Pub Date : 2024-10-28DOI: 10.1016/j.ijnonlinmec.2024.104932
Phuc L.H. Ho , Changkye Lee , Canh V. Le , Jurng-Jae Yee
Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.
{"title":"Shakedown analysis of incompressible materials under cyclic loads: A locking-free CS-FEM-Q5 numerical approach","authors":"Phuc L.H. Ho , Changkye Lee , Canh V. Le , Jurng-Jae Yee","doi":"10.1016/j.ijnonlinmec.2024.104932","DOIUrl":"10.1016/j.ijnonlinmec.2024.104932","url":null,"abstract":"<div><div>Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104932"},"PeriodicalIF":2.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-28DOI: 10.1016/j.ijnonlinmec.2024.104933
Safvan Palathingal , Dominic Vella
The shift in the backbone of the frequency–response curve and the ‘jump-down’ observed at a critical frequency observed in nano-resonators are caused by their nonlinear mechanical response. The shift and jump-down point are therefore often used to infer the mechanical properties that underlie the nonlinear response, particularly the resonator’s stretching modulus. To facilitate this, the resonators’ dynamics are often modelled using a Galerkin-type numerical approach or lumped ordinary differential equations like the Duffing equation, that incorporate an appropriate nonlinearity. To understand the source of the problem’s nonlinearities, we first develop an axisymmetric but spatially-varying model of a membrane resonator subject to a uniform oscillatory load with linear damping. We then derive asymptotic solutions for the resulting partial differential equations (PDEs) using the Method of Multiple Scales (MS), which allows a systematic reduction to a Duffing-like equation with analytically determined coefficients. We also solve the PDEs numerically via the method of lines. By comparing the numerical solutions with the asymptotic results, we demonstrate that the numerical approach reveals a non-constant maximum compliance with increasing load, which contradicts the predictions of the MS analysis. In contrast, we show that combining a Galerkin decomposition with the Harmonic Balance Method accurately captures the non-constant maximum compliance and reliably predicts jump-down behaviour. We analyse the resulting frequency–response predictions derived from these methods. We also argue that fitting based on the jump-down point may be sensitive to noise and discuss strategies for fitting frequency–response curves from experimental data to theory that are robust to this.
{"title":"Axisymmetric membrane nano-resonators: A comparison of nonlinear reduced-order models","authors":"Safvan Palathingal , Dominic Vella","doi":"10.1016/j.ijnonlinmec.2024.104933","DOIUrl":"10.1016/j.ijnonlinmec.2024.104933","url":null,"abstract":"<div><div>The shift in the backbone of the frequency–response curve and the ‘jump-down’ observed at a critical frequency observed in nano-resonators are caused by their nonlinear mechanical response. The shift and jump-down point are therefore often used to infer the mechanical properties that underlie the nonlinear response, particularly the resonator’s stretching modulus. To facilitate this, the resonators’ dynamics are often modelled using a Galerkin-type numerical approach or lumped ordinary differential equations like the Duffing equation, that incorporate an appropriate nonlinearity. To understand the source of the problem’s nonlinearities, we first develop an axisymmetric but spatially-varying model of a membrane resonator subject to a uniform oscillatory load with linear damping. We then derive asymptotic solutions for the resulting partial differential equations (PDEs) using the Method of Multiple Scales (MS), which allows a systematic reduction to a Duffing-like equation with analytically determined coefficients. We also solve the PDEs numerically via the method of lines. By comparing the numerical solutions with the asymptotic results, we demonstrate that the numerical approach reveals a non-constant maximum compliance with increasing load, which contradicts the predictions of the MS analysis. In contrast, we show that combining a Galerkin decomposition with the Harmonic Balance Method accurately captures the non-constant maximum compliance and reliably predicts jump-down behaviour. We analyse the resulting frequency–response predictions derived from these methods. We also argue that fitting based on the jump-down point may be sensitive to noise and discuss strategies for fitting frequency–response curves from experimental data to theory that are robust to this.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104933"},"PeriodicalIF":2.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-25DOI: 10.1016/j.ijnonlinmec.2024.104931
Mohammed Daher Albalwi
The flow of a density stratified fluid over obstacles has been intensively explored from a natural and scientific point of view. This flow has been successfully governed by using the forced Korteweg–de Vries-Burgers equation that generated solitons in a viscous flow. This is done by adding the viscous term beyond the Korteweg–de Vries approximation. It is based on the conservation laws of the Korteweg–de Vries-Burgers equation for mass and energy, and assumes that the upstream wavetrains are composed of solitary waves. Our results show that the influence of viscosity plays a key role in determining the upstream solitary wave amplitude of the bore. A good comparison is obtained between the numerical and analytical solutions.
