Evidence from cyclic tests on metals, elastomers and sandy soils reveals that damping forces are nearly rate-independent and structural (hysteretic or rate-independent) damping was widely adopted since the 1940s. While there is no time-domain constitutive equation for a linear spring connected in parallel with a rate-independent dashpot, the dynamic stiffness (transfer function) of this mechanical network can be constructed in the frequency-domain; and it was known since the early 1960s that this mechanical network exhibits a non-causal response. In view of its simplicity in association with the wide practical need to model rate-independent dissipation, this mechanical network was also implemented in time-domain formulations with the label complex stiffness where the force output, P(t) is related in the time-domain to the displacement input, u(t), with P(t) = k(1 + i η)u(t). This paper shows that the complex stiffness, as expressed in the time-domain by various scholars, is a fundamentally flawed construct since in addition to causality it violates equilibrium.
{"title":"Equilibrium Violation from the Complex Stiffness","authors":"N. Makris","doi":"10.1115/1.4062263","DOIUrl":"https://doi.org/10.1115/1.4062263","url":null,"abstract":"\u0000 Evidence from cyclic tests on metals, elastomers and sandy soils reveals that damping forces are nearly rate-independent and structural (hysteretic or rate-independent) damping was widely adopted since the 1940s. While there is no time-domain constitutive equation for a linear spring connected in parallel with a rate-independent dashpot, the dynamic stiffness (transfer function) of this mechanical network can be constructed in the frequency-domain; and it was known since the early 1960s that this mechanical network exhibits a non-causal response. In view of its simplicity in association with the wide practical need to model rate-independent dissipation, this mechanical network was also implemented in time-domain formulations with the label complex stiffness where the force output, P(t) is related in the time-domain to the displacement input, u(t), with P(t) = k(1 + i η)u(t). This paper shows that the complex stiffness, as expressed in the time-domain by various scholars, is a fundamentally flawed construct since in addition to causality it violates equilibrium.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47635790","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}
The use of general tensegrity systems that incorporate rigid bodies beyond axially loaded members has garnered increasing attention in practical applications. Recent preliminary studies have been conducted on the analysis and form design of general tensegrity systems with disconnecting rigid bodies. However, existing methods cannot account for connections between different rigid bodies. In practical applications, general tensegrity systems may have interconnected rigid bodies, rendering the analysis method proposed in previous studies inapplicable. To address this issue, this work proposes a comprehensive and unified analysis method for general tensegrity systems. The proposed formulation allows for the incorporation of connections between rigid bodies and general tensegrity systems with supports into the developed framework, enabling uniform analysis. Equilibrium and compatibility equations are derived through an energy approach combined with the Lagrange multiplier method. Self-stress states and mechanism modes are then computed based on these formulations. The stiffness of the mechanism mode is analyzed and validated using both the product force method and the reduced geometric stiffness matrix method. Furthermore, a prestress design approach based on Semi-Definite Programming (SDP) is proposed to determine feasible member forces that can stabilize general tensegrity systems. Illustrative examples are presented to verify the effectiveness of the proposed approach. This study expands the scope of the analysis theory for tensegrity systems and provides a fundamental and unified analysis approach that can be applied to any type of tensegrity system.
