Continuum Mechanics and Thermodynamics最新文献

A kinematic model of 4D continuum with different types of symmetry is introduced and a unified kinematic model of long-range electromagnetic and gravitational fields is proposed. We define the 4D vector potential, introduce 4D distortion tensor, and show that its antisymmetric part gives the classical definition of the electric field intensity vector and the pseudovector of magnetic induction. On the other hand, the symmetric part of the distortion tensor is interpreted as the gravitational field intensity. The structure of the gravitational field kinematic model is analyzed. For the 4D continuum, generalized compatibility equations are established including homogeneous Papkovich and Saint-Venant relations. It is shown that homogeneous Saint-Venant relations can be also integrated in quadrature’s respect to the 4D spherical deformation tensor, which can be defined through an integro-differential operator applied only to the components of the deviator tensor. We show that 4D Cesaro equations indicate the existence of two kinematic states in the spacetime in the absence of the strain deviator tensor. The first kinematic state proves the existence of an expansion metric effect of the 4D continuum since the speed of the observed point is always proportional to the distance to it. The second kinematic state indicates a purely geometric effect of uniformly accelerated expansion of event space.

Liquid crystal elastomers are a class of materials which shows unusual characteristics due to its dual nature, i.e. the orientational behavior of liquid crystals combined with the intrinsic features of elastomers. Apart from inhomogeneities, the mesogens, which are linked to the polymer chains in LCEs and are modeled as a unit nematic director, are oriented along a unique direction in case of a monodomain sample. Among other remarkable properties, LCEs exhibit a particular behavior under mechanical stretching, such as the semisoft elastic response and the onset of stripe domains in the originally monodomain sample under certain conditions. As observed in experiments, in a sample with stripe domains the mesogens of two adjacent stripes are rotated through the same angle but with opposite senses of rotation. We aim to reproduce the stripe domains in nematic LCEs under mechanical stretch and high strain rates by using a dynamic three-dimensional mixed finite element formulation, which is based on the usage of a mixed principle of virtual power, local drilling degrees of freedom for LCE-network and mesogens and frame-indifferent free energy density functions based on tensor invariants associated with the mixed fields.

A plane strain problem for forced time-harmonic vibrations of an elastic layer lying on an acoustic half-space is considered. The validity of the approximate formulation involving the classical Kirchhoff theory for plate bending as well as its shortened forms is investigated. The developed asymptotic framework demonstrates that the aforementioned theory is not able to predict the effect of the plate stiffness on the acoustic radiation. A consistent low-frequency approximation relying on plate transverse compression instead of plate bending is derived.

The corresponding mathematical model of cyclic viscoplastic deformation of damaged material, a structural element counteracting multiaxial disproportionate modes of hybrid thermomechanical loading, is considered. The model is determined by the relations between viscoplastic deformation and failure, as well as the evolution equations of damage accumulation kinetics and the material strength criterion. The description of viscoplastic deformation is based on the existence of plasticity and creep surfaces in the stress space and the principle of gradient of the velocity vectors of the corresponding deformations at the loading point. Such a description distinguishes the main effects of the cyclic behaviour of the material for complex loading trajectories. The description of kinetic damage accumulation is based on the scalar damage parameter. The formation, growth and coalescence of micro-defects are considered. A coupled formulation of the evolution equations for low-cycle fatigue and long-term strength is proposed. The condition that the damage value reaches a critical value is taken as the strength criterion. In the work, material parameters and scalar functions of the mathematical model are obtained. Based on the model, the results of the numerical simulation of the behaviour of the alloys are presented. It is shown that the model describes the durability of the materials with practical reliability.

Polyamide 12 (PA12) is a semi-crystalline thermoplastic used in the automotive and aerospace industries due to its high resistance to chemicals and abrasion and its good thermal stability. The material can be processed with various manufacturing technologies, including selective laser sintering (SLS), which offers great potential for industrial production due to its excellent and reproducible mechanical properties and thus motivates a detailed understanding of the mechanical behavior. This paper presents an approach for modeling the mechanical behavior of selectively laser-sintered polyamide 12. A continuum mechanical model is developed based on a comprehensive temperature and velocity-controlled experimental program, and its parameters are identified. After presenting the test specimens developed in-house, which utilized the geometric freedom of the SLS process, the kinematic description of the test specimens and the digital image correlation technique used for this purpose are discussed. The experimental test results are then presented, which consist of relaxation tests and experiments with a constant strain rate at various temperatures. After the two material-theoretical approaches of linear viscoelasticity and endochronic plasticity have been presented, the material model is derived in three dimensions, and the parameters are identified.

