Pub Date : 2024-02-19DOI: 10.1177/10812865241228825
Karim Ehab Moustafa Kamel, Thierry J Massart
The models developed for masonry and historical structures in the literature are usually classified into macromodels considering masonry as an equivalent continuum; and micromodels in which brick, blocks, or stones and mortar joints are represented explicitly. In this second category, many contributions dealt with regular bond masonry for which the geometrical description and the discretization are rather straightforward. For irregular masonry structures however, even though both finite element method (FEM) and discrete element method (DEM) approaches have been developed, obtaining a versatile geometry representation and its discretization remains much less straightforward. This becomes an important issue nowadays with the availability of image acquisition techniques, based on which computational models could be derived. The present contribution proposes an automated methodology to produce a line description of the mortar joints of an irregular masonry blocks/stones and mortar assembly, which can subsequently be used in modeling approaches. The starting point of the development is a generation technique based on inclusions packings which uses distance fields to the nearest neighboring inclusions to describe an assembly of blocks or stones geometrically. It is shown that such an assembly and the corresponding distance fields can be used to extract efficiently and in an automated way a line or lumped description of the corresponding mortar joint based on the concept of a medial axis. This line description can subsequently be used to define computational models. This is illustrated by the automated generation of FEM models that represent mortar joints by interface elements equipped with a cohesive law. Simulations on representative volume elements (RVEs) and on a wall are shown to illustrate the methodology that paves the way towards the image-based modeling of irregular masonry structures through the automated generation of cohesive zone-based models.
{"title":"Towards automated image-based cohesive zone modeling of cracking in irregular masonry","authors":"Karim Ehab Moustafa Kamel, Thierry J Massart","doi":"10.1177/10812865241228825","DOIUrl":"https://doi.org/10.1177/10812865241228825","url":null,"abstract":"The models developed for masonry and historical structures in the literature are usually classified into macromodels considering masonry as an equivalent continuum; and micromodels in which brick, blocks, or stones and mortar joints are represented explicitly. In this second category, many contributions dealt with regular bond masonry for which the geometrical description and the discretization are rather straightforward. For irregular masonry structures however, even though both finite element method (FEM) and discrete element method (DEM) approaches have been developed, obtaining a versatile geometry representation and its discretization remains much less straightforward. This becomes an important issue nowadays with the availability of image acquisition techniques, based on which computational models could be derived. The present contribution proposes an automated methodology to produce a line description of the mortar joints of an irregular masonry blocks/stones and mortar assembly, which can subsequently be used in modeling approaches. The starting point of the development is a generation technique based on inclusions packings which uses distance fields to the nearest neighboring inclusions to describe an assembly of blocks or stones geometrically. It is shown that such an assembly and the corresponding distance fields can be used to extract efficiently and in an automated way a line or lumped description of the corresponding mortar joint based on the concept of a medial axis. This line description can subsequently be used to define computational models. This is illustrated by the automated generation of FEM models that represent mortar joints by interface elements equipped with a cohesive law. Simulations on representative volume elements (RVEs) and on a wall are shown to illustrate the methodology that paves the way towards the image-based modeling of irregular masonry structures through the automated generation of cohesive zone-based models.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"115 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948421","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 : 2024-02-19DOI: 10.1177/10812865241228230
Meir Shillor, Ian Pahuja
This work introduces and studies a novel normal compliance contact condition with damping, the Damped Normal Compliance (DNC), which is more realistic than the usual normal compliance condition that is often used in modeling contact between solids. The condition is applied in a model for the contact of a rigid mass with a reactive obstacle and allows for energy dissipation during contact. We analyze the model and show that the condition is of mathematical, as well as applied, interest. Then, we establish its relationship with the so-called “coefficient of restitution,”[Formula: see text], and show that the concept is not well defined, since [Formula: see text] depends on the system parameters, applied force, and initial data. The various theoretical results are depicted using computer simulations.
{"title":"Damped Normal Compliance (DNC) and the restitution coefficient","authors":"Meir Shillor, Ian Pahuja","doi":"10.1177/10812865241228230","DOIUrl":"https://doi.org/10.1177/10812865241228230","url":null,"abstract":"This work introduces and studies a novel normal compliance contact condition with damping, the Damped Normal Compliance (DNC), which is more realistic than the usual normal compliance condition that is often used in modeling contact between solids. The condition is applied in a model for the contact of a rigid mass with a reactive obstacle and allows for energy dissipation during contact. We analyze the model and show that the condition is of mathematical, as well as applied, interest. Then, we establish its relationship with the so-called “coefficient of restitution,”[Formula: see text], and show that the concept is not well defined, since [Formula: see text] depends on the system parameters, applied force, and initial data. The various theoretical results are depicted using computer simulations.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948521","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 : 2024-02-16DOI: 10.1177/10812865231226183
Xiang Yu, Yibin Fu
We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau–Rayleigh and Wilkes instabilities in a solid cylinder.
