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This work deals with fracture mechanisms in quasi-brittle materials, focusing on the characterization of the Fracture Process Zone (FPZ) of specimens under tensile load. Particularly, paper was used as model material. Experiments were conducted on notched and unnotched specimens. Based on an image analysis of these observations, a stochastic finite element model was developed, using both a nonlocal stress-based approach and a discretized random field modeling of the Young's modulus. The proposed methodology allowed characterizing the damage zone and the size of the FPZ, analyzing the influence of the mesostructure, composed of flocs (fiber aggregates where the basis weight is larger than the average one) and antiflocs (complement of flocs). The area of the active FPZ and the normalized stress drop were linked using a surface energy dissipated in the active FPZ. The stress drop, until limiting value, increased with the width of the active FPZ. Finally, a relationship between the surface energy and the nonlocal internal length was established. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error analysis is provided, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation, the comparison with the classical Fourier theory and the behavior of the solution in two-dimensional examples. [ABSTRACT FROM AUTHOR]

In this paper, a refined finite element method (FEM) based on the Carrera unified formulation (CUF) is extended for stress analysis of rotors and rotating disks with variable thickness. The variational form of the 3D equilibrium equations is obtained using the principle of minimum potential energy and solved by this method. Employing the 1D CUF, a rotor is assumed to be a beam along its axis. In this case, the geometry of the rotor can be discretized into a finite number of 1D beam elements along its axis, while the Lagrange polynomial expansions may be employed to approximate the displacement field over the cross section of the beam. Therefore, the FEM matrices and vectors can be written in terms of fundamental nuclei, whose forms are independent of the order of the beam theories. The validity and capabilities of the presented procedure are investigated in a number of numerical examples, and some conclusions are reported and compared well with the analytical and 3D finite element solutions. The results obtained by the 1D CUF models are in close agreement with the reference solutions. Moreover, it is verified that the innovative procedure presented in this paper can be used as an accurate tool of structural analysis for complex rotors to reduce the computational costs. [ABSTRACT FROM AUTHOR]

The conventional Eshelby’s problems of smooth inclusions in two-dimensional space are touched in this paper. When the smooth inclusion is characterized by the Laurent polynomial, using the solution of the full-plane as basis, the solutions of a finite domain can be decomposed into a basic part and an auxiliary part. The K-M potentials, including the basic and auxiliary parts, of the circular disk, full- and half-plane problems are explicitly solved in the form of polynomials. The coefficients of the polynomials are determined by the geometric parameters characterizing the smooth inclusion and its position. The solutions for elliptical and truncated pentagram inclusions are used as examples to show the correctness and validity of the presented solutions. [ABSTRACT FROM AUTHOR]

The arch shape is a timeless structural solution as it has been widely used in the past but is still a common solution adopted nowadays for large spans. Structural efficiency depends primarily on optimal material exploitation, which allows us to minimize the structural volume. The paper is framed in the context of optimization of arch structures, and analytical design criteria are proposed, dealing with a specific class of deck bridges supported in the mid-span by arches. The investigation deals with a simplified structural scheme, constituted by statically determinate plane arches under self-weight and a single vertical load in the key section, exerted by the deck supports. The optimization criterion assumes a constant normal stress in all arch sections and the resulting arch shape is computed in closed form. Finally, the existence condition for the proposed solution is provided and some numerical examples are introduced. [ABSTRACT FROM AUTHOR]

In this paper, the Gurtin-Murdoch continuum theory is applied to develop a new continuum mechanics model for static and dynamic analyses of nanoscale rectangular plates. The relevant governing equations are established from basic principles. Analytical solutions for static and free vibration of nanoscale rectangular plates are presented for selected boundary conditions. A finite element method for the analysis of rectangular nanoplates is also developed to solve general cases that cannot be solved analytically. Expressions for stiffness and mass matrices and the load vector are derived by using a weighted residual formulation. A selected set of numerical results is presented to investigate the size-dependent static and free vibration response of plates and the influence of surface material properties and boundary conditions. [ABSTRACT FROM AUTHOR]

Simultaneous peeling of multiple strips is commonly observed particularly at small-scale detachment processes. Although theoretical treatment of this problem is addressed, numerical solution procedures for geometrically arbitrary multiple-peeling problems are still missing. In this paper, a finite element-based numerical solution procedure for 3-D large displacement multiple-peeling problems is presented. Loading/unloading of peeling strips are expressed in the form of optimality conditions, and the current positions of the peeling fronts are determined locally adapting the multiplicative decomposition and the return mapping algorithm of finite strain plasticity theories. Within an incremental-iterative solution framework, peeling fronts and the current position of other nodes are determined in a staggered way instead of using an active set-based solution algorithm. The effectiveness of the approach is demonstrated by a series of example problems including multiple peeling of an assembly of randomly oriented strips. [ABSTRACT FROM AUTHOR]