{"title":"Self-equilibrium, Mechanism Stiffness, and Self-stress Design of General Tensegrity with Rigid Bodies or Supports: A Unified Analysis Approach","authors":"Yafeng Wang, Xian Xu, Yaozhi Luo","doi":"10.1115/1.4062225","DOIUrl":"https://doi.org/10.1115/1.4062225","url":null,"abstract":"\u0000 The use of general tensegrity systems that incorporate rigid bodies beyond axially loaded members has garnered increasing attention in practical applications. Recent preliminary studies have been conducted on the analysis and form design of general tensegrity systems with disconnecting rigid bodies. However, existing methods cannot account for connections between different rigid bodies. In practical applications, general tensegrity systems may have interconnected rigid bodies, rendering the analysis method proposed in previous studies inapplicable. To address this issue, this work proposes a comprehensive and unified analysis method for general tensegrity systems. The proposed formulation allows for the incorporation of connections between rigid bodies and general tensegrity systems with supports into the developed framework, enabling uniform analysis. Equilibrium and compatibility equations are derived through an energy approach combined with the Lagrange multiplier method. Self-stress states and mechanism modes are then computed based on these formulations. The stiffness of the mechanism mode is analyzed and validated using both the product force method and the reduced geometric stiffness matrix method. Furthermore, a prestress design approach based on Semi-Definite Programming (SDP) is proposed to determine feasible member forces that can stabilize general tensegrity systems. Illustrative examples are presented to verify the effectiveness of the proposed approach. This study expands the scope of the analysis theory for tensegrity systems and provides a fundamental and unified analysis approach that can be applied to any type of tensegrity system.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45426222","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}
Pain sensation induced by kidney stone (renal calculi) in ureter, a kind of visceral ducts connecting the kidneys and bladder, critically depends upon the relative size of stone to ureter. To quantify such pain sensation, we draw a parallel analogy between the mechanisms underlying skin/teeth thermal pain (which can be quantified with a holistic pain model consisting of modified Hodgkin-Huxley model and gate control theory) and mechanism of ureteral pain to extend the holistic pain model to stone-blocked ureter. We then perform finite element simulations to obtain key mechanical stresses on ureter wall exerted by a kidney stone having varying size. These stresses are subsequently adopted to calculate the voltage potential of neuron membrane in the holistic pain model and eventually a theoretical framework to quantify the dependence of ureteral pain sensation on stone size is established, for the first time. We demonstrate that ureter pain sensation increases sharply when the diameter of kidney stone becomes 7.5% to 20% larger than the inner diameter of ureter, peaking at ~20% larger; however, increasing further the stone diameter leads only to marginally exacerbated pain sensation. Other related effects on ureter pain sensation, such as ureter wall thickness, ureter stiffness, and intra-abdominal pressure (IAP), are evaluated. Results of the present study provide insightful information for urologists to diagnose and treat patients with renal calculi in a more personalized way.
{"title":"QUANTIFICATION OF URETERAL PAIN SENSATION INDUCED BY KIDNEY STONE","authors":"Yonggang Liu, Shaobao Liu, Moxiao Li, T. Lu","doi":"10.1115/1.4062222","DOIUrl":"https://doi.org/10.1115/1.4062222","url":null,"abstract":"\u0000 Pain sensation induced by kidney stone (renal calculi) in ureter, a kind of visceral ducts connecting the kidneys and bladder, critically depends upon the relative size of stone to ureter. To quantify such pain sensation, we draw a parallel analogy between the mechanisms underlying skin/teeth thermal pain (which can be quantified with a holistic pain model consisting of modified Hodgkin-Huxley model and gate control theory) and mechanism of ureteral pain to extend the holistic pain model to stone-blocked ureter. We then perform finite element simulations to obtain key mechanical stresses on ureter wall exerted by a kidney stone having varying size. These stresses are subsequently adopted to calculate the voltage potential of neuron membrane in the holistic pain model and eventually a theoretical framework to quantify the dependence of ureteral pain sensation on stone size is established, for the first time. We demonstrate that ureter pain sensation increases sharply when the diameter of kidney stone becomes 7.5% to 20% larger than the inner diameter of ureter, peaking at ~20% larger; however, increasing further the stone diameter leads only to marginally exacerbated pain sensation. Other related effects on ureter pain sensation, such as ureter wall thickness, ureter stiffness, and intra-abdominal pressure (IAP), are evaluated. Results of the present study provide insightful information for urologists to diagnose and treat patients with renal calculi in a more personalized way.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44227700","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}
Achieving extreme deformations without electrical breakdown has been a longstanding challenge in the dielectric elastomer community. In this paper, we present a novel approach for accessing giant in-plane stretches in circular dielectric elastomer membranes by leveraging nonlinear dynamics, specifically short-duration voltage pulses. These voltage pulses – applied about nominal bias voltages where the large-stretch equilibrium does not experience dielectric breakdown – create transient stretches that, if sufficiently large, cause the membrane to dynamically snap-through to its large-stretch equilibrium. These giant deformations are reversible; pulsed voltage drops can return the membrane from its large-stretch equilibrium to its small-stretch equilibrium. Parametric analyses are used to determine combinations of pulse amplitude and duration that result in snap-through. Corresponding through-thickness electric fields are shown to be below stretch-dependent dielectric strengths from the literature, suggesting practical feasibility. Unlike other techniques for accessing extreme stretches in dielectric elastomers, the present approach relies on voltage control alone; it therefore does not require altering the external mechanical forces that cause pre-stretch and can be applied without modifying the elastomer's mechanical compliance. This research demonstrates that carefully designed voltage pulses may permit existing and emerging soft material technologies to access extreme, large-stretch equilibria without dielectric breakdown.