{"title":"Uniform solitary wave theory for viscous flow over topography","authors":"Mohammed Daher Albalwi","doi":"10.1016/j.ijnonlinmec.2024.104931","DOIUrl":"10.1016/j.ijnonlinmec.2024.104931","url":null,"abstract":"<div><div>The flow of a density stratified fluid over obstacles has been intensively explored from a natural and scientific point of view. This flow has been successfully governed by using the forced Korteweg–de Vries-Burgers equation that generated solitons in a viscous flow. This is done by adding the viscous term beyond the Korteweg–de Vries approximation. It is based on the conservation laws of the Korteweg–de Vries-Burgers equation for mass and energy, and assumes that the upstream wavetrains are composed of solitary waves. Our results show that the influence of viscosity plays a key role in determining the upstream solitary wave amplitude of the bore. A good comparison is obtained between the numerical and analytical solutions.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104931"},"PeriodicalIF":2.8,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-24DOI: 10.1016/j.ijnonlinmec.2024.104929
A.A. Nanha Djanan , B.R. Nana Nbendjo , W. Seemann
The present paper proposes a new device where it is observed the self-synchronization between two unbalanced DC motors with a limited power supply when they are indirectly coupled. The vibrating system studied consists of two portal frames type shear buildings coupled, carrying each an unbalanced DC motor. The engines are supposed to rotate in the same direction and act on each as external excitation. The dynamics investigations are done with analytical and numerical methods to achieve this purpose. The synchronous solutions are derived and their stability conditions are also explored using the averaging method. The results of this analytical investigation are confirmed later by numerical simulations. The effects of some physical parameters on the self-synchronization of DC motors are presented. The impact of the nonlinear coupling between the floors on the DC motors dynamics is also explored. The Sommerfeld effect appearing in the system is reduced by taking into account the damping coming from the environment and the coupling between the portal frame. It is observed that in-phase synchronization of the non-ideal sources assures a low amplitude of vibration in the different floors compared to opposite-phase synchronization.
{"title":"Vibration control of two portal frames type shear buildings through self-synchronous dynamics of two non-ideal sources indirectly coupled","authors":"A.A. Nanha Djanan , B.R. Nana Nbendjo , W. Seemann","doi":"10.1016/j.ijnonlinmec.2024.104929","DOIUrl":"10.1016/j.ijnonlinmec.2024.104929","url":null,"abstract":"<div><div>The present paper proposes a new device where it is observed the self-synchronization between two unbalanced DC motors with a limited power supply when they are indirectly coupled. The vibrating system studied consists of two portal frames type shear buildings coupled, carrying each an unbalanced DC motor. The engines are supposed to rotate in the same direction and act on each as external excitation. The dynamics investigations are done with analytical and numerical methods to achieve this purpose. The synchronous solutions are derived and their stability conditions are also explored using the averaging method. The results of this analytical investigation are confirmed later by numerical simulations. The effects of some physical parameters on the self-synchronization of DC motors are presented. The impact of the nonlinear coupling between the floors on the DC motors dynamics is also explored. The Sommerfeld effect appearing in the system is reduced by taking into account the damping coming from the environment and the coupling between the portal frame. It is observed that in-phase synchronization of the non-ideal sources assures a low amplitude of vibration in the different floors compared to opposite-phase synchronization.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104929"},"PeriodicalIF":2.8,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.
{"title":"Nonlinear elasticity tailoring and failure mode manipulation of functionally graded honeycombs under large deformation","authors":"Sushanta Ghuku , Sarmila Sahoo , Tanmoy Mukhopadhyay","doi":"10.1016/j.ijnonlinmec.2024.104935","DOIUrl":"10.1016/j.ijnonlinmec.2024.104935","url":null,"abstract":"<div><div>Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104935"},"PeriodicalIF":2.8,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-19DOI: 10.1016/j.ijnonlinmec.2024.104926
Amit Bhowmick, Jeevanjyoti Chakraborty
Volumetric swelling due to lithiation into active battery materials is a well-known phenomenon. A chemo-mechanical framework can suitably explain the deformations of the electrode and the generation of diffusion-induced stresses (DIS). Various experimental works have shown that the effects of DIS further cause the active material to lose its structural stability. However, relatively few frameworks exist that can investigate such phenomena in a comprehensive manner. These are mainly based on the Euler–Bernoulli beam theory and the von-Karman plate theory. In the present work we present a generalized three-dimensional instability framework incorporating the theory of incremental deformation. We use this theory on a widely used chemo-mechanical framework. Notably, similar existing instability investigations on negative electrode materials are based only on incompressible material behaviour. As opposed to it, in this work we have considered a compressible material. Also, we account for the spatial and temporal nature of growth, which is a significant departure from the existing instability frameworks. Therefore, this current work brings the investigation of structural instability of electrode material closer to physical reality. In our study, we use the compound matrix method to find the critical lithiation parameter. Then we consider three sets of problems, each with a particular combination of boundary conditions applied on the inner and outer cylindrical surfaces of hollow cylindrical anode particles. These are free-free, fixed-free, and free-fixed, where each combination represents a particular type of interaction between an electrode particle and its surroundings. Most importantly, we find that the free-free and fixed-free conditions show only a pure axial and mixed mode of instability, and do not show the pure circumferential mode. The free-fixed conditions, however, shows all three modes of instability. Additionally, the presence of mode crossover makes the instability pattern of such electrode particles significant.
