Pub Date : 2024-11-16DOI: 10.1007/s00161-024-01336-x
Michele Tepedino, Francesco D’Annibale, Ivan Giorgio, Ewa Bednarczyk, Daniel George
Orthodontic tooth movement is the fundamental phenomenon underlying the treatment of dental malocclusions. For orthodontic treatment to be efficient and effective, the amount of force applied to the teeth for every kind of movement should be appropriately dosed, because it is associated with the risk of side effects and the treatment time. However, our knowledge of the complex cascade of events that transforms a mechanical stimulus into an ordinated bone remodeling is incomplete. Predictive theoretical numerical models could be of invaluable help in understanding the bone response to orthodontic loading and in studying the effects of complex orthodontic force systems. However, either short-term or evolutive predictive models showed a large heterogeneity of material properties and governing equations. The present review provides an outline of the physical and biochemical basis of orthodontic tooth movement with a focus around the periodontal ligament interface. The use of a standardized method for designing predictive models is advocated, and perspectives for future studies are presented.
{"title":"Predictive models for bone remodeling during orthodontic tooth movement: a scoping review on the “biological metamaterial” periodontal ligament interface","authors":"Michele Tepedino, Francesco D’Annibale, Ivan Giorgio, Ewa Bednarczyk, Daniel George","doi":"10.1007/s00161-024-01336-x","DOIUrl":"10.1007/s00161-024-01336-x","url":null,"abstract":"<div><p>Orthodontic tooth movement is the fundamental phenomenon underlying the treatment of dental malocclusions. For orthodontic treatment to be efficient and effective, the amount of force applied to the teeth for every kind of movement should be appropriately dosed, because it is associated with the risk of side effects and the treatment time. However, our knowledge of the complex cascade of events that transforms a mechanical stimulus into an ordinated bone remodeling is incomplete. Predictive theoretical numerical models could be of invaluable help in understanding the bone response to orthodontic loading and in studying the effects of complex orthodontic force systems. However, either short-term or evolutive predictive models showed a large heterogeneity of material properties and governing equations. The present review provides an outline of the physical and biochemical basis of orthodontic tooth movement with a focus around the periodontal ligament interface. The use of a standardized method for designing predictive models is advocated, and perspectives for future studies are presented.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642571","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 : 2024-11-14DOI: 10.1007/s00161-024-01335-y
Larry Murcia Terranova, Christian Cardillo, Giuliano Aretusi
In this work, we investigate a dynamic internal dissipation mechanism in the context of cement-based materials by introducing a 1D-enhanced micromorphic beam model with a dynamic internal friction term. Here, we consider an inherent feature in concrete-like materials arising from the multi-scale structure, namely, microcracks. Thus, we assume that the internal dissipation of the energy depends on the overall relative sliding displacement of the opposite faces in the microcracks under the effects of an applied cyclic load whenever no significant phenomena related to damage occur at the macroscopic level. The dynamic friction term is based on a well-known model for dry friction in solids due to P. R. Dahl, where the friction force depends only on the sliding displacement and evolves in time, reproducing an elastoplastic behavior. The model proposed in this paper takes into account a mechanical energy interchange between both bending and shear distortion in the beam with the sliding occurring at the microcracks, a storage of mechanical energy because of the asperities inside the faces of the microcracks, and the dissipation of the energy that follows from the interaction between the bending and the microcracks. Numerical simulations of the kinematic descriptors and the dissipative cycles are also provided by using the Finite Element Method and the commercial software COMSOL Multiphysics®.