{"title":"Leveraging Dynamics-Induced Snap-Through Instabilities to Access Giant Deformations in Dielectric Elastomer Membranes","authors":"Christopher Cooley, R. Lowe","doi":"10.1115/1.4062224","DOIUrl":"https://doi.org/10.1115/1.4062224","url":null,"abstract":"\u0000 Achieving extreme deformations without electrical breakdown has been a longstanding challenge in the dielectric elastomer community. In this paper, we present a novel approach for accessing giant in-plane stretches in circular dielectric elastomer membranes by leveraging nonlinear dynamics, specifically short-duration voltage pulses. These voltage pulses – applied about nominal bias voltages where the large-stretch equilibrium does not experience dielectric breakdown – create transient stretches that, if sufficiently large, cause the membrane to dynamically snap-through to its large-stretch equilibrium. These giant deformations are reversible; pulsed voltage drops can return the membrane from its large-stretch equilibrium to its small-stretch equilibrium. Parametric analyses are used to determine combinations of pulse amplitude and duration that result in snap-through. Corresponding through-thickness electric fields are shown to be below stretch-dependent dielectric strengths from the literature, suggesting practical feasibility. Unlike other techniques for accessing extreme stretches in dielectric elastomers, the present approach relies on voltage control alone; it therefore does not require altering the external mechanical forces that cause pre-stretch and can be applied without modifying the elastomer's mechanical compliance. This research demonstrates that carefully designed voltage pulses may permit existing and emerging soft material technologies to access extreme, large-stretch equilibria without dielectric breakdown.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42759976","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}
A closed-form analytical solution is developed for a planar inhomogeneous beam subjected to transverse loading, using Variational Asymptotic Method (VAM). The VAM decouples the problem into a cross-sectional and an along-the-length analysis, leading to a set of ordinary differential equations. These equations along with associated boundary conditions have been solved to obtain the closed-form analytical solutions. Three distinct gradation models have been used to validate the present formulation against 3D FEA and few prominent results from the literature. Excellent agreement has been obtained for all the test cases. Key contributions of the present work are (a) the solutions have been obtained without any ad-hoc and a-prior assumptions (b) the ordered warping solutions results in Euler-Bernoulli type deformation in the zeroth-order, whereas the higher-order solutions provide novel closed-form expressions for transverse shear strain and stress. Finally, the effect of inhomogeneity on various field variables has been analyzed and discussed.
