Erdogan Madenci

Fatigue failure model with peridynamic theory

This study presents a methodology to predict the fatigue failure of materials due to cyclic loading within the realm of peridynamic theory. This approach incorporates material failure intrinsically without the need for external crack growth criteria and post-processing. Failure occurs when and where it is energetically favorable. Fatigue life prediction is a natural extension of crack initiation and growth while allowing material degradation. The present approach focuses on the crack growth phase of fatigue life rather than initiation. During the crack growth phase, material degrades, and fatigue process is viewed as a quasi-static series of discrete crack growth steps. Crack growth process is controlled by the critical value of material stretch and that cyclic loading causes degradation in the critical stretch. When the critical amount of stretch is reached, stable crack growth occurs.

Peridynamic theory for damage initiation and growth in composite laminate

A recently introduced nonlocal peridynamic theory removes the obstacles present in classical continuum mechanics that limit the prediction of crack initiation and growth in materials. Furthermore, damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials mainly due to their mathematical structure. However, the peridynamic theory removes these obstacles by taking into account non-local interactions between material points. This study presents an application of the peridynamic theory for predicting damage progression from a central crack in fiber reinforced composite plates subjected to uniaxial tension loading.

Nonlinear analysis of bonded composite single-lap joints

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karmans nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint.

Nonlinear Analysis of Bonded Composite Tubular Lap Joints

The present study describes a semi-analytical solution method for predicting the geometrically nonlinear response of a bonded composite tubular single-lap joint subjected to general loading conditions. The transverse shear and normal stresses in the adhesive as well as membrane stress resultants and bending moments in the adherends are determined using this method. The method utilizes the principle of virtual work in conjunction with nonlinear thin-shell theory to model the adherends and a cylindrical shear lag model to represent the kinematics of the thin adhesive layer between the adherends. The kinematic boundary conditions are imposed by employing the Lagrange multiplier method. In the solution procedure, the displacement components for the tubular joint are approximated in terms of non-periodic and periodic B-Spline functions in the longitudinal and circumferential directions, respectively. The approach presented herein represents a rapid-solution alternative to the finite element method. The solution method was validated by comparison against a previously considered tubular single-lap joint. The steep variation of both peeling and shearing stresses near the adhesive edges was successfully captured. The applicability of the present method was also demonstrated by considering tubular bonded lap-joints subjected to pure bending and torsion.

Mechanical characterization of ultra-thin films by combining AFM nanoindentation tests and peridynamic simulations

In this study, the loading-unloading data obtained from the nono-indentation tests in combination with the peridynamic simulations are used to determine the elastic modulus and yield stress of the material. A simple search algorithm minimizing the difference between the predicted force- indentation depth and experiments leads to the determination of the material properties. Nano-indentation experiments are performed on both a soft polymer (polymethyldisiloxane (PDMS)) representative of the bulk dimensions, and a hard thin-film polymer (polystyrene (PS)) deposited on the bulk PDMS. Both the simulation and experimental results are validated by comparison against those previously published in the literature.

