Continuum Mechanics and Thermodynamics最新文献

{"title":"A thermo-mechanically coupled constitutive model for semi-crystalline polymers at finite strains: Mechanical and thermal characterization of polyamide 6 blends","authors":"Marie-Christine Reuvers,&nbsp;Sameer Kulkarni,&nbsp;Birte Boes,&nbsp;Sebastian Felder,&nbsp;André Wutzler,&nbsp;Michael Johlitz,&nbsp;Alexander Lion,&nbsp;Tim Brepols,&nbsp;Stefanie Reese","doi":"10.1007/s00161-024-01288-2","DOIUrl":"10.1007/s00161-024-01288-2","url":null,"abstract":"<div><p>In the field of material modeling, thermoplastic polymers are often studied because of their complex material behavior and their prevalence in industry applications due to their low cost and wide range of applications. Nowadays, where reusability becomes more and more important, materials which can undergo reversible thermomechanical deformations are appealing for, e.g., the construction of car body components. To predict such complex forming processes with multiple influencing factors, such as temperature, strain rate or underlying material morphology, model formulations are needed that account for these influences simultaneously and are validated against experimental data. Unfortunately, up to now only a few contributions are available which consider all these phenomena. In addition, the range of process parameters considered is often narrow due to the experimental effort required for testing. This usually results in limited predictive capabilities of the model. To overcome these limitations, in this work, a thermo-mechanically coupled material model is developed that accounts for the underlying morphology in terms of the degree of crystallinity (DOC). The model formulation is derived in a thermodynamically consistent manner, incorporating coupled nonlinear visco-elastic and elasto-plastic material behavior at finite strains. To characterize and further validate the model, mechanical as well as thermal experiments are conducted for polyamide 6 (PA6). Here, a blending strategy of PA6 together with an amorphous co-polymer is introduced during specimen production to achieve a wider range of stable DOCs(approximately 15%). The model formulation is successfully applied to experimental results and its predictions are in good agreement with experimental observations.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 3","pages":"657 - 698"},"PeriodicalIF":1.9,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01288-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140329275","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":"Linearization and localization of nonconvex functionals motivated by nonlinear peridynamic models","authors":"Tadele Mengesha,&nbsp;James M. Scott","doi":"10.1007/s00161-024-01299-z","DOIUrl":"10.1007/s00161-024-01299-z","url":null,"abstract":"<div><p>We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise interaction of material points and as such are nonconvex with respect to nonlocal deformation. We apply variational analysis to investigate the consistency of the effective behavior of these nonlocal nonconvex functionals with established classical and peridynamic models in two different regimes. In the regime of small displacement, we show the model can be effectively described by its linearization. To be precise, we rigorously derive what is commonly called the linearized bond-based peridynamic functional as a <span>(Gamma )</span>-limit of nonlinear functionals. In the regime of vanishing nonlocality, the effective behavior of the nonlocal nonconvex functionals is characterized by an integral representation, which is obtained via <span>(Gamma )</span>-convergence with respect to the strong <span>(L^p)</span> topology. We also prove various properties of the density of the localized quasiconvex functional such as frame-indifference and coercivity. We demonstrate that the density vanishes on matrices whose singular values are less than or equal to one. These results confirm that the localization, in the context of <span>(Gamma )</span>-convergence, of peridynamic-type energy functionals exhibits behavior quite different from classical hyperelastic energy functionals.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"795 - 824"},"PeriodicalIF":1.9,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140322063","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":"Predicting mechanical failure of polycrystalline dual-phase nickel-based alloys by numerical homogenization using a phase field damage model","authors":"Jakob Huber,&nbsp;Jonas Vogler,&nbsp;Jan Torgersen,&nbsp;Ewald Werner","doi":"10.1007/s00161-024-01298-0","DOIUrl":"10.1007/s00161-024-01298-0","url":null,"abstract":"<div><p>Brazing of nickel-based alloys plays a major role in the assembly of turbine components, e.g., abradable sealing systems. In a brazed joint of nickel-based alloys a composition of brittle and ductile phases can be formed if the brazing conditions are not ideal. This heterogeneous microstructure is a crucial challenge for predicting the damage behavior of a brazed joint. The initiation and evolution of microdamage inside of the brittle phase of a virtual dual-phase microstructure representing the material in a brazed joint is studied by means of numerical simulations. A phase field approach for brittle damage is employed on the microscale. The simulation approach is capable of depicting phenomena of microcracking like kinking and branching due to heterogeneous stress and strain fields on the microscale. No information regarding the initiation sites and pathways of microcracks is needed a priori. The reliability of calculating the effective critical energy quantities as a microstructure-based criterion for macroscopic damage is assessed. The effective critical strain energy density and the effective critical energy release rate are evaluated for single-phase microstructures, and the approach is transferred to dual-phase microstructures. The local critical strain energy density turns out to be better suited as a model input parameter on the microscale as well as for a microstructure-based prediction of macroscopic damage compared to a model employing the energy release rate. Regarding the uncertainty of the model prediction, using the effective critical energy release rate leads to a standard deviation which is five times larger than the standard deviation in the predicted effective critical strain energy density.