A nonconforming generalized H-R mixed finite element is developed for static and dynamic analysis of piezoelectric composite laminated plates. The overall structure is solved discretely using 8-node hexahedral nonconforming solid elements, discarding many of the artificial assumptions in the plate and shell theories. The displacement and stress can be obtained directly through linear equations, including potential and electric displacement. The C0-continuous polynomial shape function commonly for the displacement methods is used to represent the displacement variables and stress variables, and the nonconforming term is introduced into the interior of the elements, which allows it to show better numerical performance than the similar conforming elements. The displacement and stress boundary conditions are introduced simultaneously so that the actual out-of-plane stress results are obtained at the free boundary. The free-vibrational characteristic equations for piezoelectric laminated plates are derived by combining the nonconforming generalized H-R mixed variational principle with Hamiltonian principle. The accuracy of the present method is verified by analyzing several representative numerical examples of laminated plates.

An unbounded, isotropic thermoelastic solid contains a closed, semi-infinite planar crack. Point forces are applied to the crack faces and translated toward the crack edge at a constant, subcritical speed. Fracture occurs and extension of the crack is accompanied by thermal convection. A dynamic steady state ensues in which the crack edge profile is no longer rectilinear, fixed and translates at the same speed as the point forces. An analytical solution, based on robust asymptotic expressions in integral transform space, is developed. Examination of the solution provides information on the role of convection in the determination of crack edge contour and temperature change. In particular calculations indicate that the influence of convection can decrease both with decreasing convection and increasing crack speed.

This paper presents a physics-based constitutive equation to predict the mechanical responses of thermochemically aged elastomers. High-temperature oxidation in elastomers is a complex phenomenon. The macromolecular network of elastomers’ microstructures undergoes chain scission and crosslinking under high temperature and oxygen saturation conditions. In this work, we modify the network stiffness and the chain extensibility in the well-known Arruda–Boyce constitutive equation to incorporate network changes in the microstructures of elastomers during thermochemical aging. In particular, the effects of network evolution due to aging in changing the shear modulus and the number of Kuhn monomers are considered. The modification is based on chemical characterization tests measuring the crosslink density evolution. The developed constitutive equation predicts the mechanical responses of thermochemically aged elastomers independently of any mechanical tests on aged samples. The proposed constitutive equation is validated with respect to a comprehensive set of experimental data available in the literature that were designed to capture thermochemical aging effects in elastomers. The comparison showed that the developed constitutive equation can accurately predict the tensile tests conducted on aged samples based on crosslink density evolution input. The obtained constitutive equation is physics-based, simple, and includes minimal material parameters.

The present work studies the propagation and reflection of plane waves in an elastic 2D half-space. The material microstructure is taken into account assuming the validity of the complete Toupin–Mindlin theory of isotropic gradient elasticity. This theory involves five additional microstructural material constants besides the two standard Lamé constants of elasticity. Our study builds upon the earlier work of Gourgiotis et al. (2013), which considered a simplified version of the Toupin–Mindlin theory with only one microstructural constant, in wave reflection. Our aim here is to consider the most general material response in the isotropic setting of the strain gradient theory, providing, thus, more general results as compared with those of the earlier work. More specifically, we study the effect of the gradient parameters upon the amplitudes, reflection angles and phase shift of the reflected waves, which proved to be four in the context of gradient elasticity (i.e., two waves propagating in the material volume and two surface waves with exponential decay from the surface), due to an incident either dilatational or distortional wave at the free surface of a 2D half-space. In addition, special emphasis is given here in the Rayleigh waves arising along the surface of the half-space.

We study the macroscopic (effective) longitudinal-transverse elastic constants appearing in the mixed longitudinal transverse-bulk stress-strain modes of the unidirectional multicomponent materials that are microscopically and macroscopically isotropic in the transverse plane. Unified systems of original minimum energy and iteration bounds on all 6 effective longitudinal-transverse elastic constants are derived. Illustrating numerical examples involving the two- and three-component cases are given.

