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The paper aims to presents a numerical analysis of free vibration of micromorphic structures subjected to various boundary conditions.

To accomplish this objective, first, a two-dimensional (2D) micromorphic formulation is presented and the matrix representation of this formulation is given. Then, two size-dependent quadrilateral and triangular elements are developed within the commercial finite element software ABAQUS. User element subroutine (UEL) is used to implement the micromorphic elements. These non-classical elements are capable of capturing the micro-structure effects by considering the micro-motion of materials. The effects of the side length-to-length scale parameter ratio and boundary conditions on the vibration behavior of 2D micro-structures are discussed in detail. The reliability of the present finite element method (FEM) is confirmed by the convergence studies and the obtained results are validated with the results available in the literature. Also, the results of micromorphic theory (MMT) are compared with those of micropolar and classical elasticity theories.

The study found that the size effect becomes very significant when the side length of micro-structures is close to the length scale parameter.

The study is to analyze the free vibrations of 2D micro-structures based on MMT; to develop a 2D formulation for micromorphic continua within ABAQUS; to propose quadrilateral and triangular micromorphic elements using UEL and to investigate size effects on the vibrational behavior of micro-structures with various geometries.

The purpose of this paper is to propose two linear solid-shell finite elements, a six-node prismatic element denoted SHB6-EXP and an eight-node hexahedral element denoted SHB8PS-EXP, for the three-dimensional modeling of thin structures in the context of explicit dynamic analysis.

These two linear solid-shell elements are formulated based on a purely three-dimensional (3D) approach, with displacements as the only degrees of freedom. To prevent various locking phenomena, a reduced-integration scheme is used along with the assumed-strain method. The resulting formulations are computationally efficient, as only a single layer of elements with an arbitrary number of through-thickness integration points is required to model 3D thin structures.

Via the VUEL user-element subroutines, the performance of these elements is assessed through a set of selective and representative dynamic elastoplastic benchmark tests, impact-type problems and deep drawing processes involving complex non-linear loading paths, anisotropic plasticity and double-sided contact. The obtained numerical results demonstrate good performance of the SHB-EXP elements in the modeling of 3D thin structures, with only a single element layer and few integration points in the thickness direction.

The extension of the SHB-EXP solid-shell formulations to large-strain anisotropic plasticity enlarges their application range to a wide variety of dynamic elastoplastic problems and sheet metal forming simulations. All simulation results reveal that the numerical strategy adopted in this paper can efficiently prevent the various locking phenomena that commonly occur in the 3D modeling of thin structural problems.

A simple economic analysis has revealed that in order for wind energy to be a viable alternative, wind-turbines (convertors of wind energy into electrical energy) must be able to operate for at least 20 years, with only regular maintenance. However, wind-turbines built nowadays do not generally possess this level of reliability and durability. Specifically, due to the malfunction and failure of drive-trains/gear-boxes, many wind-turbines require major repairs after only three to five years in service. The paper aims to discuss these issues.

The subject of the present work is the so-called white etch cracking, one of the key processes responsible for the premature failure of gear-box roller-bearings. To address this problem, a multi-physics computational methodology is developed and used to analyze the problem of wind-turbine gear-box roller-bearing premature-failure. The main components of the proposed methodology include the analyses of: first, hydrogen dissolution and the accompanying grain-boundary embrittlement phenomena; second, hydrogen diffusion from the crack-wake into the adjacent unfractured material; third, the inter-granular fracture processes; and fourth, the kinematic and structural response of the bearing under service-loading conditions.

The results obtained clearly revealed the operation of the white-etch cracking phenomenon in wind-turbine gear-box roller-bearings and its dependence on the attendant loading and environmental conditions.

The present work attempts to make a contribution to the resolution of an important problem related to premature-failure and inferior reliability of wind-turbine gearboxes.

Nacre is a biological material constituting the innermost layer of the shells of gastropods and bivalves. It consists of polygonal tablets of aragonite, tessellated to form individual layers and having the adjacent layers as well as the tablets within a layer bonded by a biopolymer. Due to its highly complex hierarchical microstructure, nacre possesses an outstanding combination of mechanical properties, the properties which are far superior to the ones that are predicted using techniques such as the rule of mixtures. Given these properties, a composite armor the structure of which mimics that of nacre may have improved performance over a monolithic armor having a similar composition and an identical areal density. The paper aims to discuss these issues.

In the present work, an attempt is made to model a nacre-like composite armor consisting of B₄C tablets and polyurea tablet/tablet interfaces. The armor is next tested with respect to impact by a solid right circular cylindrical (SRCC) rigid projectile, using a transient non-linear dynamics finite-element analysis. The ballistic-impact response and the penetration resistance of the armor are then compared with that of the B₄C monolithic armor having an identical areal density. Furthermore, the effect of various nacre microstructural features (e.g. surface profiling, micron-scale asperities, mineral bridges between the overlapping tablets lying in adjacent layers, and B₄C nano-crystallinity) on the ballistic-penetration resistance of the composite armor is investigated in order to identify an optimal nacre-like composite armor architecture having the largest penetration resistance.

