Papers by Author: Glaucio H. Paulino

Abstract: This work explores the design of piezoelectric resonators based on functionally graded material (FGM) concept. The goal is to design single-frequency Functionally Graded Piezoelectric Resonators (FGPR) subjected to the following requirements: (i) an assurance of the specified resonance frequency, and (ii) for most acoustic wave generation applications, the FGPR is required to oscillate in the piston mode. Several approaches can be used to achieve these goals; however, a novel approach is to design the piezoelectric transducer by using Topology Optimization Method. Accordingly, in this work, the optimal material gradation of an FGPR is found, which maximizes a specified and single resonance frequency subjected to a volume constraint. To track the desirable piston mode, a mode-tracking method utilizing the modal assurance criterion (MAC) is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element (GFE) concept, where these material properties are interpolated inside the finite element using interpolation functions. The optimization algorithm is constructed based on sequential linear programming (SLP), and the concept of the Continuum Approximation of Material Distribution (CAMD) is considered. The software is implemented in MATLAB language. In addition, to illustrate the method, a two-dimensional FGPR is designed with plane strain assumption. Performance of designed FGPR is compared with non-FGPR performance.

Abstract: This is the second article in a series of two papers describing simulation of functionally graded viscoelastic properties in asphalt concrete pavements. The techniques developed are applicable to other viscoelastic material systems with continuous, spatial grading of material properties. A full-depth asphalt concrete pavement has been simulated to demonstrate the applicability and importance of the graded viscoelastic analysis method. Based on the graded finite elements developed by Kim and Paulino[1], Buttlar et al. [2] used graded finite elements to determine typical responses to tire loading for an aged asphalt concrete pavement. In the current study, a similar pavement section is studied using the viscoelastic graded analysis (rather than elastic). Graded, layered and homogeneous material variations were used for a series of simulations, and the results from different approaches were compared.

Abstract: Asphalt concrete pavements are inherently graded viscoelastic structures. Oxidative aging of asphalt binder and temperature cycling due to climatic conditions are the major cause of such graded non-homogeneity. Current pavement analysis and simulation procedures either ignore or use a layered approach to account for non-homogeneities. For instance, the recently developed Mechanistic-Empirical Design Guide (MEPDG) [1], which was recently approved by the American Association of State Highway and Transportation Officials (AASHTO), employs a layered analysis approach to simulate the effects of material aging gradients through the depth of the pavement as a function of pavement age. In the current work, a graded viscoelastic model has been implemented within a numerical framework for the simulation of asphalt pavement responses under various loading conditions. A functionally graded generalized Maxwell model has been used in the development of a constitutive model for asphalt concrete to account for aging and temperature induced property gradients. The associated finite element implementation of the constitutive model incorporates the generalized iso-parametric formulation (GIF) proposed by Kim and Paulino [2], which leads to the graded viscoelastic elements proposed in this work. A solution, based on the correspondence principle, has been implemented in conjunction with the collocation method, which leads to an efficient inverse numerical transform procedure. This work is the first of a two-part paper and focuses on the development, implementation and verification of the aforementioned analysis approach for functionally graded viscoelastic systems. The follow-up paper focuses on the application of this approach.

Abstract: This paper deals with the application of Cohesive Zone Model (CZM) concepts to study mode I fracture in adhesive bonded joints. In particular, an intrinsic piece-wise linear cohesive surface relation is used in order to model fracture in a pre-cracked bonded Double Cantilever Beam (DCB) specimen. Finite element implementation of the CZM is accomplished by means of the user element (UEL) feature available in the FE commercial code ABAQUS. The sensitivity of the cohesive zone parameters (i.e. fracture strength and critical energy release rate) in predicting the overall mechanical response is first examined; subsequently, cohesive parameters are tuned comparing numerical simulations of the load-displacement curve with experimental results retrieved from literature.

Abstract: This paper presents a Cohesive Zone Model (CZM) approach for investigating dy- namic failure processes in homogeneous and Functionally Graded Materials (FGMs). The failure criterion is incorporated in the CZM using both a ßnite cohesive strength and work to fracture in the material description. A novel CZM for FGMs is explored and incorporated into a ßnite element framework. The material gradation is approximated at the element level using a graded element formulation. A numerical example is provided to demonstrate the eácacy of the CZM approach, in which the inàuence of the material gradation on the crack branching pattern is studied.

Abstract: The concept of functionally graded materials (FGMs) is closely related to the concept of topology optimization, which consists in a design method that seeks a continuum optimum material distribution in a design domain. Thus, in this work, topology optimization is applied to design FGM structures considering a minimum compliance criterion. The present approach applies the so-called “continuous topology optimization” formulation where a continuous change of material properties is considered inside the design domain by using the graded finite element concept. A new design is obtained where distribution of the graded material itself is considered in the design domain, and the material properties change in a certain direction according to a specified variation, leading to a structure with asymmetric stiffness properties.

Abstract: This paper presents numerical simulation of mixed-mode crack propagation in functionally graded materials by means of a remeshing algorithm in conjunction with the finite element method. Each step of crack growth simulation consists of the calculation of the mixedmode stress intensity factors by means of a non-equilibrium formulation of the interaction integral method, determination of the crack growth direction based on a specific fracture criterion, and local automatic remeshing along the crack path. A specific fracture criterion is tailored for FGMs based on the assumption of local homogenization of asymptotic crack-tip fields in FGMs. The present approach uses a user-defined crack increment at the beginning of the simulation. Crack trajectories obtained by the present numerical simulation are compared with available experimental results.

Abstract: This paper revisits the interaction integral method to evaluate both the mixed-mode stress intensity factors and the T-stress in functionally graded materials under mechanical loading. A nonequilibrium formulation is developed in an equivalent domain integral form, which is naturally suitable to the finite element method. Graded material properties are integrated into the element stiffness matrix using the generalized isoparametric formulation. The type of material gradation considered includes continuum functions, such as an exponential function, but the present formulation can be readily extended to micromechanical models. This paper presents a fracture problem with an inclined center crack in a plate and assesses the accuracy of the present method compared with available semi-analytical solutions.

Abstract: A general methodology is constructed for the fundamental solution of a crack in the homogeneous half-plane interacting with a crack at the interface between the homogeneous elastic half-plane and the nonhomogeneous elastic coating in which the shear modulus varies exponentially with one coordinate. The problem is solved under plane strain or generalized plane stress condition using the Fourier integral transform method. The stress field in the homogeneous half plane is evaluated by the superposition of two states of stresses, one is associated with a local coordinate system in the infinite fractured plate, while the other in the infinite half plane defined in a structural coordinate system.

Abstract: A micromechanics-based elastic model is developed for two-phase functionally graded composites with locally pair-wise particle interactions. In the gradation direction, there exist two microstructurally distinct zones: particle-matrix zone and transition zone. In the particle-matrix zone, the homogenized elastic fields are obtained by integrating the pair-wise interactions from all other particles over the representative volume element. In the transition zone, a transition function is constructed to make the homogenized elastic fields continuous and differentiable in the gradation direction. The averaged elastic fields are solved for transverse shear loading and uniaxial loading in the gradation direction.