internal length scale, which has proven an effective way of modeling structures at micro- to nano-scales, allowing to capture their size-dependent behavior. Specifically, stress analysis for a thin film bonded to a couple-stress elastic half-space is considered under plane strain loading conditions by assuming that both shear stress and couple tractions are exchanged between the thin film and the substrate. The problem is converted to a singular integral equation, which is solved by expanding the shear stress tractions as a Chebyshev series. The results show that the introduction of couple tractions decreases the shear stress tractions and the axial load in the thin film. When the characteristic length is sufficiently small, but still finite, the results for classical elastic behavior are approached.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"45 36","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588574","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 : 2023-12-08DOI: 10.1177/10812865231210188
L. A. Mihai
{"title":"A mathematical mechanics mixed tape: Editor’s foreword to special issue in honor of Alain Goriely","authors":"L. A. Mihai","doi":"10.1177/10812865231210188","DOIUrl":"https://doi.org/10.1177/10812865231210188","url":null,"abstract":"","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"45 43","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588691","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 : 2023-12-07DOI: 10.1177/10812865231204972
L. Greco, Domenico Castello, Massimo Cuomo
We present a new invariant numerical formulation suitable for the analysis of Kirchhoff–Love rod model based on the smallest rotation map for which the two kinematic descriptors are the placement of the centroid curve and the rotation angle that describes the orientation of the cross-section. In order to guarantee objectivity with respect to a rigid body motion, the spherical linear interpolation ( slerp) for the rotations is introduced. A new hierarchical interpolation for the rotation angle of the cross-section is proposed, composed by the drilling rotation (with respect to the unit tangent of the centroid curve) contained in the geodetic interpolation of the ends’ rotations plus an additional polynomial correction term. This correction term is needed in order to enhance the accuracy of the proposed finite element (FE) formulation. The FE model implicitly guarantees the G1 continuity conditions, thanks to a change in the parametrization of the centroid curve that leads to a generalization of the one-dimensional (1D) Hermitian interpolation. A mixed formulation is used in order to avoid locking and improve the computational efficiency of the method. A symmetric tangent stiffness operator is obtained performing the second covariant derivative of the mixed functional for which the Levi-Civita connection of the configurations manifold of the rod is needed. The objectivity, the robustness, and accuracy of the G1-conforming formulation are confirmed by means of several numerical examples.
{"title":"An objective and accurate G1-conforming mixed Bézier FE-formulation for Kirchhoff–Love rods","authors":"L. Greco, Domenico Castello, Massimo Cuomo","doi":"10.1177/10812865231204972","DOIUrl":"https://doi.org/10.1177/10812865231204972","url":null,"abstract":"We present a new invariant numerical formulation suitable for the analysis of Kirchhoff–Love rod model based on the smallest rotation map for which the two kinematic descriptors are the placement of the centroid curve and the rotation angle that describes the orientation of the cross-section. In order to guarantee objectivity with respect to a rigid body motion, the spherical linear interpolation ( slerp) for the rotations is introduced. A new hierarchical interpolation for the rotation angle of the cross-section is proposed, composed by the drilling rotation (with respect to the unit tangent of the centroid curve) contained in the geodetic interpolation of the ends’ rotations plus an additional polynomial correction term. This correction term is needed in order to enhance the accuracy of the proposed finite element (FE) formulation. The FE model implicitly guarantees the G1 continuity conditions, thanks to a change in the parametrization of the centroid curve that leads to a generalization of the one-dimensional (1D) Hermitian interpolation. A mixed formulation is used in order to avoid locking and improve the computational efficiency of the method. A symmetric tangent stiffness operator is obtained performing the second covariant derivative of the mixed functional for which the Levi-Civita connection of the configurations manifold of the rod is needed. The objectivity, the robustness, and accuracy of the G1-conforming formulation are confirmed by means of several numerical examples.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"79 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138590683","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 : 2023-12-05DOI: 10.1177/10812865231212150
Zhenmin Zou, Shuguang Li