The results obtained clearly show that a nacre-like armor possesses a superior penetration resistance relative to its monolithic counterpart, and that the nacre microstructural features considered play a critical role in the armor-penetration resistance.

The present work indicates that for a given choice of armor material, penetration resistance may be improved by choosing a structure resembling that of nacre.

The purpose of this paper is to model a nacre-like composite material, consisting of tablets and polyurea tablet/tablet interfaces, B₄C. This composite material is being considered in the construction of the so-called backing-plate, a layer within a multi-functional/multi-layer armor system.

Considering the basic functions of the backing-plate (i.e. to provide structural support for the ceramic-strike-face and to stop a high-velocity projectile and the accompanying fragments) in such an armor system, the composite-material architecture is optimized with respect to simultaneously achieving high flexural stiffness and high ballistic-penetration resistance. Flexural stiffness and penetration resistance, for a given architecture of the nacre-like composite material, are assessed using a series of transient non-linear dynamics finite-element analyses. The suitability of the optimized composite material for use in backing-plate applications is then evaluated by comparing its performance against that of the rolled homogeneous armor (RHA), a common choice for the backing-plate material.

The results obtained established: a trade-off between the requirements for a high flexural stiffness and a high ballistic-penetration resistance in the nacre-like composite material; and overall superiority of the subject composite material over the RHA when used in the construction of the backing-plate within multi-functional/multi-layer armor systems.

This study extends the authors previous research on nacre-mimetic armor to optimize the architecture of the armor with respect to its flexural stiffness and ballistic-penetration resistance, so that these properties could be increased over the levels attained in the current choice (RHA) for the backing layer of multi-functional/multi-layer armor.

The paper aims to highlight the computational implementation of a nonlinear piezoelectric constitutive model and its application in determining the impact of misalignment between initial poling direction and applied electrical field, and mechanical boundary conditions on actuator performance.

The numerical analysis is based on an existing three‐dimensional model, where the original rate‐independent evolution equations are replaced by their rate‐dependent counterparts to facilitate implementation, which is performed in a partial differential equation solver. The execution of the model is verified through several benchmark constitutive responses.

The analysis shows that small angles of poling and loading axes misalignment such as may occur in fabrication (less than 5^○) have minor impact on piezoelectric performance regardless of the type of imposed mechanical boundary conditions. On the other hand, larger angles of misalignment can have a significant impact, the feasibility of which in actuator design remains to be seen. Furthermore, it is shown that the linear response range of these actuators can be expanded by increased levels of mechanical constraint at the cost of maximum actuation stroke regardless of the degree of misalignment.

The misalignment, which occurs accidentally, but can also be introduced purposefully during the fabrication process when poled material is cut into specimen form, may exhibit desirable performance features for actuator design when combined with appropriate mechanical constraints.

The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis.

Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions.

Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements.

The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. Sliding of the joint is assumed to be governed by Coulomb friction, with a non‐associated flow rule and no cohesion. The constitutive equations are formulated in a manner appropriate for a backward difference discretization in time along the path of loading. It is shown that the backward difference assumption can lead to an explicit formulation in which no essential distinction need be drawn between opening and closing of the joint and sliding when the joint is closed. However, an inherent limitation of the dilatant Coulomb model becomes evident; the final formulation is internally consistent but does not describe reversed shear displacement in a physically reasonable way. Explicit equations for the consistent tangent stiffness and for the corrector step (or return algorithm) of the standard Newton—Raphson iterative algorithm are given. The equations have been implemented as a user element in the finite element code ABAQUS, and illustrative examples are given.

In this work, the cohesive zone model (CZM) developed by some of the authors to simulate the propagation of fatigue defects in two dimensions is extended in order to simulate the propagation of defects in 3D. The paper aims to discuss this issue.

The procedure has been implemented in the finite element (FE) solver (Abaqus) by programming the appropriate software-embedded subroutines. Part of the procedure is devoted to the calculation of the rate of energy release per unit, G, necessary to know the growth of the defect.

The model was tested on different joint geometries, with different load conditions (pure mode I, mode II pure, mixed mode I/II) and the results of the analysis were compared with analytical solutions or virtual crack closure technique (VCCT).

The possibility to simulate the growth of a crack without any re-meshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elements makes the CZM attractive also for the fatigue crack growth simulation. However, differently from VCCT, three-dimensional fatigue de-bonding/delamination with CZM is not yet state-of-art in FE softwares.

A diffusion-reaction-deformation coupled model is employed and implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS.

Chemical reaction and diffusion are treated as two distinct processes by introducing the extent of reaction and the diffusion concentration as two kinds of independent variables, for which the independent governing equations for chemical reaction and diffusion processes are obtained. Furthermore, an exponential form of chemical kinetics, instead of the linearly phenomenological relation, between the reaction rate and the chemical affinity is used to describe reaction process. As a result, complex chemical reaction can be simulated, no matter it is around or away from equilibrium.

Two numerical examples are presented, one for validation of the model and another for the modeling of the deflection of a plane caused by a chemical reaction.

1. Independent governing equations for diffusion and reaction processes are given. 2. An exponential relation between the reaction rate and its driving force is employed. 3. The UEL subroutine is used to implement the finite element procedure.