Continuum Mechanics and Thermodynamics最新文献

{"title":"On the initial boundary values problem for a mixture of two Cosserat bodies with voids","authors":"Marin Marin,&nbsp;Andreas Öchsner,&nbsp;Sorin Vlase","doi":"10.1007/s00161-024-01310-7","DOIUrl":"10.1007/s00161-024-01310-7","url":null,"abstract":"<div><p>In this study it is approached a linear model for the mixture of two Cosserat bodies having pores. It is formulated the mixed problem with initial and boundary data in this context. The main goal is to show that the coefficients that realize the coupling of the elastic effect with the one due to voids can vary, without the mixture being essentially affected. In a more precise formulation, this means that a small variation of the coefficients in the constitutive equations of the two continua causes only a small variation of the solutions of the corresponding mixed problems, that is, the continuous dependence of the solutions in relation to these coefficients is ensured. The considered mixture model is consistent because all estimates, specific to continuous dependence, are made based on rigorous mathematical relationships.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 6","pages":"1481 - 1491"},"PeriodicalIF":1.9,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01310-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304364","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}

{"title":"A bone remodeling approach encoding the effect of damage and a diffusive bio-mechanical stimulus","authors":"Daniela Addessi,&nbsp;Francesco D’Annibale,&nbsp;Luca Placidi,&nbsp;Ivan Giorgio","doi":"10.1007/s00161-024-01308-1","DOIUrl":"10.1007/s00161-024-01308-1","url":null,"abstract":"<div><p>The paper focuses on the effect of damage on the bone remodeling process. This is a crucial, although complex, aspect. A one-dimensional continuous deformable body is employed to model living bone tissue. The model incorporates the bone functional adaptation through an evolution law for an effective elastic modulus driven by mechanical feedback via a mechano-transduction diffusive signal. This type of information transduction, i.e., diffusion, is essential for the model to take into account remodeling in the case of minor injury or pathology-affected regions where there is no signal production. In addition, the model is able to also take into account potential tissue damage that may evolve over time according to a suitable evolution law. To illustrate the capability of the model to describe the mentioned complex coupled phenomena, numerical tests have been performed encompassing high external loads causing the onset of damage and cyclic loading for healing. The numerical simulations carried out via finite-element analyses yield insights into the mechanisms of bone remodeling, with the final goal of aiding clinical decisions and implant designs for bone health and repair. Overall, a key aspect of the paper is to highlight the feasibility of modeling the evolution in bone elasticity arising from the combined effect of damage and remodeling.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"993 - 1012"},"PeriodicalIF":1.9,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01308-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141096659","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}

{"title":"Electrostatic body forces in cracked dielectrics and their implication on Maxwell stress tensors","authors":"Alexander Schlosser,&nbsp;Lennart Behlen,&nbsp;Andreas Ricoeur","doi":"10.1007/s00161-024-01302-7","DOIUrl":"10.1007/s00161-024-01302-7","url":null,"abstract":"<div><p>In solid mechanics, Maxwell stresses are known to be induced if a body is exposed to magnetic and, in the case of dielectrics, electric fields. Acting as tractions at outer or inner surfaces as well as volume forces, they are superimposed with tractions and stresses due to mechanical loads and provide a more or less significant contribution, depending on loading, material properties and geometric aspects. The Maxwell stress tensor, constituting the physical and mathematical basis, however, is controversially discussed to date. Several formulations are known, most of them having been suggested more than 100 years ago. Being equivalent in vacuum, they differ qualitatively just as quantitatively in solid or fluidic matter. In particular, the dissimilar effect of body forces, emanating from a choice of established Maxwell stress tensor approaches, on crack tip loading in dielectric solids is investigated theoretically in this paper. Due to the singularity of fields involved, their impact is basically non-negligible compared to external mechanical loading. The findings obtained indicate that fracture mechanics could be the basis of an experimental validation of Maxwell stress tensors.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"877 - 890"},"PeriodicalIF":1.9,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01302-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141096654","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}