The framework of this study is to develop a methodology based on digital image correlation (DIC) applied in biaxial straining under large deformations to calibrate the rubber computational modeling by the finite element method (FEM). Since the material approaches incompressibility, different shape functions were adopted to describe the fields of pressure and displacements according to the finite element hybrid formulation. Biaxial experiments were performed in a cruciform machine and the applied methodology was validated through a classical bulge test. Despite the low biaxiality degree, reasonable results were obtained to nominal strain levels higher than 300%, with the proposed methodology. A new method for obtaining the nominal stress-strain relationship was proposed using Abaqus software. The validation was conducted by numerical simulations and biaxial extension experiments.

We first examine the problem associated with the thermoelectric and thermoelastic fields for a nonlinearly coupled thermoelectric circular inhomogeneity with interface slip and diffusion embedded in an infinite nonlinearly coupled thermoelectric matrix subjected to uniform remote electric current density and uniform remote energy flux. A closed-form solution to the time-dependent thermoelastic problem is derived using complex variable techniques. We observe that the electrically and thermally induced stresses and displacements evolve with three relaxation times: two of these are attributed to the applied electric current density while the remaining relaxation time is induced by the applied energy flux. As time approaches infinity, the internal stress field inside the circular inhomogeneity remains nonuniform. We subsequently adapt the proposed solution method to study the case of a thermoelectric circular inhomogeneity with spring-type imperfect interface.

Stress states of pre-stress filament wound parts are crucial to their design. However, proposed models exhibit certain errors that cannot be neglected. To minimize these errors, we propose an analytical model for tension-induced residual stress of composite rings with a metal liner based on elastic cylinder theory. The contributions of stress variation of inner layers on the entire part are calculated through inverse iteration method and the stress distribution of the outmost layer is accurately calculated by integral relationship. For comparisons with the analytical model, a finite element model is proposed based on several special simulation strategies. Both models are verified through winding experiments with the maximum error being under 5%. Compared with previous results of analytical models through three effect factors, the error between the two models in case of hoop stress was over 20%, thereby confirming the accuracy of our model.

Based on the bulk free energy density and the degenerate mobility constructed by the quartic double-well potential function, a phase field model is established to simulate the evolution of inclusions in interconnects due to interface diffusion in an electric field. The corresponding phase field governing equations are derived and the reliability of the program is proved by the agreement between the numerical simulation results and the theoretical analysis of the inclusion. The evolution of elliptical inclusions under different electric fields χ, different aspect ratios β, and different electric conductivity ratios λ is calculated using the mesh adaptation finite element method. The results show that the drift velocity of the circular inclusion is proportional to the electric field and inversely proportional to the electric conductivity ratio. There exist critical values of the electric field χc ⁡ , the aspect ratio βc ⁡ and the electric conductivity ratio λc ⁡ . When λ ≤ λc ⁡ , χ ≥ χc ⁡ or β ≥ βc ⁡ , the elliptical inclusions will split into several small inclusions. When λ > λc ⁡ , χ < χc ⁡ or β < βc ⁡ , the elliptical inclusions will drift along the direction of the electric field as a relatively stable shape. The smaller the electric conductivity ratio of the inclusions λ, the greater the electric field χ or the aspect ratio β, the easier it is for the elliptical inclusions to split. Moreover, the time required for splitting increases with increasing the electric conductivity ratio or the aspect ratio, and decreases with increasing the electric field. In addition, the interconnect line with two inclusions is more complex, and the inclusions will split into more small ones under the high electric field strength, and the phenomenon of multiple merging and multiple splitting will occur.

A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis, and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges not faced in PDEs. For example, there is no derivative in nonlocal models, which makes it impossible to replace derivatives with complex ones. Here we provide a way of constructing the PML for nonlocal models, which decays the waves exponentially impinging in the layer and makes reflections at the truncated boundary very tiny. To numerically solve the nonlocal PML problem, we design the asymptotically compatible (AC) scheme for a spatially nonlocal operator by combining Talbot’s contour and a Verlet-type scheme for time evolution. The accuracy and effectiveness of our approach are illustrated by various numerical examples.