{"title":"Asymptotically Accurate Analytical Solution for Timoshenko-like Deformation of Functionally Graded Beams","authors":"Amandeep, Satwinder Singh, S. Padhee","doi":"10.1115/1.4062223","DOIUrl":"https://doi.org/10.1115/1.4062223","url":null,"abstract":"\u0000 A closed-form analytical solution is developed for a planar inhomogeneous beam subjected to transverse loading, using Variational Asymptotic Method (VAM). The VAM decouples the problem into a cross-sectional and an along-the-length analysis, leading to a set of ordinary differential equations. These equations along with associated boundary conditions have been solved to obtain the closed-form analytical solutions. Three distinct gradation models have been used to validate the present formulation against 3D FEA and few prominent results from the literature. Excellent agreement has been obtained for all the test cases. Key contributions of the present work are (a) the solutions have been obtained without any ad-hoc and a-prior assumptions (b) the ordered warping solutions results in Euler-Bernoulli type deformation in the zeroth-order, whereas the higher-order solutions provide novel closed-form expressions for transverse shear strain and stress. Finally, the effect of inhomogeneity on various field variables has been analyzed and discussed.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43955357","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}
Jize Dai, Lu Lu, Sophie Leanza, J. Hutchinson, R. Zhao
Ring origami has emerged as a robust strategy for designing foldable and deployable structures due to its impressive packing abilities achieved from the snap-folding mechanism. In general, polygonal rings with rationally designed geometric parameters can fold into compacted three-loop configurations with curved segments, which result from the internal bending moment in the folded state. Inspired by the internal bending moment-induced curvature in the folded state, we explore how this curvature can be tuned by introducing initial natural curvature to the segments of the polygonal rings in their deployed stress-free state, and study how this initial curvature affects their folded configurations. Taking a clue from straight-segmented polygonal rings that fold into overlapping curved loops, we find it is possible to reverse the process by introducing curvature into the ring segments in the stress-free initial state such that the rings fold into a straight-line looped pattern with “zero” area. This realizes extreme packing. In this work, by a combination of experimental observation, finite element analysis, and theoretical modeling, we systematically study the effect of segment curvature on folding behavior, folded configurations, and packing of curved ring origami with different geometries. It is anticipated that curved ring origami can open a new avenue for the design of foldable and deployable structures with simple folded configurations and high packing efficiency.
{"title":"Curved Ring Origami: Bistable Elastic Folding for Magic Pattern Reconfigurations","authors":"Jize Dai, Lu Lu, Sophie Leanza, J. Hutchinson, R. Zhao","doi":"10.1115/1.4062221","DOIUrl":"https://doi.org/10.1115/1.4062221","url":null,"abstract":"\u0000 Ring origami has emerged as a robust strategy for designing foldable and deployable structures due to its impressive packing abilities achieved from the snap-folding mechanism. In general, polygonal rings with rationally designed geometric parameters can fold into compacted three-loop configurations with curved segments, which result from the internal bending moment in the folded state. Inspired by the internal bending moment-induced curvature in the folded state, we explore how this curvature can be tuned by introducing initial natural curvature to the segments of the polygonal rings in their deployed stress-free state, and study how this initial curvature affects their folded configurations. Taking a clue from straight-segmented polygonal rings that fold into overlapping curved loops, we find it is possible to reverse the process by introducing curvature into the ring segments in the stress-free initial state such that the rings fold into a straight-line looped pattern with “zero” area. This realizes extreme packing. In this work, by a combination of experimental observation, finite element analysis, and theoretical modeling, we systematically study the effect of segment curvature on folding behavior, folded configurations, and packing of curved ring origami with different geometries. It is anticipated that curved ring origami can open a new avenue for the design of foldable and deployable structures with simple folded configurations and high packing efficiency.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41416394","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}
A contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational methodology for developing plasticity-induced cumulative damage models for multilayered structures.
{"title":"A Cohesive-Zone-Based Contact Mechanics Analysis of Delamination in Homogeneous and Layered Half-Spaces Subjected to Normal and Shear Surface Tractions","authors":"J. Cen, K. Komvopoulos","doi":"10.1115/1.4062141","DOIUrl":"https://doi.org/10.1115/1.4062141","url":null,"abstract":"\u0000 A contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational methodology for developing plasticity-induced cumulative damage models for multilayered structures.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41756371","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}
The effect of three different friction interface models on an elastic half-space is presented. Three constitutive friction models are studied: Coulomb, Soil-Concrete Interface and Bouc-Wen, using a computational mechanics framework that can represent the contact patch's material response to static and dynamic surface tractions. This response is observed as strains and stresses present from reciprocating sliding using an elasto-plastic friction(EPF) algorithm that also captures energy dissipation and hysteresis due to friction sliding. Additionally, the use of the 4-parameter Bouc-Wen model represents a new development in contact mechanics that allows microslip of the contact interface to be modeled. Hysteresis loops are generated for the three friction models based on a quasi-static assumption. This algorithm is built into a meso-scale FEM solver that is able to simulate different loading conditions and provide insight about how the friction models respond to load conditions and inform on experimental data. The energy dissipation from reciprocating friction sliding will be generated for each friction model as a metric that captures surface wear and potentially material damage.