{"title":"Equivalence of measures and stochastic equations of hydrodynamic theory of plasma","authors":"Artur V. Dmitrenko","doi":"10.1007/s00161-024-01304-5","DOIUrl":"10.1007/s00161-024-01304-5","url":null,"abstract":"<div><p>Stochastic equations of hydrodynamic theory of plasma are presened. The article shows that for transfer processes in liquid and gas, on the one hand, and in plasma, on the other hand, there exist sets of stochastic differential equations for substantial quantities based on the equality of measures between deterministic motion and random motion. It is shown that the application of these stochastic equations makes it possible to obtain new theoretical solutions for the occurrence of turbulence also for a plasma as a result of its heating in an external electric field instead of only for a classical gas, as it was proved previously. Theoretical solutions for the conductivity of turbulent plasma during its heating in an external electric field are considered. At a first time taking into account the turbulence parameters theoretical relations for the electron drift velocity and corresponding relations for electron mobility, for the frequency of electron collisions, and for the Coulomb integral are obtained. All theoretical relations are applied to calculate the conductivity during the turbulent heating of plasma in an electric field. Here experiments with hydrogen plasma are being considered. The theoretical explanation of the cause for the existence of a constant conductivity in the field of strength <span>(E = 0.6-19)</span> V/cm and its fall at <span>(19&lt;E&lt;100)</span> V/cm is given. The calculated dependences of plasma conductivity are in satisfactory agreement with experimental data at the electric-field strength in the turbulent region <span>(E = 0.6-100)</span> V/cm and in the region <span>(E &lt; 0.6)</span> V/cm.The equation for the critical electric-field strength is presented.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"911 - 934"},"PeriodicalIF":1.9,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141085401","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}

{"title":"Dynamic large strain formulation for nematic liquid crystal elastomers","authors":"Francesca Concas,&nbsp;Michael Groß","doi":"10.1007/s00161-024-01307-2","DOIUrl":"10.1007/s00161-024-01307-2","url":null,"abstract":"<div><p>Liquid crystal elastomers (LCEs) are a class of materials which exhibit an anisotropic behavior in their nematic state due to the main orientation of their rod-like molecules called mesogens. The reorientation of mesogens leads to the well-known actuation properties of LCEs, i.e. exceptionally large deformations as a consequence of particular external stimuli, such as temperature increase. Another key feature of nematic LCEs is the capability to undergo deformation by constant stresses while being stretched in a direction perpendicular to the orientation of mesogens. During this plateau stage, the mesogens rotate towards the stretching direction. Such characteristic is defined as semisoft elastic response of nematic LCEs. We aim at modeling the semisoft behavior in a dynamic finite element method based on a variational-based mixed finite element formulation. The reorientation process of the rigid mesogens relative to the continuum rotation is introduced by micropolar drilling degrees of freedom. Responsible for the above-mentioned characteristics is an appropriate free energy function. Starting from an isothermal free energy function based on the small strain theory, we aim to widen it into the framework of large strains by identifying tensor invariants. In this work, we analyze the isothermal influence of the tensor invariants on the mechanical response of the finite element formulation and show that its space-time discretization preserves mechanical balance laws in the discrete setting.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"969 - 992"},"PeriodicalIF":1.9,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01307-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140954615","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}

