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The paper presents an approach for effective solution of the stress-strain state and wear prediction problem for the case of contact between fuel rod and grid surfaces of a nuclear reactor. Boundary-initial value elastic-plastic problem statement, due to the quasi-static character of the forced oscillations, which was approved by eigen frequencies analysis, was reduced to boundary one. The influence of inhomogeneous temperature field and varying pressure in the outer surface of fuel rod’s shell are considered. For this, a sequence of special procedures for searching the most effective ways of numerical simulation with limited computational resources was considered. The method of weighted residuals and the finite difference method were used to solve the problem of nonlinear forced oscillations under periodic loading of the fuel rod, described as beam under bending. The analytical solution for the fuel rod’s shell displacements in thermo-elasticity problem is obtained, approximated for spatial case and added to the general three-dimensional Finite Element model. The same procedure was adopted for the maximum amplitude values of the displacements which were obtained in the geometrically nonlinear beam problem solution. After that the general elastic-plastic contact problem of the interaction between the fuel rod and the grid surfaces was solved, taking into account preliminary obtained stress distributions achieved by temperature and amplitude displacements influence. The theory of plasticity of an isotropic material with isotropic hardening was used as a model. The limits of linear solutions for beam deflections as well as deflection dependencies upon time are demonstrated and analyzed. The numerically obtained distributions of strains and stresses are presented. By use of the obtained maximum stress values an attempt for the wear estimation in contact zone was done and the fuel rod’s operating time without critical wear during the contact with the grid surface was determined. The obtained results may be considered as corresponding to practical operating data.

Silicon has a large impact on today’s world economy, also known as Silicon Age. For instance, it is an extremely important material for renewable energy systems like photovoltaics. Thereby, the use of polycrystalline silicon has a very wide range of application. For a safe and economic operation with this material, the most accurate prediction or measurement of the elastic properties possible is of interest in the first place even if the focus is on the analysis of the inelastic behavior and related reliability and service life predictions. The problem of effective elastic parameters of polycrystals is also a question of material symmetry. The silicon single crystals obey cubic symmetry while for the aggregate, at random orientation of its constituents, isotropy results. We here give a synopsis on established analytical approaches used to predict effective values as well as a review on experimental outcomes at crystal and aggregate level. In context of present material, the methods are applied and effective properties are predicted analytically while results are compared in terms of the different approaches applied and the material data sets accessed. The results are also contrasted to the measured findings. The resulting deviations are discussed whereby the reasons for these discrepancies are identified. For the application of the effective properties in practicable calculations, this implies that special emphasis must be placed on the origin of these data. The results of mono- and polycrystal properties for both, experimental and analytical findings, are tabulated in clear and concise form, so that they are readily accessible to design engineers.

Peridynamics is a non-local continuum theory which accounts for long-range internal force/moment interactions. Peridynamic equations of motion are integro-differential equations, and only few analytical solutions to these equations are available. The aim of this paper is to formulate governing equations for buckling of beams and to derive analytical solutions for critical buckling loads based on the nonlinear peridynamic beam theory. For three types of boundary conditions, explicit expressions for the buckling loads are presented. The results are compared with the classical results for buckling loads. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the current approach. The results show that with an increase of the horizon size the critical buckling load slightly decreases for the fixed overall stiffness of the beam.

Strain-gradient elasticity is a special case of high-gradient theories in which the potential energy density depends on the first and second gradient of the displacement field. The presence of a coupling term in the material law leads to a non-diagonal quadratic form of the stored energy, which makes it difficult for the derivation of fundamental theorems. In this article, two variational principles of the minimum of potential and complementary energies are argued in the context of the coupled strain-gradient elasticity theory. The basis of the proofs of both variational principles is the equivalent transformation of the stain and strain-gradient energy density that allows to avoid the complication related to the presence of the fifth-rank coupling tensor [Formula: see text] in the equation for the potential energy density and leads to diagonalization of the quadratic form of the stored energy. This transformation enables to inverse Hook’s law, to determine compliance tensors, and to obtain closed-form relation for the complementary energy. After that the proofs of both principles of a minimum of potential and complementary energies are provided in the usual manner adopted in the classical theory of elasticity.