在这项工作中,我们通过引入带有动态内部摩擦项的一维增强微观梁模型,研究了水泥基材料的动态内部耗散机制。在此,我们考虑了混凝土类材料因多尺度结构而产生的固有特征,即微裂缝。因此,我们假定,当宏观层面没有出现明显的破坏现象时,能量的内部耗散取决于微裂缝中相对面在外加循环载荷作用下的整体相对滑动位移。动态摩擦项基于 P. R. Dahl 提出的著名固体干摩擦模型,其中摩擦力仅取决于滑动位移并随时间变化,再现了弹塑性行为。本文提出的模型考虑了梁的弯曲变形和剪切变形与微裂缝处发生的滑动之间的机械能交换、微裂缝面内的尖角所产生的机械能储存以及弯曲和微裂缝之间的相互作用所产生的能量耗散。此外,还使用有限元法和商用软件 COMSOL Multiphysics® 对运动描述符和耗散循环进行了数值模拟。
{"title":"An enhanced beam model incorporating a hysteresis-based solid friction damping mechanism for cementitious materials","authors":"Larry Murcia Terranova, Christian Cardillo, Giuliano Aretusi","doi":"10.1007/s00161-024-01335-y","DOIUrl":"10.1007/s00161-024-01335-y","url":null,"abstract":"<div><p>In this work, we investigate a dynamic internal dissipation mechanism in the context of cement-based materials by introducing a 1D-enhanced micromorphic beam model with a dynamic internal friction term. Here, we consider an inherent feature in concrete-like materials arising from the multi-scale structure, namely, microcracks. Thus, we assume that the internal dissipation of the energy depends on the overall relative sliding displacement of the opposite faces in the microcracks under the effects of an applied cyclic load whenever no significant phenomena related to damage occur at the macroscopic level. The dynamic friction term is based on a well-known model for dry friction in solids due to P. R. Dahl, where the friction force depends only on the sliding displacement and evolves in time, reproducing an elastoplastic behavior. The model proposed in this paper takes into account a mechanical energy interchange between both bending and shear distortion in the beam with the sliding occurring at the microcracks, a storage of mechanical energy because of the asperities inside the faces of the microcracks, and the dissipation of the energy that follows from the interaction between the bending and the microcracks. Numerical simulations of the kinematic descriptors and the dissipative cycles are also provided by using the Finite Element Method and the commercial software COMSOL Multiphysics<sup>®</sup>.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636841","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 : 2024-11-14DOI: 10.1007/s00161-024-01333-0
Aleksandr Yu. Chirkov, Lidiia Nazarenko, Holm Altenbach
This paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gradients is applied, simplifying the choice of approximating functions. The concept of energy balance is adopted to calculate the energy release rate with a virtual increase in crack length. The increment of the potential energy of an elastic body is determined by accounting for the strain and stress gradient contribution. Numerical calculations were performed using a quasi-uniform triangular mesh of the cross-type. The mesh refinement was applied in the vicinity of the crack tip, at the concentrated support, and the point of application of the transverse force, and uniform mesh partitioning was utilized in the rest of the beam. The fine-mesh analysis was carried out on the successively condensed meshes in the stress concentration domain for different values of the length scale parameter. The crack opening displacements and the distribution of strains and Cauchy stresses for various values of the length scale parameter are presented. An increase in this parameter increases the stiffness of the crack, which leads to a decrease in the crack opening displacements and a smooth closure of its faces at the crack tip. In addition, accounting for the scale parameter reduces the calculated values of strains and stresses near the crack tip. Based on the energy balance criterion, local fracture parameters such as the release rate of elastic energy at the crack tip and the stress intensity factor are determined for different values of the mesh step. The numerical calculations indicate the convergence of the obtained approximations. The main feature of solutions, which includes the strain gradient contribution, is the decrease in the values of the calculated parameters associated with the fracture energy compared to the classical elasticity theory.
{"title":"Mixed FEM implementation of three-point bending of the beam with an edge crack within strain gradient elasticity theory","authors":"Aleksandr Yu. Chirkov, Lidiia Nazarenko, Holm Altenbach","doi":"10.1007/s00161-024-01333-0","DOIUrl":"10.1007/s00161-024-01333-0","url":null,"abstract":"<div><p>This paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gradients is applied, simplifying the choice of approximating functions. The concept of energy balance is adopted to calculate the energy release rate with a virtual increase in crack length. The increment of the potential energy of an elastic body is determined by accounting for the strain and stress gradient contribution. Numerical calculations were performed using a quasi-uniform triangular mesh of the cross-type. The mesh refinement was applied in the vicinity of the crack tip, at the concentrated support, and the point of application of the transverse force, and uniform mesh partitioning was utilized in the rest of the beam. The fine-mesh analysis was carried out on the successively condensed meshes in the stress concentration domain for different values of the length scale parameter. The crack opening displacements and the distribution of strains and Cauchy stresses for various values of the length scale parameter are presented. An increase in this parameter increases the stiffness of the crack, which leads to a decrease in the crack opening displacements and a smooth closure of its faces at the crack tip. In addition, accounting for the scale parameter reduces the calculated values of strains and stresses near the crack tip. Based on the energy balance criterion, local fracture parameters such as the release rate of elastic energy at the crack tip and the stress intensity factor are determined for different values of the mesh step. The numerical calculations indicate the convergence of the obtained approximations. The main feature of solutions, which includes the strain gradient contribution, is the decrease in the values of the calculated parameters associated with the fracture energy compared to the classical elasticity theory.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01333-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-10-09DOI: 10.1007/s00161-024-01326-z
Yanfei Lu
In this paper, the bone tissue was modeled as a linear viscoelastic material saturated with interstitial fluid. We considered a specific case of harmonic loading and related the mechanical stimuli to the loading frequency. In this way, we could include the inertial effect in the model while not having to deal with the perturbation during each loading period. Two types of mechanical signals were considered: strain energy and dissipation energy. A parametric study revealed the dependency of the two signals on loading frequency and material property. The evolution of the apparent mass density supported the parametric study’s findings. Under the three different frequency loadings, the strain energy-stimulated samples experienced identical remodeling scenarios. The samples stimulated with dissipation energy, on the other hand, exhibited a strong frequency dependence. An additional study was performed to investigate the effect of long-term variations in the loading frequency on the remodeling process. This demonstrated the model’s capabilities in designing and evaluating load regimes for rehabilitation following a bone injury or bone reconstruction.
