Pub Date : 2024-07-26DOI: 10.1177/10812865241252368
Lennart Behlen, Daniel Wallenta, Andreas Ricoeur
The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.
以无限介质板中椭圆介质腔的解析解为基础，研究了通过让半小轴趋向于零而得到的格里菲斯裂缝问题。在此过程中，纠正了文献中常用的错误保角映射，这种映射只在物理空间的一部分正确再现电场。将椭圆形界面解释为暴露在斜向远程电场中的机械开裂面，计算出表面电荷和静电牵引力。与已建立的电容器类比模型（根据未变形裂缝配置中的位移和电动势近似得出电荷密度和库仑牵引力）相比，目前的研究提供了精确的解决方案，考虑到了裂缝曲率和电场倾斜度的不同影响。裂纹权重函数最终用于计算应力和电位移强度因子。结果表明，在相关参数范围内，电容器类比的表面电荷可以很好地替代精确的电边界条件，而裂纹尖端附近不准确的库仑牵引力可能会导致模式 I 应力强度因子被大大高估。
{"title":"Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?","authors":"Lennart Behlen, Daniel Wallenta, Andreas Ricoeur","doi":"10.1177/10812865241252368","DOIUrl":"https://doi.org/10.1177/10812865241252368","url":null,"abstract":"The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776122","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 : 2024-07-26DOI: 10.1177/10812865231219163
JD Humphrey
Rupture of intracranial aneurysms, either fusiform or saccular in shape, associates with significant morbidity and mortality. The progressive enlargement and eventual rupture of these lesions depends strongly on the associated mechanics and mechanobiology. In this paper, we review results from past biomechanical analyses of intracranial aneurysms and highlight lessons learned in the general area of vascular mechanobiology with the goal of guiding future research.
{"title":"Mechanics and mechanobiology of intracranial aneurysms","authors":"JD Humphrey","doi":"10.1177/10812865231219163","DOIUrl":"https://doi.org/10.1177/10812865231219163","url":null,"abstract":"Rupture of intracranial aneurysms, either fusiform or saccular in shape, associates with significant morbidity and mortality. The progressive enlargement and eventual rupture of these lesions depends strongly on the associated mechanics and mechanobiology. In this paper, we review results from past biomechanical analyses of intracranial aneurysms and highlight lessons learned in the general area of vascular mechanobiology with the goal of guiding future research.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"160 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776126","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 : 2024-07-26DOI: 10.1177/10812865241249751
Mordecai Oore, Sageev Oore
An explicit analytical solution for an elliptical hole in an infinite elastic plate is derived for uniaxial load from the earliest work on this configuration. This is used along with the biaxial loading case and more recent solutions, available in curvilinear coordinates, to transform the stress fields into Cartesian coordinates along the x and y axes, reducing the curvilinear solutions to simplified short-form expressions of x and y. The present closed-form results are the functions of polynomials of the second and third order of x or y along the x or y axes, respectively, and have the most concise form to the best of the authors’ knowledge. The displacements for plain stress condition are calculated directly from the present stress field expressions, as functions of second-order polynomials of x or y and demonstrate overall consistency. Application of the present stress field and displacements results to special cases, such as a circular hole, a crack, and an elliptical hole in a pressurized cylindrical shell, are shown to agree with published solutions where available.