A semi-analytical solution is obtained in this paper for the micromechanical analysis of the square and hexagonal unit cells using complex potentials. It provides a means of numerical characterisation of unidirectionally fibre-reinforced composites for their effective properties. This process is considered as the forward problem and its inverse counterpart is also established in this paper to extract fibre properties from effective properties of composites. It is formulated into a mathematical optimisation problem in which the difference between predicted and provided effective properties is employed as the objective function with the fibre properties as the optimisation variables. The attempt of such an inverse problem is to address the lack of fibre properties for many types of composites commonly in use. The novelty of the paper lies in both sides of the analyses, forward and inverse, as none is available in the literature in the forms as presented in this paper and, more importantly, in the objective of this paper as an attempt to address the pressing and yet long-standing issue of lack of fibre properties. As a verification of the forward analysis, the predicted effective properties of a composite match perfectly with the finite element method (FEM) results. The same case is also employed to verify the inverse analysis by turning the prediction the other way round. Both the forward and inverse analyses have been validated against a series of experimental data. While the forward analysis is generally applicable to any input data as the properties of the constituents, the inverse analysis is sensitive to the input data. Potentially, the inverse analysis would offer a much-needed and also effective tool for the characterisation of fibres. However, reasonable predictions of fibre properties can only be obtained if input data are reasonably consistent.
{"title":"An inverse application of unit cells for extracting fibre properties from effective properties of composites","authors":"Zhenmin Zou, Shuguang Li","doi":"10.1177/10812865231212150","DOIUrl":"https://doi.org/10.1177/10812865231212150","url":null,"abstract":"A semi-analytical solution is obtained in this paper for the micromechanical analysis of the square and hexagonal unit cells using complex potentials. It provides a means of numerical characterisation of unidirectionally fibre-reinforced composites for their effective properties. This process is considered as the forward problem and its inverse counterpart is also established in this paper to extract fibre properties from effective properties of composites. It is formulated into a mathematical optimisation problem in which the difference between predicted and provided effective properties is employed as the objective function with the fibre properties as the optimisation variables. The attempt of such an inverse problem is to address the lack of fibre properties for many types of composites commonly in use. The novelty of the paper lies in both sides of the analyses, forward and inverse, as none is available in the literature in the forms as presented in this paper and, more importantly, in the objective of this paper as an attempt to address the pressing and yet long-standing issue of lack of fibre properties. As a verification of the forward analysis, the predicted effective properties of a composite match perfectly with the finite element method (FEM) results. The same case is also employed to verify the inverse analysis by turning the prediction the other way round. Both the forward and inverse analyses have been validated against a series of experimental data. While the forward analysis is generally applicable to any input data as the properties of the constituents, the inverse analysis is sensitive to the input data. Potentially, the inverse analysis would offer a much-needed and also effective tool for the characterisation of fibres. However, reasonable predictions of fibre properties can only be obtained if input data are reasonably consistent.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"120 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138599665","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 : 2023-12-04DOI: 10.1177/10812865231213022
Pengyu Pei, Guang Yang, Jinyu Zhou, Junfeng Lu
Upon reevaluating the influence of residual stresses generated by thermal mismatches in fibrous composites during the curing process, we introduce a modified model for the extraction of a single fiber from an elastic matrix. In contrast to previous models, which solely factored residual stress effects into the boundary conditions at the fiber–matrix interface while omitting them from the constitutive relations, our current model acknowledges bulk residual stress as finite values. Consequently, it yields non-conventional constitutive relations to describe the incremental deformation caused by external pulling forces. We have developed a practical semi-analytical series solution for the radial displacement of the matrix and an exact solution for the radial displacement of the fiber. To validate our modified model, we simplify it to a scenario where the influence of residual stress on the stress–strain relationship is excluded and compare it with results from existing literature. This comparison underscores the soundness of our modified model. We present a phase diagram to illustrate how the impact of residual stress on stress field prediction varies based on the ratio of the fiber modulus to the matrix modulus. This phase diagram serves as a valuable tool for evaluating whether it is advisable to transition from the previous mechanical model, which disregards the influence of residual stress on the stress–strain relationship, to the new model, which takes this influence into account within the stress–strain relationship.