{"title":"A frequency-dependent model for bone remodeling using a micromorphic porous medium subjected to harmonic mechanical loading","authors":"Yanfei Lu","doi":"10.1007/s00161-024-01326-z","DOIUrl":"10.1007/s00161-024-01326-z","url":null,"abstract":"<div><p>In this paper, the bone tissue was modeled as a linear viscoelastic material saturated with interstitial fluid. We considered a specific case of harmonic loading and related the mechanical stimuli to the loading frequency. In this way, we could include the inertial effect in the model while not having to deal with the perturbation during each loading period. Two types of mechanical signals were considered: strain energy and dissipation energy. A parametric study revealed the dependency of the two signals on loading frequency and material property. The evolution of the apparent mass density supported the parametric study’s findings. Under the three different frequency loadings, the strain energy-stimulated samples experienced identical remodeling scenarios. The samples stimulated with dissipation energy, on the other hand, exhibited a strong frequency dependence. An additional study was performed to investigate the effect of long-term variations in the loading frequency on the remodeling process. This demonstrated the model’s capabilities in designing and evaluating load regimes for rehabilitation following a bone injury or bone reconstruction.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 6","pages":"1741 - 1753"},"PeriodicalIF":1.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01326-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142385170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-10-03DOI: 10.1007/s00161-024-01331-2
Francesco D’Annibale, Arnaldo Casalotti
In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface.
{"title":"On the nonlinear dynamics of in-contact rigid bodies experiencing stick–slip and wear phenomena","authors":"Francesco D’Annibale, Arnaldo Casalotti","doi":"10.1007/s00161-024-01331-2","DOIUrl":"10.1007/s00161-024-01331-2","url":null,"abstract":"<div><p>In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 6","pages":"1815 - 1831"},"PeriodicalIF":1.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01331-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142368828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-09-28DOI: 10.1007/s00161-024-01330-3
O. A. Florea, E. M. Craciun, A. Öchsner, A. N. Emin
This study examines a mixed initial-boundary value problem in thermoelastic materials with a double porosity structure, taking into account the effects of microtemperature. The existence of a solution is established by converting the problem into a Cauchy-type problem. Given the complexity of the equations, unknowns, and conditions, we apply contraction semigroup theory within a specific Hilbert space. We prove the existence of a solution using the Lax-Milgram theorem. Additionally, the uniqueness of the solution is demonstrated based on the Lumer-Phillips corollary, which corresponds to the Hille-Yosida theorem. In the final section, we show the continuous dependence of the solution on the mixed initial-boundary value problem for double porous thermoelasticity with microtemperature.
{"title":"A qualitative analysis on the double porous thermoelastic bodies with microtemperature","authors":"O. A. Florea, E. M. Craciun, A. Öchsner, A. N. Emin","doi":"10.1007/s00161-024-01330-3","DOIUrl":"10.1007/s00161-024-01330-3","url":null,"abstract":"<div><p>This study examines a mixed initial-boundary value problem in thermoelastic materials with a double porosity structure, taking into account the effects of microtemperature. The existence of a solution is established by converting the problem into a Cauchy-type problem. Given the complexity of the equations, unknowns, and conditions, we apply contraction semigroup theory within a specific Hilbert space. We prove the existence of a solution using the Lax-Milgram theorem. Additionally, the uniqueness of the solution is demonstrated based on the Lumer-Phillips corollary, which corresponds to the Hille-Yosida theorem. In the final section, we show the continuous dependence of the solution on the mixed initial-boundary value problem for double porous thermoelasticity with microtemperature.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 6","pages":"1801 - 1813"},"PeriodicalIF":1.9,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01330-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142329613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-09-21DOI: 10.1007/s00161-024-01329-w
Yuriy Pyr’yev, Larry Murcia Terranova
The paper analyzes the vibrational behavior of cylinders in the offset printing machine caused by a cylinder gap shock. Specifically, it assesses the stability of a system of two cylinders. The analysis of the proposed model is reduced to solving a set of Hill equations. The singularity of the obtained equations is the relationship between the natural frequencies of the system and modulation depth. Numerical simulations, along with the generalized Hill’s determinant method, were employed to determine the critical parameters of parametric resonance, thereby establishing the conditions necessary for the stability of periodic vibrations.