Analysis of Bolted-Bonded Composite Lap Joints

Bolted, bonded, and hybrid bolted/bonded joints are three-dimensional in nature. Although the finite element method (FEM) is capable of addressing such joint configurations, it requires considerable computer resources, especially in the presence of multiple bolts. The presence of unknown contact regions between the bolts and laminates and the small length scale of the adhesive thickness require a fine mesh to achieve a reliable prediction of the stress field. Therefore, the identification of the critical design parameters and optimization of the joint strength have become a computational challenge with the finite element method. The present study presents a semi-analytical solution method that permits the determination of point-wise variations of displacement and stress components in singlelap bolted/bonded joints of composite laminates under in-plane as well as lateral loading. The derivation of governing equations of equilibrium of the joint is based on the principle of virtual work, where the displacement fields in the laminates are represented by local and global functions that are not required to satisfy the kinematic boundary conditions directly. The representations of the laminate and bolt displacements are based on the Mindlin plate theory and three-dimensional Timoshenko beam theory, respectively. For the adhesive, the displacement field is expressed in terms of those of laminates by using the shear-lag model to approximate both shearing and peeling deformations; hence, no assumed displacements are necessary for the adhesive. I. Introduction OLTED, bonded, and hybrid bolted/bonded joints are three-dimensional in nature. Although the finite element method (FEM) is capable of addressing such joint configurations, it requires considerable computer resources, especially in the presence of multiple bolts. The presence of unknown contact regions between the bolts and laminates and the small length scale of the adhesive thickness require a fine mesh to achieve a reliable prediction of the stress field. Therefore, identification of critical design parameters and optimization of the joint strength have become a computational challenge with the finite element method. In order to alleviate extensive computations in the case of a bolted or bonded joint analysis, semi-analytical methods exist to predict the stress field in both bolted and bonded lap joints. While the tools developed for the bolted joint analyses are limited to 2-D stress field in the laminates, the semi-analytical solution tools for bonded joint analysis include three-dimensional deformations but are limited to thin plate theory. Although there have been a substantial number of experimental, analytical, and numerical investigations on the stress analysis of bolted and bonded composite laminates, previous studies concerning the analysis of bolted/bonded lap joints in the open literature are limited to those by Hart-Smith,

Validated analysis method for bolted composite lap joints

This study presents a validated analysis method to determine the stress field and bolt load distribution in single- and double-lap joints. The joints are made of composite laminates and metals. The solution procedure accounts for the variation of stresses in the thickness direction by augmenting a two-dimensional analysis with a one-dimensional through-the- thickness analysis. The combined in-plane and through-the-thickness analysis produces the bolt/hole displacement in the thickness direction, as well as the stress state in each ply. The two-dimensional in-plane solution method based on the combined complex potential and variational formulation satisfies the equilibrium equations exactly, and satisfies the boundary conditions and constraints by minimizing the total potential. Under general loading conditions, this method is applied to various bolt configurations without requiring symmetry conditions while explicitly accounting for the contact phenomenon and the interaction among the bolts. It provides accurate contact stresses and contact regions, as well as the bolt load distribution, as part of the solution procedure. It is capable of accounting for finite laminate planform dimensions, laminate thickness and lay-up, interaction among bolts, bolt flexibility, bolt size, and bolt-hole clearance. The through-the-thickness analysis is based on the model of a beam on an elastic foundation. The bolt represented as a short beam rests on springs where the spring coefficients represent the resistance of the composite laminate to bolt deformation. Validation of the model is demonstrated by considering single- and double-lap joints of metal plates bolted to composite laminates.

Stress analysis of composite cylindrical shells with an elliptical cutout

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

Thermo-mechanical analysis of bonded cylindrically curved composite shell structures

§The present study describes a semi-analytical solution method for predicting the geometrically nonlinear response of a bonded cylindrically curved shell structure subjected to combined mechanical and thermal loading conditions. This approach yields the transverse shear and normal stresses in the adhesive, as well as the membrane stress resultants and bending moments in the adherends. The solution method utilizes the principle of virtual work in conjunction with nonlinear thin-shell theory to model the adherends and a cylindrical shear lag model to represent the kinematics of the thin adhesive layer between the adherends. The kinematic boundary conditions are imposed by employing the Lagrange multiplier method. This approach presents a rapid-solution alternative to the finite element method. The applicability of the present method is demonstrated by modeling a cylindrical component of a rigidizable/inflatable (RI) truss structure as a tubular bonded lap-joint subjected to uniaxial tension or torsion loading along with environmental temperature changes. The steep variation of both peeling and shearing stresses near the adhesive edges is successfully captured.

Effect of Core Termination Features on Failure Modes in Sandwich Panels by Using Peridynamic Theory

This study investigates the failure modes of termination region of sandwich panels. A submodeling approach utilizing finite element method for the global model and peridynamic theory for the submodel is used. Effects of termination region features are investigated.