Continuum Mechanics and Thermodynamics最新文献

In our study we approach a Cosserat thermoelastic body in which we take into account both the usual temperature and the microtemperature, that is, the temperature of the microparticles of the body. After constructing the mixed problem with initial and boundary values, in this context, we define an appropriate Hilbert space in which we obtain a temporal evolutionary equation which is equivalent to the already constructed mixed problem. With the help of some known results from the theory of contraction semigroups we prove both the existence and the uniqueness of the solution of the evolution equation, therefore of the considered mixed problem. Furthermore, the same semigroup theory allows us to obtain the continuous dependence of the solution of the mixed problem, both with respect to the initial data and with respect to the loading.

Purely compressed shells are often elegant and highly efficient structural forms, but this leanness may create risk if they are subjected to unexpected patterns and magnitudes of loading, such as may arise due to seismic events. In the same way that historic masonry structures were designed to sustain loads by activating purely compressive force paths, a modern metamaterial can be designed for specific purposes following the same logic. Conventional analysis methods for compression-only shells and vaults, often developed for masonry structures, have tended not to model combined vertical and horizontal loads directly. This has created a significant challenge for engineers assessing historic vaults or designing new shells. To address this gap, this paper presents an enhanced method based on membrane equilibrium analysis (MEA) and the static theorem of limit analysis. This approach is the first application of MEA to directly consider vertical and horizontal body forces acting on a compression-only shell through a parametric formulation of an Airy stress function. The method is applied to a case study of a sail vault subjected to vertical and horizontal loads. Moreover, it is demonstrated how this approach can be used to define iso-resistant shapes that offer more sustainable design options while preserving structural capacity.

This paper presents and analyzes the cyclic indentation response of a linear viscoelastic material over the entire time range of the relaxation processes using conical or spherical indenters. Finite Element simulations of cyclic indentation on two Generalized Maxwell materials with different relaxation spectra were performed. A variety of cyclic responses to indentation were generated and analyzed using an analytical method based on elastic contact. It is shown that the elastic contact depth and contact stiffness from the loading curves should be used to identify the relaxation modulus corresponding to the time of loading. The stabilization of the loop has also been studied through the energy ratio, a parameter that describes the evolution of the dissipated energy with cycles. A simple time shift between cyclic creep and monotonous indentation creep of a linear viscoelastic material is demonstrated. The simulated indentation curves and the parameters derived from them were found to be qualitatively similar to the experimental cyclic indentation data on HDPE polymer at different loading rates. Assuming that the first loading is affected by plasticity due to the use of a sharp indenter, a correction was suggested to obtain the elastic relaxation modulus from the experiments. The values of the modulus identified in this way for HDPE compared well with the relaxation modulus identified for this material from previous cyclic tensile experiments. The small discrepancy was attributed to the non-linear viscoelasticity or the viscoplasticity of the polymer.

In the field of mechanical engineering, structural systems that can present different types of symmetries are frequently encountered. The choice of such solutions with symmetries is generally the result of considering factors such as reducing design and production costs, logistical considerations, but also for aesthetic reasons. The existence of these symmetries inside some structures brings new properties in the mechanical behavior and can be useful in simplifying the calculation, in the static and dynamic case. Symmetries can bring new properties when the problem of studying vibrations is raised. Thus, the dynamic analysis time can be reduced and the designer can get a quick picture of the behavior of the structure in operation. The paper aims to study a special situation of symmetry that can be encountered in engineering practice, namely the existence of three planes of symmetry within a structure. Such structures can be found frequently in the field of mechanical engineering but also in the construction of buildings. The presented properties can contribute to the reduction of dynamic analysis time and therefore to the reduction of design costs. An example from real life is analyzed in the work, highlighting the listed properties.

In the present work a formulation of evolutive laws and complementarity conditions in non-smooth elastoplasticity is discussed. The treatment addresses the problem of non-smooth elastoplasticity which is represented by functions characterized by singularities and defined by non-smooth yielding limit conditions and non-differentiable functions. The mathematical theory of subdifferential calculus is properly advocated to provide the suitable mathematical framework in order to treat non-differentiable functions and non-smooth problems. Extended expressions of evolutive laws and complementarity conditions in non-smooth elastoplasticity are illustrated within the adopted generalized mathematical treatment. Relations between the presented mathematical formulations and the expressions in classical elastoplasticity are pointed out and discussed. The proposed treatment has significant advantages since it provides a geometrical framework to the maximum dissipation principle for non-smooth problems in elastoplasticity. Furtherly, the proposed treatment gives insights in the interpretation of the adopted geometrical framework for different types of evolutive laws for new materials and solids such as for instance in some types of new metamaterials with non-smooth constitutive behavior. In addition, the present formulation is also useful in the design of metamaterials, such as pantographic ones, where the plasticity of the pivots is relevant.