{"title":"A modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region","authors":"Pengyu Pei, Guang Yang, Jinyu Zhou, Junfeng Lu","doi":"10.1177/10812865231213022","DOIUrl":"https://doi.org/10.1177/10812865231213022","url":null,"abstract":"Upon reevaluating the influence of residual stresses generated by thermal mismatches in fibrous composites during the curing process, we introduce a modified model for the extraction of a single fiber from an elastic matrix. In contrast to previous models, which solely factored residual stress effects into the boundary conditions at the fiber–matrix interface while omitting them from the constitutive relations, our current model acknowledges bulk residual stress as finite values. Consequently, it yields non-conventional constitutive relations to describe the incremental deformation caused by external pulling forces. We have developed a practical semi-analytical series solution for the radial displacement of the matrix and an exact solution for the radial displacement of the fiber. To validate our modified model, we simplify it to a scenario where the influence of residual stress on the stress–strain relationship is excluded and compare it with results from existing literature. This comparison underscores the soundness of our modified model. We present a phase diagram to illustrate how the impact of residual stress on stress field prediction varies based on the ratio of the fiber modulus to the matrix modulus. This phase diagram serves as a valuable tool for evaluating whether it is advisable to transition from the previous mechanical model, which disregards the influence of residual stress on the stress–strain relationship, to the new model, which takes this influence into account within the stress–strain relationship.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"35 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602600","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 : 2023-12-04DOI: 10.1177/10812865231205814
Danila Aita, Gabriele Milani, A. Taliercio
This paper aims to illustrate and compare different approaches for the limit analysis of masonry domes of revolution with an oculus at the top. It specifically focuses on the influence of the limited compressive and tensile strength of masonry on the bearing capacity of the dome. The first assessment is conducted through a semi-analytical formulation that revisits Durand-Claye’s method within the framework of the lower bound theorem of limit analysis. The second investigation is performed using a kinematic approach, which allows for closed-form solutions by exploiting the upper bound theorem of limit analysis and the virtual work theorem. These approaches are applied to a case study that was experimentally tested, involving a hemispherical dome with an oculus. The dome is subjected to its self-weight and a vertical load at the crown. Parametric investigations are presented to compare the results obtained through the proposed methods with those derived from the classical limit analysis of masonry structures, based on Heyman’s hypotheses.
{"title":"Limit analysis of masonry domes with oculus and lantern: A comparison between different approaches","authors":"Danila Aita, Gabriele Milani, A. Taliercio","doi":"10.1177/10812865231205814","DOIUrl":"https://doi.org/10.1177/10812865231205814","url":null,"abstract":"This paper aims to illustrate and compare different approaches for the limit analysis of masonry domes of revolution with an oculus at the top. It specifically focuses on the influence of the limited compressive and tensile strength of masonry on the bearing capacity of the dome. The first assessment is conducted through a semi-analytical formulation that revisits Durand-Claye’s method within the framework of the lower bound theorem of limit analysis. The second investigation is performed using a kinematic approach, which allows for closed-form solutions by exploiting the upper bound theorem of limit analysis and the virtual work theorem. These approaches are applied to a case study that was experimentally tested, involving a hemispherical dome with an oculus. The dome is subjected to its self-weight and a vertical load at the crown. Parametric investigations are presented to compare the results obtained through the proposed methods with those derived from the classical limit analysis of masonry structures, based on Heyman’s hypotheses.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"83 17","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138604699","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 : 2023-12-01DOI: 10.1177/10812865231200242
T. Pence
In soft tissue, growth-induced instability is increasingly being viewed as a key agent in certain morphological developments, such as the folding of the cerebral cortex. As such, the study of growth-induced instability in the context of morphoelastic large deformation continuum mechanics is a burgeoning field of study. In this work, we examine some of the connections between these new developments and earlier work that can be viewed as the conventional—or no-growth—hyperelastic theory. By a systematic examination of a standard problem, certain direct correspondences are clarified which effectively permit results of a very general nature in the conventional theory to inform ongoing work in the morphoelastic theory.