根据有关该构造的最早研究成果，得出了无限弹性板中椭圆孔的单轴载荷显式解析解。本封闭式结果分别是 x 或 y 的二阶和三阶多项式沿 x 或 y 轴的函数，是作者所知的最简洁的形式。平应力条件下的位移是直接从本应力场表达式中计算出来的，是 x 或 y 的二阶多项式的函数，并显示出整体一致性。将本应力场和位移结果应用于特殊情况，如受压圆柱形壳体中的圆孔、裂缝和椭圆孔，结果表明与已公布的解法一致。
{"title":"Explicit solutions in Cartesian coordinates for an elliptic hole in an infinite elastic plate","authors":"Mordecai Oore, Sageev Oore","doi":"10.1177/10812865241249751","DOIUrl":"https://doi.org/10.1177/10812865241249751","url":null,"abstract":"An explicit analytical solution for an elliptical hole in an infinite elastic plate is derived for uniaxial load from the earliest work on this configuration. This is used along with the biaxial loading case and more recent solutions, available in curvilinear coordinates, to transform the stress fields into Cartesian coordinates along the x and y axes, reducing the curvilinear solutions to simplified short-form expressions of x and y. The present closed-form results are the functions of polynomials of the second and third order of x or y along the x or y axes, respectively, and have the most concise form to the best of the authors’ knowledge. The displacements for plain stress condition are calculated directly from the present stress field expressions, as functions of second-order polynomials of x or y and demonstrate overall consistency. Application of the present stress field and displacements results to special cases, such as a circular hole, a crack, and an elliptical hole in a pressurized cylindrical shell, are shown to agree with published solutions where available.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"63 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785488","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}
Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face’s midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems.
{"title":"Transient heat transfer analysis of a sandwich panel with a cracked honeycomb core","authors":"Wenzhi Yang, Ruchao Gao, Jinxing Liu, Zengtao Chen","doi":"10.1177/10812865241261638","DOIUrl":"https://doi.org/10.1177/10812865241261638","url":null,"abstract":"Sandwich structures with ceramic honeycomb cores are extensively employed in thermal protection systems owing to their exceptional ability to resist high temperatures. This work aims at exploring the effect of cracking on the transient thermal process of the sandwich panel subject to impulsive and cyclic thermal loadings. Both the conventional and re-entrant hexagonal alumina honeycombs are considered for the core material. By the integral transform method, combined with singular integral equations, the transient temperatures of the whole sandwich panel are determined from the semi-analytical solution. The straightforward temperature difference of the crack face’s midpoints is exploited to characterize the heat intensification near the crack. Parametric investigations are carried out for the internal cell angle, the relative density, crack length, crack position, and thickness of face sheets, which provides a better understanding of the honeycomb materials working in thermal protection systems.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"86 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785487","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 : 2024-07-26DOI: 10.1177/10812865241241002
Julian Karl Bauer, Constantin Krauß, Juliane Blarr, Philipp L Kinon, Luise Kärger, Thomas Böhlke
We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.
{"title":"Evaluation of a decomposition-based interpolation method for fourth-order fiber-orientation tensors: An eigensystem approach","authors":"Julian Karl Bauer, Constantin Krauß, Juliane Blarr, Philipp L Kinon, Luise Kärger, Thomas Böhlke","doi":"10.1177/10812865241241002","DOIUrl":"https://doi.org/10.1177/10812865241241002","url":null,"abstract":"We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"61 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776121","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 : 2024-07-26DOI: 10.1177/10812865241258377
Vu Thi Ngoc Anh, Pham Chi Vinh, Tran Thanh Tuan
In this paper, we establish the transfer matrix for an orthotropic elastic layer made of nanomaterial that is modeled by the weakly nonlocal elasticity model. This model is proposed recently and different from other existing nonlocal models of elasticity it has been proved to be well-posed for any problem of plane waves. Since the established transfer matrix is totally explicit, it is a convenient tool in investigating various problems of plane waves propagating in layered nonlocal elastic media. To prove this point, we use it to derive the dispersion equation of Lamb waves propagating in a composite plate consisting of two weakly nonlocal orthotropic layers. The dispersion equation in explicit form of Lamb waves has been derived, and it is shown that the derivation of this equation is much more simple than the one using the traditional technique. The obtained explicit dispersion equation will be used to establish techniques monitoring the health of layered nanostructures.