This research investigates the scattering behavior of Love waves, also known as Q waves in seismology, induced by an interface crack between an orthotropic elastic layer and an isotropic elastic half-space where the orthotropic layer serves as a wave guide medium. The Dispersion relation and phase velocity have been obtained by using convenient boundary conditions for the Love wave propagation. Using the method of Fourier transform and integral equation, the study derives the conditions governing wave propagation and scattering phenomena in the interfaced medium. The expression of the most important fracture quantities, such as dynamic stress intensity factor (DSIF) and crack opening displacement (COD) have been obtained and demonstrated graphically. Results demonstrate the dependence of scattering characteristics on the material properties, crack dimensions, layer height and wave frequencies. The findings contribute to a deeper understanding of Love wave propagation in composite materials, with implications for non-destructive testing and evaluation of structural integrity in engineering applications.

The dimensions of seismic metamaterials pose limitations that make attenuating ultra-low frequency seismic surface waves (with a starting frequency near 0 Hz) in confined spaces through structural design a significant challenge. This paper introduces a locally resonant seismic metamaterial (SM) characterized by an ultra-low frequency wide bandgap, created by placing a nylon barrier embedded with steel oscillators between two steel plates. The bandgap is calculated using dispersion analysis and phononic crystals method, delineating the attenuation range of the seismic metamaterial. Parameter analysis results show that greater oscillator mass, thinner nylon barrier thickness, and higher external barrier height favor broader bandgap width and reduced bandgap frequency. By introducing the concept of multiple oscillators and “uniform and gradient,” the isolation performance of the SM is significantly enhanced, while the impact of the Fano-like phenomenon on attenuation is simultaneously reduced. This indicates that multi-oscillator and “uniform and gradient” are ideal solutions for opening ultra-low frequency bandgaps. Finally, the dynamic response of the SM is clarified through time-domain analysis, further validating the effectiveness of the research. We hope that this study can promote the engineering application of common building materials in the shielding of deep subwave length frequency seismic waves.

We develop a theory for thermal convection in a double porosity material of Brinkman–Forchheimer type when there is a single temperature. The saturating fluid is one of Kelvin–Voigt type, and the equation for the temperature is one due to C.I. Christov. It is shown that the global nonlinear stability threshold coincides with the linear stability one. A thoroughly analytical discussion of both linear instability analysis and global nonlinear energy stability is provided. Numerical results show that the relative permeability and Brinkman viscosity between the macro and micro pores are key parameters which play a dominant role in determining the critical Rayleigh number for the onset of convective motions.

This paper concerns the general axisymmetric problem in plasticity in conjunction with the hypothesis of Haar and von Karman for calculating stress fields. No other restriction is imposed on the yield criterion. The stress equations comprising the yield criterion and the equilibrium equations without body forces are statically determined in the sense that there are four equations involving only the four components of stress. Therefore, the result of the present paper is independent of the plastic flow rule. It is also immaterial whether elastic strains are included. It is shown that the problem above reduces to a purely geometric problem of determining an orthogonal coordinate system whose scale factors satisfy a parametric equation. Any orthogonal net satisfying this equation determines a net of principal stress trajectories giving a solution to the stress equations. The general method applies to finding the specific equations for several widely used yield criteria. Characteristic analysis of the equations that describe the mapping between the principal line coordinate system and a cylindrical coordinate system is performed. A numerical scheme based on the method of characteristics is developed and employed for calculating the stress field near a rotational ellipsoid whose surface is traction-free.

The paper deals with the derivation of asymptotically correct equations governing the long-wave bending response of a rectangular ultrathin elastic isotropic plate taking into account surface effects within the framework of the Gurtin-Murdoch theory of surface elasticity. The upper and lower faces are assumed to be pre-stressed by residual surface stresses which can be either tensile or compressive. The original 3D equations of elasticity are split into equations corresponding to the in-plane boundary layer and equations predicting out-of-plane bending deformation. By performing asymptotic integration through the thickness of the 3D equations associated with bending deformations and satisfying the balance equations on both faces, we derive asymptotically correct relations for displacements and stresses, as well as a new Timoshenko-type equation capturing surface stresses and inertia. A comparative analysis of the derived governing equation with similar available equations based on kinematic hypotheses revealed significant differences in the effective bending stiffness and factors of the inertia term. As examples, we studied free low-frequency vibrations and self-buckling of a square nanoplates made of different materials and compared effects of residual stresses on the natural frequencies and the critical value of the plate side using the novel model and the models relying on hypotheses for the normal component of the stress tensor.