{"title":"Instability analysis of Li-ion battery electrode particles induced by chemomechanical growth using incremental deformation theory","authors":"Amit Bhowmick, Jeevanjyoti Chakraborty","doi":"10.1016/j.ijnonlinmec.2024.104926","DOIUrl":"10.1016/j.ijnonlinmec.2024.104926","url":null,"abstract":"<div><div>Volumetric swelling due to lithiation into active battery materials is a well-known phenomenon. A chemo-mechanical framework can suitably explain the deformations of the electrode and the generation of diffusion-induced stresses (DIS). Various experimental works have shown that the effects of DIS further cause the active material to lose its structural stability. However, relatively few frameworks exist that can investigate such phenomena in a comprehensive manner. These are mainly based on the Euler–Bernoulli beam theory and the von-Karman plate theory. In the present work we present a generalized three-dimensional instability framework incorporating the theory of incremental deformation. We use this theory on a widely used chemo-mechanical framework. Notably, similar existing instability investigations on negative electrode materials are based only on incompressible material behaviour. As opposed to it, in this work we have considered a compressible material. Also, we account for the spatial and temporal nature of growth, which is a significant departure from the existing instability frameworks. Therefore, this current work brings the investigation of structural instability of electrode material closer to physical reality. In our study, we use the compound matrix method to find the critical lithiation parameter. Then we consider three sets of problems, each with a particular combination of boundary conditions applied on the inner and outer cylindrical surfaces of hollow cylindrical anode particles. These are free-free, fixed-free, and free-fixed, where each combination represents a particular type of interaction between an electrode particle and its surroundings. Most importantly, we find that the free-free and fixed-free conditions show only a pure axial and mixed mode of instability, and do not show the pure circumferential mode. The free-fixed conditions, however, shows all three modes of instability. Additionally, the presence of mode crossover makes the instability pattern of such electrode particles significant.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104926"},"PeriodicalIF":2.8,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-16DOI: 10.1016/j.ijnonlinmec.2024.104927
Mahanthesh Basavarajappa , Dambaru Bhatta
This study investigates the stability analysis of Rayleigh-Bénard configuration for a viscoelastic fluid subject to thermorheological effects, using the -Chebyshev- method. The fluid is modeled as a third-order viscoelastic fluid. This study accentuates how salting the fluid layer affects the thresholds for the onset of instability in a fluid of third order encompassing physically realistic rigid boundaries. The dynamic model incorporates advection-diffusion of temperature and solute concentration and a modified Navier–Stokes equation. We determine instability thresholds for the complex non-Newtonian fluid by analyzing the linear stability of the steady-state conduction solution. Our analysis proves the strong form of the principle of exchange of stabilities, demonstrating that convective motions can only occur through stationary motion. Additionally, a nonlinear stability analysis using the energy method is performed, deriving an unconditional nonlinear stability criterion. The results provide a comprehensive understanding of how variable viscosity and viscoelasticity impact system stability. Both the viscosity parameter and the third-grade fluid parameter exhibit stabilizing effects. Notably, we observe a discrepancy between the linear and global nonlinear stability results, indicating the presence of a subcritical instability region. This study contributes to the understanding of complex fluid dynamics in non-linear mechanical systems, with potential applications in various industrial and natural processes.
{"title":"Stability analysis for viscoelastic fluid with thermorheological effects: Linear and nonlinear approaches","authors":"Mahanthesh Basavarajappa , Dambaru Bhatta","doi":"10.1016/j.ijnonlinmec.2024.104927","DOIUrl":"10.1016/j.ijnonlinmec.2024.104927","url":null,"abstract":"<div><div>This study investigates the stability analysis of Rayleigh-Bénard configuration for a viscoelastic fluid subject to thermorheological effects, using the <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-Chebyshev-<span><math><mi>τ</mi></math></span> method. The fluid is modeled as a third-order viscoelastic fluid. This study accentuates how salting the fluid layer affects the thresholds for the onset of instability in a fluid of third order encompassing physically realistic rigid boundaries. The dynamic model incorporates advection-diffusion of temperature and solute concentration and a modified Navier–Stokes equation. We determine instability thresholds for the complex non-Newtonian fluid by analyzing the linear stability of the steady-state conduction solution. Our analysis proves the strong form of the principle of exchange of stabilities, demonstrating that convective motions can only occur through stationary motion. Additionally, a nonlinear stability analysis using the energy method is performed, deriving an unconditional nonlinear stability criterion. The results provide a comprehensive understanding of how variable viscosity and viscoelasticity impact system stability. Both the viscosity parameter and the third-grade fluid parameter exhibit stabilizing effects. Notably, we observe a discrepancy between the linear and global nonlinear stability results, indicating the presence of a subcritical instability region. This study contributes to the understanding of complex fluid dynamics in non-linear mechanical systems, with potential applications in various industrial and natural processes.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"168 ","pages":"Article 104927"},"PeriodicalIF":2.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-15DOI: 10.1016/j.ijnonlinmec.2024.104928
M.R.T. Arruda , J. Shen
This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.