{"title":"Connections between the morphoelastic treatment of growth-induced instabilities and earlier hyperelastic treatments of buckling under thrust","authors":"T. Pence","doi":"10.1177/10812865231200242","DOIUrl":"https://doi.org/10.1177/10812865231200242","url":null,"abstract":"In soft tissue, growth-induced instability is increasingly being viewed as a key agent in certain morphological developments, such as the folding of the cerebral cortex. As such, the study of growth-induced instability in the context of morphoelastic large deformation continuum mechanics is a burgeoning field of study. In this work, we examine some of the connections between these new developments and earlier work that can be viewed as the conventional—or no-growth—hyperelastic theory. By a systematic examination of a standard problem, certain direct correspondences are clarified which effectively permit results of a very general nature in the conventional theory to inform ongoing work in the morphoelastic theory.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":" 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138615704","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 : 2023-11-08DOI: 10.1177/10812865231202024
Maria Laura De Bellis, Marcello Vasta, Alessio Gizzi, Anna Pandolfi
We present a fiber-distributed model of the reinforcing collagen of the human cornea. The model describes the basic connections between the components of the tissue by defining an elementary block (cell) and upscaling it to the physical size of the cornea. The cell is defined by two sets of collagen fibrils running in approximately orthogonal directions, characterized by a random distribution of the spatial orientation and connected by chemical bonds of two kinds. The bonds of the first kind describe the lamellar crosslinks, forming the ribbon-like lamellae; while the bonds of the second kind describe the stacking crosslinks, piling up the lamellae to form the structure of the stroma. The spatial replication of the cell produces a truss structure with a considerable number of degrees of freedom. The statistical characterization of the collagen fibrils leads to a mechanical model that reacts to the action of the deterministic intraocular pressure with a stochastic distribution of the displacements, here characterized by their mean value and variance. The strategy to address the solution of the heavy resulting numerical problem is to use the so-called stochastic finite element improved perturbation method combined with a fully explicit solver. The results demonstrate that the variability of the mechanical properties affects in a non-negligible manner the expected response of the structure to the physiological action.
{"title":"A numerical model of the human cornea accounting for the fiber-distributed collagen microstructure","authors":"Maria Laura De Bellis, Marcello Vasta, Alessio Gizzi, Anna Pandolfi","doi":"10.1177/10812865231202024","DOIUrl":"https://doi.org/10.1177/10812865231202024","url":null,"abstract":"We present a fiber-distributed model of the reinforcing collagen of the human cornea. The model describes the basic connections between the components of the tissue by defining an elementary block (cell) and upscaling it to the physical size of the cornea. The cell is defined by two sets of collagen fibrils running in approximately orthogonal directions, characterized by a random distribution of the spatial orientation and connected by chemical bonds of two kinds. The bonds of the first kind describe the lamellar crosslinks, forming the ribbon-like lamellae; while the bonds of the second kind describe the stacking crosslinks, piling up the lamellae to form the structure of the stroma. The spatial replication of the cell produces a truss structure with a considerable number of degrees of freedom. The statistical characterization of the collagen fibrils leads to a mechanical model that reacts to the action of the deterministic intraocular pressure with a stochastic distribution of the displacements, here characterized by their mean value and variance. The strategy to address the solution of the heavy resulting numerical problem is to use the so-called stochastic finite element improved perturbation method combined with a fully explicit solver. The results demonstrate that the variability of the mechanical properties affects in a non-negligible manner the expected response of the structure to the physiological action.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"105 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342213","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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