Waste biomass-based natural fibers are being extensively researched nowadays as a composite material with various waste-based high-density polyethylene (HDPE) to utilize the waste biomass and recycle the plastic waste in an effective approach. In this study, chemically modified spent coffee husk (CH) has been applied with different ratios of HDPE to produce composite material and characterized comprehensively to determine the mechanical stability of the products. The injection molding method was used for composite development containing HDPE with untreated and 10 wt% NaOH-treated CH weight ratios of 0%, 15%, 20%, and 25% together with 10 wt% coupling agent and filler materials of acrylonitrile butadiene styrene (ABS) and kaolin clay, respectively. Physicochemical characteristics of untreated CH, 10 wt% NaOH treated CH, pristine HDPE and HDPE-CH composites have been analyzed comprehensively in this study. Adding 25 wt% fiber with 65 wt% HDPE and 10 wt% of ABS (7 wt%)-kaolin clay (3 wt%) increased the tensile and bending properties significantly. This composite presented the maximum tensile, flexural, and impact strengths, which were 36 MPa, 7.5 MPa, and 2.8 KJ/m2, respectively. The tensile strength and bending strength of NaOH-treated coffee husk fibers (CHF) were enhanced by 32% and 29%, respectively. The microstructural characteristics of HDPE with treated and untreated CHF composites analyzed by scanning electron microscopy (SEM) demonstrated the fibers’ and matrix’s excellent adhesion and compatibility. Thus, HDPE polymer-treated CH composite presented excellent stability, which can be expected as a new addition for construction, food packaging, and other industrial applications.

The equilibrium equations and the traction boundary conditions are evaluated on the basis of the condition of the stationarity of the Lagrangian for coupled strain gradient elasticity. The quadratic form of strain energy can be written as a function of the strain and the second gradient of displacement and contains a fourth-, a fifth- and a sixth-order stiffness tensor $${\mathbb {C}}_4$$ C 4 , $${\mathbb {C}}_5$$ C 5 and $${\mathbb {C}}_6$$ C 6 , respectively. Assuming invariance under rigid body motions the balance of linear and angular momentum is obtained. The uniqueness theorem (Kirchhoff) for the mixed boundary value problem is proved for the case of the coupled linear strain gradient elasticity (novel). To this end, the total potential energy is altered to be presented as an uncoupled quadratic form of the strain and the modified second gradient of displacement vector. Such a transformation leads to a decoupling of the equation of the potential energy density. The uniqueness of the solution is proved in the standard manner by considering the difference between two solutions.

A variant of the model of coupled thermohydrodynamics and heat balance is proposed. We use Sedov’s variational principle and develop (a closed energy–consistent mathematical gradient model for a four-dimensional generalized space–time continuum). In accordance with Sedov’s method for modeling dissipative processes, the principle of stationarity of a functional is generalized to the principle of stationarity of a non-integrable variational form. The physical properties of the transversely-isotropic four-dimensional continuum are determined by generalized properties tensors of the third, fourth and fifth ranks, constructed so that the internal forces and moments depend only on distortions. In general, the presented model contains gradient and scale parameters, which determine relaxation effects in both thermomechanical and thermal processes. Variants of Brinkman-type fluid models of heat transfer processes for compressible and incompressible media are obtained as a result of the analysis of the general equations of motion of the space–time continuum. In particular, the equations of thermoelasticity, thermohydrodynamics, Navier-Stokes equations for compressible and incompressible media, Darcy equations, Brinkman equations are obtained.