{"title":"Exploring dynamic response in a three-layer dome with non-homogeneous elastic core under a concentrated impact at its apex","authors":"Alexander Grigorenko,&nbsp;Petro Lugovyi,&nbsp;Sergii Orlenko,&nbsp;Kostiantyn Kotenko","doi":"10.1007/s00161-024-01306-3","DOIUrl":"10.1007/s00161-024-01306-3","url":null,"abstract":"<div><p>The dynamics of a three-layer dome with a discrete-symmetric lightweight reinforced with ribs under a concentrated impact on its top was studied. The study explores the behavior of a three-layer dome, uniquely designed with discrete, symmetrically placed, lightweight ribs for reinforcement, when subjected to a concentrated impact at its apex. The supporting layers of the dome are made with different thicknesses. Each supporting layer of the dome differs in thickness, offering a complex structure for analysis. In the analysis of the elements of the elastic structure, the Timoshenko model of the theory of shells and rods was used under independent static and kinematic hypotheses for each layer. According to the Hamilton–Ostrogradsky variational principle, the equations of motion of asymmetric three-layer hemispherical shells with a discrete-symmetric lightweight rib-reinforced aggregate under axisymmetric local impulse loading were obtained. An appropriate finite element model of the shell was created, which reflects the relationship between the potential energy of deformations in the body and the potential of applied forces. A detailed finite element model was developed to capture the interplay between the dome’s deformation energy and the force applied, facilitating a nuanced exploration of the dome’s dynamic response. The numerical results of the study of the dynamics of a three-layer elastic structure with asymmetric thickness based on the finite element method were obtained The influence of geometrical and physical–mechanical parameters of asymmetric layers of a spherical dome on its dynamic behavior during a concentrated impact on its top was studied and new mechanical effects were investigated. Through numerical analysis, the dome’s asymmetrical layer thickness and the physical and mechanical characteristics of these layers were examined to determine how they influence the dome’s reaction to concentrated impacts. This investigation reveals novel mechanical behaviors and underscores the significance of geometrical and material properties in the dome’s dynamic performance</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"955 - 968"},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140919602","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}

{"title":"Swirl flow stability: thermodynamic analysis and experiments","authors":"František Maršík,&nbsp;Zdeněk Trávníček,&nbsp;Bernhard Weigand,&nbsp;Florian Seibold,&nbsp;Zuzana Antošová","doi":"10.1007/s00161-024-01303-6","DOIUrl":"10.1007/s00161-024-01303-6","url":null,"abstract":"<div><p>The current paper presents a theoretical analysis of swirl flow stability, both inside a tube (vortex tube) and in a free annular swirl flow. The starting concept is the study of the evolution of velocity and temperature fluctuations. Methods of non-equilibrium thermodynamics are used to describe the magnitude of fluctuations and their properties. The important role of the total enthalpy follows from a variational analysis. Moreover, the thermodynamic criterion of the stability is formulated using the total enthalpy, and compared with experiments, numerical results and classical Rayleigh theory support its applicability. It was shown that the solid body vortex is at the margin of stability, which is experimentally observed. Analogously, the potential vortex is by the thermodynamic criterion stable; however, by the Rayleigh criteria it is on the onset of stability. The classical Taylor experiment of flow between two rotating cylinders is analysed from the point of view of this criterion. These results are underlined by swirl tube experiments at the Institute of Aerospace Thermodynamics at Stuttgart University and the annular nozzle experiments performed in the Institute of Thermomechanics CAS in Prague. Both independent experiments confirm the transformation of the initial annular vortex into a stable potential-type vortex. The results of this theory can also be used to explain the exceptional stability of tropical cyclones.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"891 - 910"},"PeriodicalIF":1.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01303-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140907409","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}