Our study falls within the linear theory of thermoelasticity of Cosserat media. Unlike other works that fall into similar contexts and that use the entropy balance low, our approach is based on an entropy production inequality. The entropy flux tensor is introduced and thermoelastic media are considered for which the stress tensors are dependent on the temperature gradients. In this way, a fourth-order differential equation satisfied by temperature is obtained. In this context the mixed initial-boundary value problem is formulated for which an uniqueness result regarding the solution of this problem is proven. Also, a continuous dependence result is deduced for the solution of the mixed formulated problem with regard to the charges and the initial values.

Underground tunnels serve as vital infrastructure for road and rail transportation, oil and gas pipelines, power grids, and military applications; they are inherently subject to harsh environments characterized by extreme temperatures, chemical erosion, and sudden impacts. To address these challenges, the sophisticated coupled thermoelastic diffusion dynamic model has been developed based on Biot’s wave equation, Fick’s law, viscoelastic theory, and Ezzat’s fractional-order thermoelastic theory. The research presented here delves into the intricate thermoviscoelastic diffusion dynamic response of the system, exploring how it reacts when simultaneously confronted with a thermal source, normal load, and chemical shock directly applied to the surface of the cylindrical tunnel cavity. The Laplace transform and the Crump numerical inversion method have been used to obtain the non-dimensional displacement, temperature, chemical potential, concentration, radial stress, hoop stress, and axial stress. A meticulous analysis reveals the intricate interplay between the fractional coefficient, temporal evolution, and diverse shock load types on these variables. The fractional-order coefficients have a certain effect on the analysis of all physical variables except the non-dimensional chemical potential. The action time has a significant effect on all non-dimensional physical variables. The two different viscoelastic relaxation time factors have no significant effect on non-dimensional temperature and chemical potential, however, have obvious effects on non-dimensional concentration, radial stress, hoop stress, and axial stress.

This paper proposes a method for determining the mechanical properties of thin films of highly elastic materials. The method is based on an experiment of indenting a circular specimen with a hole in the center by a ball indenter. The value of the maximum indenting force is used as experimental data. This method determines the neo-Hookean model parameter for incompressible materials, factoring in indenter-specimen friction across various hole and indenter sizes.

We consider a transversely isotropic piezoelectric spheroidal inhomogeneity embedded in an infinite transversely isotropic piezoelectric matrix subjected to a uniform remote axisymmetric electromechanical loading. The inhomogeneity-matrix interface is spring-type in elasticity and weakly conducting in dielectricity. The same degree of interface imperfection in elasticity is realized in both the normal and tangential directions and the interface is characterized by two imperfect interface functions. We identify the two interface functions leading to a uniform interior electroelastic field within the spheroidal inhomogeneity. Explicit expressions for the internal uniform stresses and electric displacement within the inhomogeneity are presented and illustrated. The uniformity property within an imperfectly bonded spheroidal piezoelectric inhomogeneity under a uniform remote antisymmetric electromechanical loading is also proved and illustrated.

At the microscale and nanoscale, materials exhibit size-dependent behaviors that classical models cannot capture. This analysis introduces a size-dependent higher-order thermoelastic heat conduction model, incorporating spatial and temporal nonlocal effects in a micropolar visco-thermoelastic medium subjected to laser pulse heat flux. The two-phase delay model, featuring higher-order temporal derivatives, captures the complex interactions among mechanical, thermal, and viscous properties in materials where size effects are significant. By including phase lag, the model effectively addresses non-Fourier heat conduction in short-duration laser pulse scenarios. It accurately predicts temperature distribution, stress response, and microrotation effects in microscale and nanoscale materials. The study visually represents how factors such as micropolarity, higher-order effects, phase delay, nonlocal index, and viscosity influence the size-dependent mechanical behavior of the half-space structure. The numerical results highlight the importance of size-dependent phenomena in nanostructures, revealing deviations from classical predictions due to nonlocal interactions. Overall, the proposed spatiotemporal nonlocal homogenization model serves as a valuable tool for analyzing the complex mechanical and thermal characteristics of nanomaterials.