{"title":"Vibration analysis associated with the operation of printing units in offset printing machines: applications towards metamaterials","authors":"Yuriy Pyr’yev, Larry Murcia Terranova","doi":"10.1007/s00161-024-01329-w","DOIUrl":"10.1007/s00161-024-01329-w","url":null,"abstract":"<div><p>The paper analyzes the vibrational behavior of cylinders in the offset printing machine caused by a cylinder gap shock. Specifically, it assesses the stability of a system of two cylinders. The analysis of the proposed model is reduced to solving a set of Hill equations. The singularity of the obtained equations is the relationship between the natural frequencies of the system and modulation depth. Numerical simulations, along with the generalized Hill’s determinant method, were employed to determine the critical parameters of parametric resonance, thereby establishing the conditions necessary for the stability of periodic vibrations.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 6","pages":"1787 - 1799"},"PeriodicalIF":1.9,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01329-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142276038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 : 2024-09-16DOI: 10.1007/s00161-024-01324-1
Ahmed E. Abouelregal, Fahad Alsharari, S. S. Alsaeed, Mohammed Aldandani, Hamid M. Sedighi
This study examines how heat travels as thermoelastic waves in a uniform, isotropic, and infinitely large solid material due to a constant line heat source. We leverage the theory of thermoelasticity with two phase lags to account for the time difference between temperature changes and the material’s stress response. By employing a potential function approach alongside Laplace and Hankel transforms, we can convert the governing equations into more manageable domains. This enables us to derive mathematical formulas for temperature, displacement, and stress distributions within the solid. Through a complex inversion process of the Laplace transforms, we obtain analytical formulas for these field distributions. These formulas, however, are only valid for short time periods and are most applicable in the initial stages of wave propagation. We then use these analytical formulas to visualize how temperature, displacement, and stress are distributed, revealing the influence of the heat source and phase lag parameters on these fields. This approach provides valuable insights into the characteristics of wave propagation, the heat source’s impact, and the time-dependent nature of the thermoelastic response. Furthermore, to demonstrate the method’s versatility and ability to connect with established theories, we incorporate specific examples from other thermoelasticity theories. This broadens our understanding of thermoelastic behavior under various conditions.
{"title":"A semi-analytical approach for thermoelastic wave propagation in infinite solids subject to linear heat supply using two-phase lag theory","authors":"Ahmed E. Abouelregal, Fahad Alsharari, S. S. Alsaeed, Mohammed Aldandani, Hamid M. Sedighi","doi":"10.1007/s00161-024-01324-1","DOIUrl":"10.1007/s00161-024-01324-1","url":null,"abstract":"<div><p>This study examines how heat travels as thermoelastic waves in a uniform, isotropic, and infinitely large solid material due to a constant line heat source. We leverage the theory of thermoelasticity with two phase lags to account for the time difference between temperature changes and the material’s stress response. By employing a potential function approach alongside Laplace and Hankel transforms, we can convert the governing equations into more manageable domains. This enables us to derive mathematical formulas for temperature, displacement, and stress distributions within the solid. Through a complex inversion process of the Laplace transforms, we obtain analytical formulas for these field distributions. These formulas, however, are only valid for short time periods and are most applicable in the initial stages of wave propagation. We then use these analytical formulas to visualize how temperature, displacement, and stress are distributed, revealing the influence of the heat source and phase lag parameters on these fields. This approach provides valuable insights into the characteristics of wave propagation, the heat source’s impact, and the time-dependent nature of the thermoelastic response. Furthermore, to demonstrate the method’s versatility and ability to connect with established theories, we incorporate specific examples from other thermoelasticity theories. This broadens our understanding of thermoelastic behavior under various conditions.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 6","pages":"1711 - 1728"},"PeriodicalIF":1.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235251","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 : 2024-09-16DOI: 10.1007/s00161-024-01327-y