This paper aims to study the optimal synthesis of an adjustable six-bar mechanism to generate a closed path that passes through target points. The proposed mechanism has been designed by the inspiration of two common linkages, crank-rocker and slider-crank mechanisms. In this research, an analytical approach is utilized to evaluate the position of members of the adjustable six-bar mechanism, and dimensional synthesis is carried out using a cuckoo optimization algorithm (COA). First, a comparison between the path generated by dimensional optimization of the primary four-bar linkage and the obtained results from works of the literature demonstrated the superior performance of COA. Afterward, having the optimal dimensions of the primary four-bar linkage, the other design variables of the adjustable six-bar linkage are achieved by reoptimizing the mechanism. The results indicate that a more accurate generated path could be obtained for the adjustable six-bar mechanism compared with the four-bar linkage.

The octet truss lattice is known to be stretch dominated and to offer superior mechanical properties compared with foams of identical (low) density and solid composition. In the lattices, size effects in effective modulus were observed; they were of small magnitude, 30% in torsion and 10% in bending. The Cosserat characteristic lengths in torsion (1 mm) and in bending (0.5 mm) are considerably smaller than the cell size, 4.5 mm. The lattice is therefore considered to be weakly Cosserat elastic in comparison with designed lattices for which size effects can exceed a factor of 30, and also in comparison with foams for which size effects can exceed a factor of 8.

A mathematical model which describes the frictionless contact problem with normal compliance and unilateral constraint is considered in this paper. The material is elastic. The contact condition is the normal compliance condition with unilateral constraint. This mathematical model is solved by the interpolating element-free Galerkin method numerically. Compared with the element-free Galerkin method, the interpolating element-free Galerkin method can impose the Dirichlet boundary conditions exactly. Numerical examples demonstrate the effectiveness of the interpolating element-free Galerkin method.

One of the most important components of the early design process for layered systems is gaining a knowledge of the behavior of materials under varied contact situations. Functionally graded materials (FGMs) have grown in popularity in layered systems as a result of their numerous benefits, such as permitting the reduction of local stress concentrations and thermal stresses often experienced in traditional composites. This paper suggests an analytical approach to solving the continuous and discontinuous contact problems of a functionally graded (FG) layer subjected to a distributed load. Elasticity theory and integral transform methods provide the basis of the aforementioned analytical approach. The FG layer rests on a half-plane that is homogeneous, and there is no adhesion or bonding at the contact surface. For this problem, we assume an exponentially varying shear modulus and mass density in the FG layer. In the solution, the body force of the FG layer is considered. The problem is solved analytically by applying boundary conditions for both continuous and discontinuous contact cases. The presented results show the effects of load factor, amplitude of distributed load, inhomogeneity parameters, and interface material property mismatch on contact stress distributions, initial separation load (critical load), initial separation distance, starting and end point of separation, and separation interval.

A working line for the development of strength prediction models for foamed cellular concrete (FCC) consists of taking models designed for normal concrete (NC) and adapting them to incorporate the particular characteristics of this material. In this work, a new strength prediction model for FCC is presented. In it, the specific densities of composing materials and their relative amounts to cement, by weight, are considered as input variables. Introducing the specific density of the foam and the foam-cement ratio by weight as input parameters of the model allows for consideration of the variability of the characteristics of the produced foam and, with it, the control of its influence on the mechanical characteristics of FCC. Quantifying the quantities of materials through their relationships with cement by weight is a common procedure in concrete technology, and allows proper control, with greater ease and accuracy, both in manufacturing plants and laboratories. In addition to the development of the mathematical expression of the model, its calibration and validation are presented. For this, experimental campaigns and statistical analysis were conducted. The influence of each input variable considered by the model on the compressive strength of the material is evidenced through parametric analysis. In this way, it was possible to achieve a mathematical expression for determining FCC theoretical porosity, and throughout it, the material’s compressive strength. Also, the expression is composed of parameters of simple determination, both on construction sites and in laboratories. Additionally, it was also shown that the proposed equation for the theoretical porosity is applicable for FCC that incorporates sand or not, and it can also be used with foams with different densities.

We present a numerical model to simulate the damage and fracture process occurred in ceramic materials under thermal shock conditions. In particular, the variational principle is applied to gradient damage analysis in the establishment of the numerical model. The experiments on quenching tests of circular specimens are used to validate the efficiency of the model, proving that the proposed model is capable of reproducing faithfully the entire damage-fracture process of the ceramic specimens. Moreover, influences of different physical parameters are examined and discussed. We find that an internal length scale parameter, which can be considered as a material parameter, plays an important role in the entire fracture process.