{"title":"Transfer matrix for a weakly nonlocal elastic layer and Lamb waves in layered nonlocal composite plates","authors":"Vu Thi Ngoc Anh, Pham Chi Vinh, Tran Thanh Tuan","doi":"10.1177/10812865241258377","DOIUrl":"https://doi.org/10.1177/10812865241258377","url":null,"abstract":"In this paper, we establish the transfer matrix for an orthotropic elastic layer made of nanomaterial that is modeled by the weakly nonlocal elasticity model. This model is proposed recently and different from other existing nonlocal models of elasticity it has been proved to be well-posed for any problem of plane waves. Since the established transfer matrix is totally explicit, it is a convenient tool in investigating various problems of plane waves propagating in layered nonlocal elastic media. To prove this point, we use it to derive the dispersion equation of Lamb waves propagating in a composite plate consisting of two weakly nonlocal orthotropic layers. The dispersion equation in explicit form of Lamb waves has been derived, and it is shown that the derivation of this equation is much more simple than the one using the traditional technique. The obtained explicit dispersion equation will be used to establish techniques monitoring the health of layered nanostructures.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776125","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 : 2024-07-26DOI: 10.1177/10812865241258723
Arkadi Berezovski
Depending on whether the experiments are quasi-static or fast dynamics, the measured twin boundary velocity values range from zero to the material’s sound speed. The twin boundary velocity is not yet predicted theoretically in the continuum mechanics framework. The extension of continual description is provided in the paper by means of internal variables. It is shown that a diffusional slow motion of twin boundaries can be represented using a single internal variable. The dual internal variable technique is employed for the description of the fast dynamics of twin boundaries.
{"title":"An internal variable model of macroscopic twin boundary dynamics","authors":"Arkadi Berezovski","doi":"10.1177/10812865241258723","DOIUrl":"https://doi.org/10.1177/10812865241258723","url":null,"abstract":"Depending on whether the experiments are quasi-static or fast dynamics, the measured twin boundary velocity values range from zero to the material’s sound speed. The twin boundary velocity is not yet predicted theoretically in the continuum mechanics framework. The extension of continual description is provided in the paper by means of internal variables. It is shown that a diffusional slow motion of twin boundaries can be represented using a single internal variable. The dual internal variable technique is employed for the description of the fast dynamics of twin boundaries.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"69 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776118","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 : 2024-07-26DOI: 10.1177/10812865241252375
Alexander M Khludnev
We consider a non-coercive boundary value problem for two elastic Kirchhoff–Love plates connected to each other by a thin junction. The non-coercivity of the problem is due to the Neumann-type conditions imposed at the external boundaries of the plates. A solution existence is proved for suitable given external forces. Passages to limits are justified as a rigidity parameter of the junction tends to infinity and to zero. We prove that the model corresponding to the first limit case describes an equilibrium of elastic plates with a thin rigid junction; the second limit model fits to the equilibrium state of two elastic plates independent of each other.
{"title":"Non-coercive problems for elastic plates with thin junction","authors":"Alexander M Khludnev","doi":"10.1177/10812865241252375","DOIUrl":"https://doi.org/10.1177/10812865241252375","url":null,"abstract":"We consider a non-coercive boundary value problem for two elastic Kirchhoff–Love plates connected to each other by a thin junction. The non-coercivity of the problem is due to the Neumann-type conditions imposed at the external boundaries of the plates. A solution existence is proved for suitable given external forces. Passages to limits are justified as a rigidity parameter of the junction tends to infinity and to zero. We prove that the model corresponding to the first limit case describes an equilibrium of elastic plates with a thin rigid junction; the second limit model fits to the equilibrium state of two elastic plates independent of each other.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"27 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776119","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 : 2024-07-26DOI: 10.1177/10812865241259134
Péter Máté, András Szekrényes
Cylindrical shells curved in only one direction show an interesting behaviour when bent, especially if they remain completely in the elastic region and do not undergo plastic forming. This can be observed in their most common application: the measuring tape. They can be coiled easily because of the loss of stability of their cross-sections, which makes transportation of long shells efficient. This property could be very useful if one could use such a one-way curved shell as a beam, which could be transported and deployed easily. The aim of this study is to observe the behaviour of such a shell, under pure bending load, with special emphasis on the stability loss of the cross-section. In this paper, analytical, semi-analytical, and finite-element methods are used for the description of the shell. The solution derived here uses a variable cross-section Euler–Bernoulli beam model combined with elements of the Kirchhoff plate theory without the shallow shell assumption. It is assumed that the cross-section remains circular and does not change its length. For a universal description, dimensionless parameters and variables are introduced. The semi-analytical investigation revealed that the snap-through ability of the shell may not exist for certain cross-sections which can be presented on a stability map. The derived model reveals the existence of a limiting point between the cross-section deformation modes for larger cross-section angles. In the article, ready-to-use analytical and semi-analytical solutions are given for the critical load and stability map of these shells, which are compared to similar shallow shell models from the literature and the finite-element solution of the problem. The finite-element method also revealed that for a dimensionless description, a length-cross-section radius parameter should be introduced to describe the three-point bending scenario.