Young's modulus of α'- and α-crystals of poly (l-lactic acid) (PLLA), more precisely, of aggregates of isotropically arranged lamellae, has been estimated based on dynamic-mechanical analysis of sets of isotropic film samples containing largely different though well-defined amounts of crystals. Evaluation of the modulus of elasticity of these film samples yielded the dependence of Young's modulus as a function of the enthalpy-based crystallinity, increasing with the crystal fraction in the assessed range, from zero to about 75% crystallinity. Extrapolation towards 100% crystallinity suggests values of Young's modulus of around 3.7 and 4.6 GPa for isotropic aggregates of α'- and α-crystals, respectively, being only slightly higher than the modulus of the unaged glassy amorphous phase of 3.0 GPa. Noting the inherent anisotropy of the crystal modulus, suggested in the literature, the average modulus determined in this work seems to be controlled by weaker interchain secondary bonding but not the modulus in chain direction. Great effort has been undertaken to minimize errors by keeping the lamellar thickness in samples of different crystallinity constant, and by providing evidence for independence of the moduli on the spherulitic superstructure.

Chemical treatment is a significant factor in improving the natural fiber quality for composite materials production. In this study, the alkaline treatment of Ethiopian Arabica coffee husk by sodium hydroxide (NaOH) was performed to improve the fiber quality. A total of 10% (w/w) NaOH has been applied for the alkaline treatment. Comprehensive physicochemical characterizations, such as proximate analysis, cellulosic composition, porosity, and structural analysis of treated and untreated coffee husk, have been conducted and compared. The experimental results showed that lignin and hemicellulose were reduced by 72% and 52%, respectively, thus improving the overall fiber quality. Therefore, this study indicated alkaline treatment of Ethiopian coffee husk is effective for fiber quality enhancement. It can be applied as a potential feedstock for fiber production in the composite production sector.

The objective of this work is inclusion of the Steigmann-Ogden interface in the Method of Conditional Moments to investigate the influence of surface effects on the effective properties of random particulate composites. The particular focus is centered on accounting for the surface bending stiffness. To this end, the notion of the energy-equivalent inhomogeneity developed for Gurtin–Murdoch interface is generalized to include the surface bending contribution. The crucial aspect of that generalization is identification of the formula defining energy associated with the surface bending. With the help of that formula, the real nano-particle and its surface are replaced by equivalent inhomogeneity with properties incorporating the surface effects. Closed-form expressions for the effective moduli of a composite with a matrix and randomly distributed spherical inhomogeneities are derived. The normalized shear moduli of nanoporous material as a function of void volume fraction is analyzed and evaluated in the context of other theoretical predictions.

We use the algebraic orthogonality of rotation-free and divergence-free fields in the Fourier space to derive the solution of a class of linear homogenization problems as the solution of a large linear system. The effective constitutive tensor constitutes only a small part of the solution vector. Therefore, we propose to use a synchronous and local iterative method that is capable to efficiently compute only a single component of the solution vector. If the convergence of the iterative solver is ensured, i.e., the system matrix is positive definite and diagonally dominant, it outperforms standard direct and iterative solvers that compute the complete solution. It has been found that for larger phase contrasts in the homogenization problem, the convergence is lost, and one needs to resort to other linear system solvers. Therefore, we discuss the linear system’s properties and the advantages as well as drawbacks of the presented homogenization approach.

Peridynamics (PD) has been introduced to account for long range internal force/moment interactions and to extend the classical continuum mechanics (CCM). PD equations of motion are derived in the form of integro-differential equations and only few analytical solutions to these equations are presented in the literature. The aim of this paper is to present analytical solutions to PD beam equations for both static and dynamic loading conditions. Applying trigonometric series, general solutions for the deflection function are derived. For several examples in the static case including simply supported beam and cantilever beam, the coefficients in the series are presented in a closed analytical form. For the dynamic case, the solution is derived for a simply supported beam applying the variable separation with respect to the time and the axial coordinate. Several numerical cases are presented to illustrate the derived solutions. Furthermore, PD results are compared against results obtained from the classical beam theory (CBT). A very good agreement between these two different approaches is observed for the case of the small horizon sizes (HSs), which shows the capability of the current approach.