{"title":"Modeling and FE simulation of coupled water diffusion and viscoelasticity in relaxation tests of polyamide 6","authors":"Alexander Dyck,&nbsp;Leonhard Groß,&nbsp;Johannes Keursten,&nbsp;Loredana Kehrer,&nbsp;Thomas Böhlke","doi":"10.1007/s00161-024-01305-4","DOIUrl":"10.1007/s00161-024-01305-4","url":null,"abstract":"<div><p>Polyamides can absorb or desorb water from or to their surrounding environment. The impact of this process is significant as water molecules lead locally to a swelling and a coupling of diffusion and deformation behavior. To model these phenomena, a strongly coupled chemo-mechanical (or diffuso-mechanical) model is required, considering both local water concentration and the viscoelastic material behavior of polyamide. In the present work, we derive and apply such a model to polyamide 6. A diffusion equation describing changes in water concentration is coupled to the balance of linear momentum in polyamide 6. The interaction between deformation and concentration is derived from thermodynamic considerations by introducing a free energy consisting of a mechanical and a chemical part. The mechanical part describes a linear viscoelastic model and includes chemical strains due to the presence of water molecules. The chemical part builds upon the theory of Flory and Huggins, that takes into account changes in enthalpy and entropy of mixing due to the interaction of polymer and water molecules. The coupling of deformation to water concentration arises due to a dependency of the water flux on the hydrostatic stress inside the polyamide. We successfully apply the derived model in Finite-Element simulations to predict the drying of polyamide 6 specimens without any coupling to mechanical loads. In addition, we reproduce experimentally obtained data from relaxation measurements, where the drying of polyamide specimens leads to an increase in relaxation modulus.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"935 - 953"},"PeriodicalIF":1.9,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01305-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140890484","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}

{"title":"Analytical modeling of the mixed-mode behavior in functionally graded coating/substrate systems","authors":"Rossana Dimitri,&nbsp;Marco Trullo,&nbsp;Martina Rinaldi,&nbsp;Caterina Fai,&nbsp;Francesco Tornabene","doi":"10.1007/s00161-024-01301-8","DOIUrl":"10.1007/s00161-024-01301-8","url":null,"abstract":"<div><p>This work aims at studying the interfacial behavior of functionally graded coatings (FGCs) on different substrates, here modeled as asymmetric double cantilever beams, in line with the experimental tests. An enhanced beam theory (EBT) is proposed to treat the mixed-mode phenomena in such specimens, whose interface is considered as an assembly of two components of the coating/substrate system bonded together partially by an elastic interface. This last one is modeled as a continuous distribution of elastic–brittle springs acting along the tangential and/or normal direction depending on the interfacial mixed-mode condition. Starting with the Timoshenko beam theory, we determine the differential equations of the problem directly expressed in terms of the unknown interfacial stresses, both in the normal and tangential directions. Different distribution laws are implemented to define the functional graduation of the material in the thickness direction of the specimens, whose variation is demonstrated numerically to affect both the local and global response in terms of interfacial stresses, internal actions, energy quantities and load–displacement curves. The good accuracy of the proposed method is verified against predictions by a classical single beam theory (SBT), with interesting results that could serve as reference solutions for more expensive experimental investigations on the topic.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"839 - 875"},"PeriodicalIF":1.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140538544","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}

{"title":"Elasto-plasticity theory for large plastic deformation and its use for the material stiffness determination","authors":"Martin Weber,&nbsp;Holm Altenbach","doi":"10.1007/s00161-024-01297-1","DOIUrl":"10.1007/s00161-024-01297-1","url":null,"abstract":"<div><p>In this paper, we present a finite elasto-plasticity theory for large plastic deformations. For the elastic part of the model, we use the St. Venant–Kirchhoff elasticity. The plastic part is described by the isomorphy concept, the yield condition is covered by the isotropic <span>(J_2)</span> theory of (Huber in Czas Techn 22:34,1904; von Mises in Math Phys 4:582–592, 1913) and (Hencky in ZAMM 9:215–220, 1924), and the yield condition uses the principle of maximum plastic dissipation. The numeric of this theory is discussed and finally implemented in a Fortran code to use it as material law in the UMAT subroutine of the finite element program Abaqus. The material law is validated using different test calculations like tensile and shear tests as well as a large deformation simulation compared to the Abaqus internal material law. Further, we apply this material model to determine the effective material stiffness tetrad of large deformed inhomogeneous materials. For these purposes, we additionally present an automated method for determining material stiffnesses of an arbitrary material in Abaqus.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 5","pages":"1305 - 1321"},"PeriodicalIF":1.9,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01297-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140340918","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}