{"title":"Stability analysis of thin cylindrical shells under pure and three-point bending","authors":"Péter Máté, András Szekrényes","doi":"10.1177/10812865241259134","DOIUrl":"https://doi.org/10.1177/10812865241259134","url":null,"abstract":"Cylindrical shells curved in only one direction show an interesting behaviour when bent, especially if they remain completely in the elastic region and do not undergo plastic forming. This can be observed in their most common application: the measuring tape. They can be coiled easily because of the loss of stability of their cross-sections, which makes transportation of long shells efficient. This property could be very useful if one could use such a one-way curved shell as a beam, which could be transported and deployed easily. The aim of this study is to observe the behaviour of such a shell, under pure bending load, with special emphasis on the stability loss of the cross-section. In this paper, analytical, semi-analytical, and finite-element methods are used for the description of the shell. The solution derived here uses a variable cross-section Euler–Bernoulli beam model combined with elements of the Kirchhoff plate theory without the shallow shell assumption. It is assumed that the cross-section remains circular and does not change its length. For a universal description, dimensionless parameters and variables are introduced. The semi-analytical investigation revealed that the snap-through ability of the shell may not exist for certain cross-sections which can be presented on a stability map. The derived model reveals the existence of a limiting point between the cross-section deformation modes for larger cross-section angles. In the article, ready-to-use analytical and semi-analytical solutions are given for the critical load and stability map of these shells, which are compared to similar shallow shell models from the literature and the finite-element solution of the problem. The finite-element method also revealed that for a dimensionless description, a length-cross-section radius parameter should be introduced to describe the three-point bending scenario.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776120","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 : 2024-07-26DOI: 10.1177/10812865241257850
Jacobo Ayensa-Jiménez, Javier Orera-Echeverría, Manuel Doblare
Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description, or we simply do not know how to describe such materials in terms of relations between external and internal variables. In many disciplines, neural network methods have emerged as powerful tools to identify very complex and nonlinear correlations. In this work, we use the very recently developed concept of physically guided neural networks with internal variables (PGNNIVs) to discover constitutive laws using a model-free approach and training solely with measured force–displacement data. PGNNIVs make a particular use of the physics of the problem to enforce constraints on specific hidden layers and are able to make predictions without internal variable data. We demonstrate that PGNNIVs are capable of predicting both internal and external variables under unseen loading scenarios, regardless of the nature of the material considered (linear, with hardening or softening behavior and hyperelastic), unravelling the constitutive law of the material hence explaining its nature altogether, endowing the method with some explanatory character that distances it from the traditional black box approach.
{"title":"Predicting and explaining nonlinear material response using deep physically guided neural networks with internal variables","authors":"Jacobo Ayensa-Jiménez, Javier Orera-Echeverría, Manuel Doblare","doi":"10.1177/10812865241257850","DOIUrl":"https://doi.org/10.1177/10812865241257850","url":null,"abstract":"Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description, or we simply do not know how to describe such materials in terms of relations between external and internal variables. In many disciplines, neural network methods have emerged as powerful tools to identify very complex and nonlinear correlations. In this work, we use the very recently developed concept of physically guided neural networks with internal variables (PGNNIVs) to discover constitutive laws using a model-free approach and training solely with measured force–displacement data. PGNNIVs make a particular use of the physics of the problem to enforce constraints on specific hidden layers and are able to make predictions without internal variable data. We demonstrate that PGNNIVs are capable of predicting both internal and external variables under unseen loading scenarios, regardless of the nature of the material considered (linear, with hardening or softening behavior and hyperelastic), unravelling the constitutive law of the material hence explaining its nature altogether, endowing the method with some explanatory character that distances it from the traditional black box approach.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"69 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776124","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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