The formation of strain localization influences the stability and stiffness of the soil mass or geosystem. The thickness of shear bands provides insight into overall strength and stiffness inside the granular body, and the shear band angle gives information about the failure surface in a given soil or soil mass. Thus, it is important to be able to predict when a shear band forms and how this zone of intense deformation is located and oriented within the granular medium. A rational finite element analysis for capturing the formation and development of shear bands has been formulated by using a micropolar continuum in finite element analysis. Hardening parameters including nonsymmetric stress and length scale are implemented for a realistic stress–strain analysis. Implementation and simulations of the model will be discussed in the Part II of this research. The micro–macro structure relation for finite element analysis based on this formulation paper will be simulated in the corresponding paper. [ABSTRACT FROM AUTHOR]

This paper addresses the development of a novel updated Lagrangian variational formulation and its associated finite element model for the geometrically nonlinear quasi-static analysis of cantilever beams. The formulation is based on an incremental complementary energy principle. The proposed finite element model only contains nodal bending moments as degrees of freedom. The model is used for the analysis of problems modeled by the so-called elastica theory. Numerical solutions satisfying all equilibrium equations in a strong sense can be obtained for arbitrarily large displacements and rotations. A Newton-Raphson method is adopted to trace the post-buckling response. Numerical results are presented and compared with those produced by the standard total Lagrangian two-node displacement-based finite element model. [ABSTRACT FROM AUTHOR]

This paper addresses the formulation and numerical efficiency of various numerical models of different nonconserving time integrators for studying wave propagation in nonlinear hyperelastic waveguides. The study includes different nonlinear finite element formulations based on standard Galerkin finite element model, time domain spectral finite element model, Taylor-Galerkin finite element model, generalized Galerkin finite element model and frequency domain spectral finite element model. A comparative study on the computational efficiency of these different models is made using a hyperelastic rod model, and the optimal computational scheme is identified. The identified scheme is then used to study the propagation of transverse and longitudinal waves in a Timoshenko beam with Murnaghan material nonlinearity. [ABSTRACT FROM AUTHOR]

Generalized thermo-elastic theory, which is based on the non-Fourier theory, indicates that there is a time delay between the heat flux vector and the temperature gradient. At present, the traditional numerical method for solving the thermo-elastic problem subjected to high-frequency heat source generally fails to properly capture discontinuities of impulsive waves in space and produces spurious numerical oscillations in the simulation of high modes and sharp gradients. In the paper, a time discontinuous Galerkin finite element method (DGFEM) for the solution of generalized thermo-elastic coupled problems is presented on the basis of well-known Lord-Shulman theory. The essential feature of the DGFEM is that the general temperature-displacement vector and its temporal gradient are assumed to be discontinuous and interpolated individually at each time level in time domain, respectively. In order to filter out the spurious wave-front oscillations, an artificial damping scheme is implemented in the final finite element formula. Numerical results show that the present DGFEM shows good abilities and provides much more accurate solutions for generalized thermo-elastic coupled behavior. It can capture the discontinuities effectively at the wave front and filter out the effects of spurious numerical oscillation induced by a high-frequency thermal shock. [ABSTRACT FROM AUTHOR]

This paper addresses the application of the extended finite element method (XFEM) to the modeling of two-dimensional coupled magneto-mechanical field problems. Continuum formulations of the stationary magnetic and the coupled magneto-mechanical boundary problem are outlined, and the corresponding weak forms are derived. The XFEM is applied to generate numerical models of a representative volume element, characterizing a magnetoactive composite material. Weak discontinuities occurring at material interfaces are modeled numerically by an enriched approximation of the primary field variables. In order to reduce the complexity of the representation of curved interfaces, an element local approach is proposed which allows an automated computation of the level set values. The composite's effective behavior and its coupled magneto-mechanical response are computed numerically by a homogenization procedure. The scale transition process is based on the energy equivalence condition, which is satisfied by using periodic boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, a new type of hybrid fundamental solution-based finite element method (HFS-FEM) is developed for analyzing plane piezoelectric problems with defects by employing fundamental solutions (or Green's functions) as internal interpolation functions. The hybrid method is formulated based on two independent assumptions: an intra-element field covering the element domain and an inter-element frame field along the element boundary. Both general elements and a special element with a central elliptical hole or crack are developed in this work. The fundamental solutions of piezoelectricity derived from the elegant Stroh formalism are employed to approximate the intra-element displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. By using Stroh formalism, the computation and implementation of the method are considerably simplified in comparison with methods using Lekhnitskii's formalism. The special-purpose hole element developed in this work can be used efficiently to model defects such as voids or cracks embedded in piezoelectric materials. Numerical examples are presented to assess the performance of the new method by comparing it with analytical or numerical results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, systematic approaches to determine the polynomial stress functions for anisotropic plane problems are presented based on the Lekhnitskii's theory of anisotropic elasticity. It is demonstrated that, for plane problems, there are at most four independent polynomials for arbitrary n-th order homogeneous polynomial stress functions: three independent polynomials for n equal to two and four for n greater than or equal to three. General expressions for such polynomial stress functions are derived in explicit forms. Unlike the isotropic case, the polynomials for anisotropic problems are functions of material constants, because the elastic constants cannot be eliminated in the governing equation for general anisotropic cases. The polynomials can be used as analytical trial functions to develop the new 8-node hybrid element (ATF-Q8) for anisotropic problems. This ATF-Q8 element demonstrated excellent performance in comparison with traditional numerical methods through several testing examples. [ABSTRACT FROM AUTHOR]