The distribution of flexibility and bending stiffness of beams is altered by the crack size and location, the shape of beam cross-section, and the beam length. However, up to now, most of the studies are mainly on the solid rectangular section beams, rarely on the beams with variable cross-sections. A novel continuous stiffness methodology for four classical cross-section beams is proposed based on fracture mechanics and energy theory to estimate the effects of edge-crack depth and location and the shape of cross-section on the distribution of bending stiffness. First, the continuous bending stiffness of beams with shallow and deep cracks is derived and solved using the Newton–Raphson technique. The extent and degree of influence of crack depth, crack location, beam’s length, and beam’s cross-section on the distribution of bending stiffness are studied. Second, the correctness of the proposed continuous stiffness method is verified using the experimental and theoretical data and the results of the solid rectangular section beams in the literature. Finally, the natural frequency ratios of the beams with different cross-sections, crack depths, crack positions, and beam lengths are studied in detail using the precious integration method (PIM), ANSYS element modeling (AEM) method, ANSYS solid modeling (ASM) method, and Rotational Spring Modeling (RSM), respectively. The availability and reliability of the proposed approach are verified further. The study of the proposed continuous stiffness method may provide some valuable references for modeling cracks of the different cross-section beams.

Fracture failures of ship plates subjected to in-plane biaxial low-cycle fatigue loading are generally the coupling result of accumulative plasticity and biaxial low-cycle fatigue damage. A biaxial low-cycle fatigue crack growth analysis of a hull structure that accounts for the accumulative plasticity effect can be more suitable for the actual evaluation of the overall fracture performance of the hull structure in severe sea conditions. An analytical model of biaxial low-cycle fatigue crack propagation with a control parameter for ΔCTOD is presented for a hull inclined-crack plate. A test was conducted for cruciform specimens made of Q235 steel with an inclined crack to validate the presented analysis. The biaxial accumulative plasticity behavior and the effects of biaxiality and stress ratios were investigated. The results of this study reveal a strong dependence of biaxial low-cycle fatigue crack propagation on biaxial accumulated plasticity.

The most important feature of peridynamic modeling is the use of summation of force interactions between material points for a continuum description of material behavior. Contrary to the local theory of elasticity, the peridynamic equation of motion proposed by Silling (J. Mech. Phys. Solids 2000; 48:175–209) is free of spatial derivatives of the displacement field. A linearization theory of the peridynamic properties of thermoelastic composites (CMs) with ordinary state-based peridynamic properties of phases of arbitrary geometry is analyzed for either periodic or random structure CMs under volumetric homogeneous remote boundary conditions. The effective properties are represented by the introduced micropolarization tensor averaged over the external interaction interface of the inclusion, rather than over the entire space. The basic hypotheses of peridynamic micromechanics are proposed by a generalization of the local micromechanics concepts. The solution method for the general integral equations (GIE) is obtained without any auxiliary assumptions, such as the effective field hypothesis (EFH) implicitly used in popular micromechanical methods of local elasticity. In particular, in the proposed generalized effective field method (EFM), the effective field is estimated from self-consistent estimates by the closure of the corresponding general integral equations for random structure CMs. In doing so, the hypothesis of the ellipsoidal symmetry (describing the random structure of CMs) is not used and the classical EFH is relaxed.

In this paper, an active vibration control model of the three-dimensional (3-D) braided piezoelectric composite beam (BPCB) is developed by using piezoelectric ceramic layers as sensor and actuator. The mechanical parameters of 3-D braided composites with different braided angles and volume fractions are predicted through finite element simulation of a representative volume unit (RVU). Based on Euler–Bernoulli beam theory, the kinematical equation and state space model of the 3-D BPCB are created. The effect of the sensor and the actuator of the 3-D BPCB is discussed. The linear quadratic regulator (LQR) method is adopted as an active control method to analyze the vibration control of the 3-D BPCB, and the optimal weighted matrix is selected by using a genetic algorithm (GA) to evaluate the cost function. Finally, the effect of different braided angles and volume fractions of the 3-D BPCB on the active vibration control is investigated.