本文比较了应用于 ABAQUS 标准 UMAT 用户子程序的不同方法估算切线刚度的计算效率，使用的是隐式表述与预测器校正器方法。它使用两种新方法来估算预测器-校正器迭代过程的刚度矩阵，分别称为 "扰动法 "和 "隐式转显式法"。使用扰动法时，只需使用正割矩阵即可建立 UMAT，因为会自动计算近似切向材料矩阵，从而促进在 ABAQUS 标准中更快地实施新的材料构成关系。此外，还研究了使用新算法的可能性，该算法利用新的等值线预测校正器算法将 UMAT 隐式公式转换为显式公式。在这项研究中，使用了一种新的混凝土损伤模型，该模型考虑了具有模式 I 断裂的拉伸和压缩行为的断裂能量正则化。利用科学界测试破坏模型的经典和已知基准，从时间和迭代次数的角度对这两种计算雅各矩阵的方法进行了比较。
{"title":"Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics","authors":"M.R.T. Arruda , J. Shen","doi":"10.1016/j.ijnonlinmec.2024.104928","DOIUrl":"10.1016/j.ijnonlinmec.2024.104928","url":null,"abstract":"<div><div>This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104928"},"PeriodicalIF":2.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.ijnonlinmec.2024.104921
Manuel Núñez
The theory of high Mach number flows creating a thin layer between a shock wave and a delta wing surface rests on a certain functional equation or its associated differential one, both of which are nonstandard and the existence of solutions cannot be guaranteed. There exists a free parameter within these equations in the form of the shape of the wing, about which we wish to obtain necessary conditions for a thin shock layer to exist. We get some direct estimates in terms of bounds on the side flow at the initial condition, as well as some indirect ones related to the regularity of the shock wave, which is itself linked to the energy of the flow.
{"title":"On the equations of thin shock layer theory","authors":"Manuel Núñez","doi":"10.1016/j.ijnonlinmec.2024.104921","DOIUrl":"10.1016/j.ijnonlinmec.2024.104921","url":null,"abstract":"<div><div>The theory of high Mach number flows creating a thin layer between a shock wave and a delta wing surface rests on a certain functional equation or its associated differential one, both of which are nonstandard and the existence of solutions cannot be guaranteed. There exists a free parameter within these equations in the form of the shape of the wing, about which we wish to obtain necessary conditions for a thin shock layer to exist. We get some direct estimates in terms of bounds on the side flow at the initial condition, as well as some indirect ones related to the regularity of the shock wave, which is itself linked to the energy of the flow.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104921"},"PeriodicalIF":2.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-10-11DOI: 10.1016/j.ijnonlinmec.2024.104925
Zheng Chen, Hui Ren, Wei Fan, Ping Zhou
An accurate and locking-free geometric exact beam formulation (GEBF) on the special orthogonal group SO(3) is developed for slender beams with large deformations and large rotations. Due to the nonlinear nature of the spatial rotations, the classical GEBFs usually have a non-constant mass matrix and complex expressions of inertia forces; meanwhile, the singularity and locking issues are also key matters of concern. Aiming at resolving these drawbacks, two main contributions are achieved in the present work. First, the angular velocity is independently interpolated, resulting in a constant mass matrix and explicitly representable inertial forces, which can offer significant advantages for efficient dynamic simulations. Second, inspired by the assumed natural strain method in shell theory, the stretch-shear strain is interpolated to obtain simplified and locking-free elastic forces, which is a new attempt to alleviate the locking problems for the GEBFs. In addition, the special orthogonal group SO(3) is utilized for updating incremental rotation vectors to eliminate singularities, and objective strain measurement is achieved by employing relative rotation vector interpolation. The effectiveness and superiority of the developed low-order and high-order elements are demonstrated through numerical simulations of standard benchmark examples. The present work contributes to the advancement of accurate and reliable formulation for slender beams; the constant mass matrix, the locking-free characteristics, and the elegant form of the formulation make it particularly suitable for multibody dynamic analysis.
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