{"title":"Energy Dissipation on an elastic interface as a metric for evaluating three friction models","authors":"I. Lawal, M. Brake","doi":"10.1115/1.4062138","DOIUrl":"https://doi.org/10.1115/1.4062138","url":null,"abstract":"\u0000 The effect of three different friction interface models on an elastic half-space is presented. Three constitutive friction models are studied: Coulomb, Soil-Concrete Interface and Bouc-Wen, using a computational mechanics framework that can represent the contact patch's material response to static and dynamic surface tractions. This response is observed as strains and stresses present from reciprocating sliding using an elasto-plastic friction(EPF) algorithm that also captures energy dissipation and hysteresis due to friction sliding. Additionally, the use of the 4-parameter Bouc-Wen model represents a new development in contact mechanics that allows microslip of the contact interface to be modeled. Hysteresis loops are generated for the three friction models based on a quasi-static assumption. This algorithm is built into a meso-scale FEM solver that is able to simulate different loading conditions and provide insight about how the friction models respond to load conditions and inform on experimental data. The energy dissipation from reciprocating friction sliding will be generated for each friction model as a metric that captures surface wear and potentially material damage.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47718190","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}
We present a new formulation for the multilayer Isogeometric Kirchhoff--Love (KL) shells, where the individual layers are assumed to interact through no-penetration and frictional contact. This work is largely motivated by the experiments and analysis presented in [1]. We utilize a regularized version of Coulomb's friction law to model the tangential traction between the contacting shell surfaces. To ensure objectivity (i.e., reference-frame invariance) in the frictional model, we propose two different strategies to extrapolate the velocity vectors of the contact pair at the contact interface: (i) Using the underlying KL kinematics of the individual shell layers and (ii) Using the Taylor series-based extension from [2]. We compare the performance of both approaches through a numerical benchmark example. We then validate our multilayer shell formulation using the ‘bending response of a book with internal friction’ experiments of [1].
{"title":"Multilayer Shells Interacting Through Friction","authors":"M. Alaydin, Y. Bazilevs","doi":"10.1115/1.4062139","DOIUrl":"https://doi.org/10.1115/1.4062139","url":null,"abstract":"\u0000 We present a new formulation for the multilayer Isogeometric Kirchhoff--Love (KL) shells, where the individual layers are assumed to interact through no-penetration and frictional contact. This work is largely motivated by the experiments and analysis presented in [1]. We utilize a regularized version of Coulomb's friction law to model the tangential traction between the contacting shell surfaces. To ensure objectivity (i.e., reference-frame invariance) in the frictional model, we propose two different strategies to extrapolate the velocity vectors of the contact pair at the contact interface: (i) Using the underlying KL kinematics of the individual shell layers and (ii) Using the Taylor series-based extension from [2]. We compare the performance of both approaches through a numerical benchmark example. We then validate our multilayer shell formulation using the ‘bending response of a book with internal friction’ experiments of [1].","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42429565","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}
The formulation used by the most of studies on elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for torus. In this paper, we will carry on author's previous work [B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of our own maple code, we are able to simulate some typical problems of torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. One of the most interesting discovery is that the crowns of a torus are the turning point of the Gaussion curvature at ϕ = 0, π, where the mechanics response of inner and outer torus is almost separated.
{"title":"The Mechanics Difference Between The Outer Torus and Inner Torus","authors":"B. Sun, Guangming Song","doi":"10.1115/1.4062136","DOIUrl":"https://doi.org/10.1115/1.4062136","url":null,"abstract":"\u0000 The formulation used by the most of studies on elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for torus. In this paper, we will carry on author's previous work [B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of our own maple code, we are able to simulate some typical problems of torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. One of the most interesting discovery is that the crowns of a torus are the turning point of the Gaussion curvature at ϕ = 0, π, where the mechanics response of inner and outer torus is almost separated.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45959591","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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