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"775 - 793"},"PeriodicalIF":1.9,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01298-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140329194","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":"Two-field mixed hp-finite elements for time-dependent problems in the refined theories of thermodynamics","authors":"Balázs Tóth,&nbsp;Zsombor Molnár,&nbsp;Róbert Kovács","doi":"10.1007/s00161-024-01300-9","DOIUrl":"10.1007/s00161-024-01300-9","url":null,"abstract":"<div><p>Modern manufacturing technologies allow heterogeneous materials with complex inner structures (e.g., foams) to be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not necessarily valid. According to various experimental observations, the Guyer–Krumhansl equation is a promising candidate for modeling such complex structures. However, practical applications need a reliable and efficient algorithm capable of handling both complex geometries and advanced heat equations. In the present paper, we derive new two-field variational formulations which treat the temperature and the heat flux as independent field variables, and we develop new, advanced <i>hp</i>-type mixed finite element methods, which can be reliably applied. We investigate their convergence properties for various situations, challenging in relation to stability and the treatment of fast propagation speeds. That algorithm is also proved to be outstandingly efficient, providing solutions four magnitudes faster than commercial algorithms.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"825 - 838"},"PeriodicalIF":1.9,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01300-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140291682","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 of sodiation-induced deformation of Sn anode based on the stress-driven nonlocal integral elasticity","authors":"Zuoquan Zhu,&nbsp;Mengmeng Lv,&nbsp;Zongchao Liu,&nbsp;Jing Wan","doi":"10.1007/s00161-024-01290-8","DOIUrl":"10.1007/s00161-024-01290-8","url":null,"abstract":"<div><p>The anode material Sn used in sodium-ion batteries displays high theoretical capacity, complex phase transformation, and significant volume change during the charging/discharging process. In particular, the effects of small scale on the mechanical behavior of Sn anode at the nanoscale are very active research fields. However, the majority of these results are based on nonlocal gradient formulations. In this study, we proposed and established a model that combines the electrochemical reaction with stress-driven nonlocal integral elasticity for the nanoelectrode to analyze the evolution of diffusion-induced deformation during the sodiation process. Several critical features, such as the small-scale parameter, two-phase reaction, and concentration-dependent elastic modulus, were incorporated into the established model. The model demonstrated that a small scale could significantly affect the deformation behavior. The results obtained using the finite element method showed that the mechanical reliability of the Sn anode could be significantly enhanced when the anode was sodiated with larger nonlocal parameters and smaller slenderness. In addition, the axial action force exhibited a strong size effect and was influenced by the nondimensional thickness parameter of the anode. This work provides a framework for multi-scale research on high-capacity sodium-ion battery electrodes.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"725 - 735"},"PeriodicalIF":1.9,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140291636","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":"Heat conduction in multi-component step-wise FGMs","authors":"Olga Szlachetka,&nbsp;Ivan Giorgio","doi":"10.1007/s00161-024-01296-2","DOIUrl":"10.1007/s00161-024-01296-2","url":null,"abstract":"<div><p>This paper provides a thorough investigation of a heat conduction problem that pertains to tolerance modelling in layered materials made up of multiple components. These media are functionally graded materials and thus have varying properties that affect their effectiveness. The proposed equations explain the conduction of heat in layered composites. The formulation involves partial differential equations, which utilise smooth and slowly varying functions. Notably, an extension of the unified tolerance modelling procedure is presented generalising existing models for two-component step-wise functionally graded materials (FGMs). This extension allows for the analysis of specific issues related to heat conduction in multi-component stratified composites with a transversal gradation of effective properties. This is the most important novelty achievement of the present paper because it will contribute to advancing knowledge and allows researchers, engineers, and practitioners to use the method in a broader context, addressing a more extensive set of real-world situations not limited to the number of component materials.