Emilio Barchiesi, Stefanos Mavrikos, Ivan Giorgio, Costas Grigoropoulos, Maria Farsari, Francesco dell’Isola, Gordon Zyla
Mechanical metamaterials consist of specially engineered features designed to tailor and enhance the mechanical properties of their constituent materials. In this context, 2D pantographic fabrics have gained attention for their unique deformation behavior, providing remarkable resilience and damage tolerance. This study explores micro-metric metamaterials with 3D pantographic motifs, aiming to transfer these properties to small scales. 3D micro-metric structures were designed using 2D pantographic fabrics arranged in multiple layers, each featuring unit cells with quasi-perfect pivots. Relatively large specimens of 3D micro-metric pantographs, measuring 158 (upmu )m x 250 (upmu )m x 450 (upmu )m, were fabricated in various configurations using two-photon polymerization. These specimens were mechanically characterized through in-situ scanning electron microscopy microindentation under conditions of cyclic deformation. Structural failures were subsequently assessed via helium-ion microscopy. The 3D micro-metric pantographs exhibited complex mechanical properties, some aligning with those of 2D pantographic fabrics, while new properties, such as a dissipative response and softening, were identified. Nonetheless, the 3D micro-metric pantographs demonstrated great resilience against deformation and enhanced resistance to undesired out-of-plane motions, indicating their potential for novel applications in advanced engineering fields. Additionally, the findings can potentially lead to optimizing and enriching theoretical models describing the mechanical behavior of pantographic metamaterials.
机械超材料由专门设计的特征组成,旨在调整和增强其组成材料的机械特性。在此背景下,二维泛影织物因其独特的变形行为而备受关注,它具有显著的弹性和损伤耐受性。本研究探讨了具有三维泛影图案的微米超材料,旨在将这些特性转移到小尺度上。三维微米结构是利用多层排列的二维泛影织物设计的,每一层都具有准完美枢轴的单元格。利用双光子聚合技术,以不同的配置制作了相对较大的三维微米受电弓标本,尺寸为 158 英寸 x 250 英寸 x 450 英寸。在循环变形条件下,通过原位扫描电子显微镜显微压痕对这些试样进行了机械表征。随后通过氦离子显微镜对结构失效进行了评估。三维微米受电弓表现出复杂的机械特性,其中一些与二维受电弓织物的特性一致,同时还发现了新的特性,如耗散响应和软化。尽管如此,三维微米受电弓还是表现出了极强的抗变形能力,并增强了对不希望发生的平面外运动的抵抗力,这表明它们具有在先进工程领域进行新型应用的潜力。此外,这些研究结果还有可能优化和丰富描述受电弓超材料力学行为的理论模型。
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Pub Date : 2024-09-10DOI: 10.1007/s00161-024-01325-0
G. La Valle, F. Fabbrocino, B. Desmorat
Experimental observations have revealed a change in the concavity of the resultant force-displacement plot in the extension test for pantographic sheets. In this paper, we aim to relate these macroscopically observed mechanical properties with the microscale properties of the hinges (or pivots) connecting the pantographic fibers. The material constituting the hinges is modeled at the microscale as an isotropic elastoplastic 3D Cauchy continuum. The elastic regime is assumed to be linear, while the plastic regime exhibits either saturating or non-saturating hardening. In the case of circular homogeneous cylindrical hinges, monotonic loading is considered to derive a mesoscale constitutive relation linking the torsional angle to the total applied torque. It is demonstrated that (non-)saturating hardening at the microscale results in (non-)saturating hardening of the twist angle/torque plot at the mesoscale, which itself is responsible for the change of concavity in bias extensional test of pantographic sheets.
实验观察表明,受压纸张在拉伸试验中的结果力-位移图的凹度发生了变化。在本文中,我们旨在将这些宏观观察到的机械特性与连接受印纤维的铰链(或枢轴)的微观特性联系起来。构成铰链的材料在微观尺度上被建模为各向同性的弹塑性 3D Cauchy 连续体。假设弹性机制是线性的,而塑性机制则表现为饱和或非饱和硬化。在圆形均质圆柱铰链的情况下,考虑了单调加载,以推导出将扭转角与总外加扭矩联系起来的中尺度构成关系。研究表明,微观尺度上的(非)饱和硬化会导致中观尺度上扭转角/扭矩图的(非)饱和硬化,这本身就是受压板偏压延伸测试中凹度变化的原因。
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