A photo-optical and radiophysical study into the destruction process of the internal structure of plexiglass (PMMA) after its exposure to an ionizing electron irradiation and a subsequent external mechanical point impact was carried out. Enlarged macrophotography of the picture of the radiation-mechanical internal destruction of plexiglass was performed at different shooting modes. An analysis and explanation of physics of the formation mechanism of the tree-like branched fractal structure of PMMA destruction is carried out based on the dynamics of impulse compression and a spherical single wave arising at the impact action. The radiophysical parameters of PMMA with radiation damage were measured using the waveguide method in the microwave range.

The linear theory of coupled gradient elasticity has been considered for hemitropic second gradient materials, specifically the positive definiteness of the strain and strain gradient energy density, which is assumed to be a quadratic form of the strain and of the second gradient of the displacement. The existence of the mixed, fifth-rank coupling term significantly complicates the problem. To obtain inequalities for the positive definiteness including the coupling term, a diagonalization in terms of block matrices is given, such that the potential energy density is obtained in an uncoupled quadratic form of a modified strain and the second gradient of displacement. Using orthonormal bases for the second-rank strain tensor and third-rank strain gradient tensor results in matrix representations for the modified fourth-rank and the sixth-rank tensors, such that Sylvester’s formula and eigenvalue criteria can be applied to yield conditions for positive definiteness. Both criteria result in the same constraints on the constitutive parameters. A comparison with results available in the literature was possible only for the special case that the coupling term vanishes. These coincide with our results.

The main aim of this work is to track the evolution of the stiffness tetrad during large plastic strain. Therefore, the framework of a general finite plasticity theory is developed. Some special cases are examined, and the case of a material plasticity theory is considered more closely. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach. As sample materials, we use three types of fiber-reinforced composites. For numerical experiments and verification of the model’s predictions, finite element simulations of representative volume elements for uni-, bi- and tri-directional reinforced materials with periodic boundary conditions are used. From these, we extract the stiffness tetrads before and after large deformations of the material. We quantify the change of the stiffness tetrads due to the fiber reorientation. Finally, we propose an analytical evolution with three parameters that account reasonably well for the evolution of the stiffness tetrad.

Analyses of longitudinal fracture behavior of inhomogeneous beams which have continuously varying sizes of the cross-section along the beam length are carried-out. Beams of a rectangular cross-section are studied. It is assumed that beams exhibit continuous (smooth) material inhomogeneity along the width and height of the cross-section. A longitudinal crack located arbitrary along the beam height is analyzed. First, a cantilever beam with linearly varying width and height along the beam length is considered. The material of the beam has non-linear elastic mechanical behavior. The external loading consists of one bending moment applied at the free end of the lower crack arm. The fracture behavior is analyzed in terms of the strain energy release rate assuming that the modulus of elasticity is distributed continuously in the beam cross-section. The balance of the energy is considered in order to derive the strain energy release rate. A solution to the strain energy release rate is obtained also by considering the complementary strain energy for verification. The longitudinal fracture behavior of the inhomogeneous non-linear elastic cantilever beam configuration is studied also for the cases when the variation of the width and height of the cross-section is described by sine and power laws.&nbsp

Turning process is a major part of machining processes in the manufacturing industries to perform the required products therefore, development of an optimisation techniques to sustain the manufactu...

In a locality wherever intense low process is completed while not appropriate waste management measures, low effluents area unit the principal reason behind organic pollution. Low husk contains caffeine, tannins, and chlorogenic acid, creating it a dangerous exposed husk. The low method has been delivery environmental issues to the environment thanks to the discharge of pollution with a large quantity of organic waste. the target of this work is to research the negative impacts of low husk on the atmosphere to scale back environmental pollution in step with the planet Health Organization, one among the foremost vital problems that enterprises confront as they look for ways to limit their use of the artifact by changing it into value-add products/applications is that the harmful impact of low husk on the atmosphere (WHO).The significance of the experiment is to form low husk as an alternate resource to switch fiber. Methylene chloride liquid-liquid extraction was developed to avoid caffeine, tannin, and CGA spectral overlapping within the three hundred -700 nm wavelength vary. The results indicated increment deadly materials that have an effect on the atmosphere. From the experiment performed low husk are often used as an alternate resource for getting composites for might applications and solve the environmental issues.