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 5","pages":"1393 - 1411"},"PeriodicalIF":1.9,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01296-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140188694","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":"Peridynamic simulation of creep deformation and damage","authors":"Deepak Behera,&nbsp;Pranesh Roy,&nbsp;Erdogan Madenci","doi":"10.1007/s00161-024-01295-3","DOIUrl":"10.1007/s00161-024-01295-3","url":null,"abstract":"<div><p>This study presents a nonordinary state-based (NOSB) peridynamic (PD) modeling of creep deformation and damage. The force density vectors in PD equilibrium equations are derived by considering the Liu and Murakami creep model with a damage parameter. The bond-associated (BA) deformation gradient is derived by using the PD differential operator (PDDO). Traction and displacement boundary conditions are directly imposed through a novel strategy while solving for the strong form of PD equilibrium equations. The PD form of traction components enables the imposition of traction conditions in the actual “boundary layer” region without any unphysical displacement kinks near the boundaries. The approach is validated under uniaxial and 2D plane stress assumptions by considering creep deformation due to constant stress at high temperatures. The creep strain predictions are in excellent agreement with the experimental data and analytical solutions. Subsequently, creep crack growth in a compact tension (CT) specimen is simulated by using the damage variable in Liu and Murakami constitutive model.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 5","pages":"1283 - 1304"},"PeriodicalIF":1.9,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140142070","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":"Exact solution of one problem of imposition of large deformations in a compound slab with pre-deformed layers of incompressible nonlinear elastic micropolar material","authors":"V. A. Levin,&nbsp;K. M. Zingerman,&nbsp;A. E. Belkin","doi":"10.1007/s00161-024-01294-4","DOIUrl":"10.1007/s00161-024-01294-4","url":null,"abstract":"<div><p>An exact solution is obtained for a new class of problems on the imposition of large deformations in nonlinear elastic micropolar bodies. The problem of determining the stress state in a compound slab having the shape of a rectangular parallelepiped, composed of pre-deformed layers and subjected to biaxial tension or compression is solved. The layers are made of isotropic incompressible nonlinear elastic micropolar materials. The layers are preliminarily deformed by straightening of circular cylindrical sectors. The solution is based on a class of universal deformations for isotropic incompressible nonlinear elastic micropolar materials. Numerical studies were carried out. The dependencies of stresses, resulting forces and moments on the parameters of initial and additional deformations are presented. Significant nonlinear effects are revealed. The influence of micropolar effects on the stress state has been studied. The solution can be used to verify software designed to numerically solve problems on the imposition of large deformations in bodies made of nonlinear elastic micropolar materials.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"763 - 774"},"PeriodicalIF":1.9,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140142068","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":"Variable properties reconstruction for functionally graded thermoelectroelastic cylinder","authors":"Alexander Vatulyan,&nbsp;Sergey Nesterov,&nbsp;Rostislav Nedin","doi":"10.1007/s00161-024-01292-6","DOIUrl":"10.1007/s00161-024-01292-6","url":null,"abstract":"<div><p>In this research, we present an approach to identify variable characteristics of an inhomogeneous thermoelectroelastic radially polarized elongated hollow cylinder. The cylinder’s thermomechanical characteristics depend on the radial coordinate. We consider two loading types for the cylinder—the mechanical and the thermal ones. The radial displacement is considered as the additional data collected on the outer cylinder’s surface under the first type load, while the temperature measured over a certain time interval is considered for the second type load. The direct problem after non-dimensioning and applying the Laplace transform is solved by jointly applying the shooting method and the transform inversion based on expanding the actual space in terms of the shifted Legendre polynomials. The effect of the laws of change in variable characteristics on the input data values taken in the experiment is analyzed. A nonlinear inverse problem on the reconstruction of the cylinder’s variable properties is formulated and solved on the basis of an iterative technique. The initial approximation is set in the class of positive bounded linear functions whose coefficients are determined from the condition of minimizing the residual functional. To find the corrections at each stage of the iterative process, the Fredholm integral equations of the first kind are solved by means of the Tikhonov method. A series of computational experiments on recovering one and two variable characteristics is conducted. The effect of coupling parameters and input noise on the reconstruction results is revealed.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"745 - 762"},"PeriodicalIF":1.9,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140123875","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":"Asymptotic behaviour for convection with anomalous diffusion","authors":"Brian Straughan,&nbsp;Antonio Barletta","doi":"10.1007/s00161-024-01291-7","DOIUrl":"10.1007/s00161-024-01291-7","url":null,"abstract":"<div><p>We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work, we demonstrate that regardless of the size of the Rayleigh number, the perturbation solution will decay exponentially in time for the superdiffusion case. In addition, we establish a similar result for convection in a bidisperse porous medium where both macro- and microporosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"36 4","pages":"737 - 743"},"PeriodicalIF":1.9,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01291-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043376","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}