In this paper, the development of a new quadrilateral membrane finite element with drilling degrees of freedom is discussed. A variational principle employing an independent rotation field around the normal of a plane continuum element is derived. This potential is based on the Cosserat continuum theory where skew symmetric stress and strain tensors are introduced in connection with the rotation of a point. From this higher continuum theory a formulation that incorporates rotational degrees of freedom is extracted, while the stress tensor is symmetric in a weak form. The resulting potential is found to be similar to that obtained by the procedure of Hughes and Brezzi. However, Hughes and Brezzi derived their potential in terms of pure mathematical investigations of Reissner’s potential, while the present procedure is based on physical considerations. This framework can be enhanced in terms of assumed stress and strain interpolations, if the numerical model is based on a modified Hu-Washizu functional with symmetric and asymmetric terms. The resulting variational statement enables the development of a new finite element that is very efficient since all parts of the stiffness matrix can be obtained analytically even in terms of arbitrary element distortions. Without the addition of any internal degrees of freedom the element shows excellent performance in bending dominated problems for rectangular element configurations. [ABSTRACT FROM AUTHOR]

In this paper, an efficient method is developed for the formation of null bases of four-node quadrilateral plate bending finite element models, corresponding to highly sparse and banded flexibility matrices. This is achieved by introducing a new four-node quadrilateral plate bending element, and using special graphs associated with the finite element models. The results are compared to those of the previously developed graph theoretical and algebraic force methods, and also the displacement approach. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of active constrained layer damping (ACLD) of laminated thin composite panels using vertically and obliquely reinforced 1–3 piezoelectric composite materials as the material of the constraining layer of the ACLD treatment. A finite element model has been developed for analyzing the ACLD of laminated antisymmetric cross-ply and antisymmetric angle-ply thin composite panels integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuations of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. The analysis revealed that the vertically reinforced 1–3 piezoelectric composites which are in general being used for the distributed sensors can be potentially used for the distributed actuators of high performance light-weight smart thin composite panels. [ABSTRACT FROM AUTHOR]

In this paper a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to impact internal pressure is considered. The axisymmetric conditions are assumed for the 2D-FG cylinder. The finite element method with graded material properties within each element is used to model the structure, and the Newmark direct integration method is implemented to solve the time dependent equations. The time histories of displacements, stresses and 2D wave propagation are investigated for various values of volume fraction exponents. Also the effects of mechanical properties distribution in radial and axial direction on the time responses of the FG cylinder as well as the stress distribution are studied and compared with a cylinder made of 1D-FGM. The achieved results show that using 2D-FGM leads to a more flexible design. To verify the presented method and data, the results are compared to published data. [ABSTRACT FROM AUTHOR]

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics. [ABSTRACT FROM AUTHOR]

The application of computational fluid dynamics (CFD) in the design of water turbines and pumps started about 30 years ago. This paper reviews the main steps and breakthroughs in the methods that were made during this period, through the eyes of one particular water turbine company which spear-headed some of the first developments for practical applications. Practical examples are used to illustrate the developments of the tools from 1978 to 2008 and to give an overview of the complete revolution in hydraulic turbine design that has occurred over this time. Several periods with distinct levels of complexity, and hence accuracy of the physical models and of the simulation methods can be distinguished. The first steps coincided with the introduction of the Finite Element Method into CFD, and were characterized by simplified Quasi-3D Euler solutions and Fully 3D potential flow solutions. Over the years the complexity continuously increased in stages: via 3D Euler solutions, to steady RANS simulations of single blade passages using finite volume methods, extending to steady simulations of whole machines, until today unsteady RANS equations are solved with advanced turbulence models. The most active areas of research and development are now concerned with including the effects of 2-phase flows (free surface flow in Pelton turbines and cavitation) and fluid–structure interaction. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal vibration elimination technique and the experimental demonstration of a cylindrical linear step motor dynamic behavior. Electrical, mechanical and magnetic motion equations are used to analyze the system behavior, employing a general-purpose method and finite element method. The oscillatory transient region of the step response and the inertial effect of the mover are investigated. The influence of the command time between steps and amplitude of commands on the damping capacity is determined. Thus, the optimal command time interval and amplitude degrees are found that remove the vibration completely in the least time. A comparison of the theory with the measured results shows the validity of this analysis. [ABSTRACT FROM AUTHOR]