{"title":"On the incremental equations in surface elasticity","authors":"Xiang Yu, Yibin Fu","doi":"10.1177/10812865231226183","DOIUrl":"https://doi.org/10.1177/10812865231226183","url":null,"abstract":"We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau–Rayleigh and Wilkes instabilities in a solid cylinder.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"42 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948424","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 : 2024-02-16DOI: 10.1177/10812865231226311
Chiara Lonati, Alfredo Marzocchi
In this review, we discuss some conditions for achieving non-interpenetration and self-contact of solids, in particular for regular, inextensible, and closed elastic rods. We establish some equivalences between conditions that were stated sometimes independently, underlying their local or global character. We then examine three conditions related to virtual displacements and to topological characters of knots, that can be generalized to filaments, considering the midline of the loop as an inextensible regular knot.
{"title":"On self-contact and non-interpenetration of elastic rods","authors":"Chiara Lonati, Alfredo Marzocchi","doi":"10.1177/10812865231226311","DOIUrl":"https://doi.org/10.1177/10812865231226311","url":null,"abstract":"In this review, we discuss some conditions for achieving non-interpenetration and self-contact of solids, in particular for regular, inextensible, and closed elastic rods. We establish some equivalences between conditions that were stated sometimes independently, underlying their local or global character. We then examine three conditions related to virtual displacements and to topological characters of knots, that can be generalized to filaments, considering the midline of the loop as an inextensible regular knot.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948422","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 : 2024-02-14DOI: 10.1177/10812865231221994
Sankalp Tiwari, Anindya Chatterjee
The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress problems in linear elasticity. In both methods, we split the sought stress σ into two parts, where neither part is required to satisfy strain compatibility. The first part, σ p, is any stress in equilibrium with the loading. The second part, σ h is a self-equilibrated stress field on the unloaded body. In both methods, σ h is expanded using tensor-valued global stress basis functions developed elsewhere. In the first method, the coefficients in the expansion are found by minimizing the strain energy based on the well-known complementary energy principle. For the second method, which is restricted to planar homogeneous isotropic bodies, we show that we merely need to minimize the squared L2 norm of the trace of stress. For demonstration, we solve nine stress problems involving sharp corners, multiple-connectedness, non-zero net force and/or moment on an internal hole, body force, discontinuous surface traction, material inhomogeneity, and anisotropy. The first method presents a new application of a known principle. The second method presents a hitherto unreported principle, to the best of our knowledge.
使用全局位移基函数来求解线性弹性中的边界值问题已得到广泛认可。之前还没有工作使用全局应力张量基础来求解此类问题。我们提出了两种解决线性弹性中应力问题的方法。在这两种方法中，我们将寻求的应力 σ 分成两部分，其中任何一部分都不需要满足应变兼容性。第一部分，σ p，是与载荷平衡的任何应力。第二部分，σ h 是未加载体上的自平衡应力场。在这两种方法中，σ h 都是使用其他地方开发的张量值全局应力基函数展开的。在第一种方法中，根据著名的互补能原理，通过最小化应变能找到展开中的系数。第二种方法仅限于平面均质各向同性体，我们证明只需最小化应力迹的平方 L2 准则即可。为了演示，我们解决了九个应力问题，涉及尖角、多连通性、内孔上的非零净力和/或力矩、体力、不连续表面牵引、材料不均匀性和各向异性。第一种方法是对已知原理的新应用。据我们所知，第二种方法提出了一种迄今为止尚未报道过的原理。
{"title":"Solution of planar elastic stress problems using stress basis functions","authors":"Sankalp Tiwari, Anindya Chatterjee","doi":"10.1177/10812865231221994","DOIUrl":"https://doi.org/10.1177/10812865231221994","url":null,"abstract":"The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress problems in linear elasticity. In both methods, we split the sought stress σ into two parts, where neither part is required to satisfy strain compatibility. The first part, σ<jats:sub> p</jats:sub>, is any stress in equilibrium with the loading. The second part, σ<jats:sub> h</jats:sub> is a self-equilibrated stress field on the unloaded body. In both methods, σ<jats:sub> h</jats:sub> is expanded using tensor-valued global stress basis functions developed elsewhere. In the first method, the coefficients in the expansion are found by minimizing the strain energy based on the well-known complementary energy principle. For the second method, which is restricted to planar homogeneous isotropic bodies, we show that we merely need to minimize the squared L<jats:sup>2</jats:sup> norm of the trace of stress. For demonstration, we solve nine stress problems involving sharp corners, multiple-connectedness, non-zero net force and/or moment on an internal hole, body force, discontinuous surface traction, material inhomogeneity, and anisotropy. The first method presents a new application of a known principle. The second method presents a hitherto unreported principle, to the best of our knowledge.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"42 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948423","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 : 2024-02-14DOI: 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}
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