A review of peridynamic theory and nonlocal operators along with their computer implementations
Not Available
97 MATHEMATICS AND COMPUTING↗
Engineering topics
Madenci, Erdogan
Publications and source records attributed to Madenci, Erdogan.
Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations
Here, this study introduces a general approach for the imposition of local boundary conditions in non- ordinary state-based peridynamics (NOSB PD) to eliminate the displacement kinks near the boundary without a fictitious layer under quasi-static loading conditions. It identifies the underlying reason for the unphysical displacement kinks. Under an imposed linear displacement field, the NOSB PD equilibrium equation is not satisfied near the boundary due to the unsymmetric horizon of material points. However, the equilibrium equation derived by using the PD differential operator is satisfied at such material points. Therefore, the material body is divided into three regions to satisfy the equilibrium equations and to impose displacement and tractions boundary conditions. This approach does not deviate from the original NOSB PD; however, it provides a simple solution to eliminate the displacement kink near the boundary, which leads to unphysical stress concentrations. Its efficacy is demonstrated by considering elastic rectangular and square plates subjected to various types of boundary conditions leading to homogeneous as well as nonhomogeneous deformations. The creep response of a rectangular plate further proves the robustness of the present approach. Also, a quasi-static crack propagation from a pre-existing crack in a square plate under mode-I, mode-II and mixed-mode loading conditions demonstrates its capability for failure prediction based on the critical stretch criteria. Finally, its applicability for 3D analysis is demonstrated by considering a rectangular prism under applied stretch and normal stress.
42 ENGINEERING↗
Editorial: The World Is Nonlocal
Nonlocal modeling has come a long way. Researchers in the continuum mechanics and computational mechanics communities increasingly recognize that nonlocality is critical in realistic mathematical models of many aspects of the physical world. Physical interaction over a finite distance is fundamental at the atomic and nanoscale level, in which atoms and molecules interact through multibody potentials. Long-range forces partially determine the mechanics of surfaces and the behavior of dissolved molecules and suspended particles in a fluid. Nonlocality is therefore a vital feature of any continuum model that represents these physical systems at small length scales.
99 GENERAL AND MISCELLANEOUS↗
Thermomechanical peridynamic analysis with irregular non-uniform domain discretization [Thermomechanical peridynamic analysis with non-uniform domain discretization]
Non-uniform discretization of the solution domain in models based on peridynamic theory can improve computational efficiency by allowing for local refinement where needed for accuracy, and helps remove the effect of mesh bias in the simulations. However, the use of non-uniform discretization and a variable horizon requires consideration of possible unbalanced interactions between two material points, adjustment of peridynamic material parameters, and arbitrary shapes of interaction domains. This study presents a modification to the original peridynamic theory in which the strain energy associated with an interaction between two material points is split according to the volumetric ratio arising from the presence of non-uniform discretization and a variable horizon. It also removes the requirement for correction of peridynamic material parameters due to surface effects. Furthermore, the accuracy of this approach is verified against benchmark solutions, and its applicability to engineering problems is demonstrated by considering thermally induced cracking in a nuclear fuel pellet.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Prediction of Composite Laminate Strength Properties Using a Refined Zigzag Plate Element
This study presents an approach that uses the refined zigzag element, RZE(exp2,2) in conjunction with progressive failure criteria to predict the ultimate strength of composite laminates based on only ply-level strength properties. The methodology involves four major steps: (1) Determination of accurate stress and strain fields under complex loading conditions using RZE(exp2,2)-based finite element analysis, (2) Determination of failure locations and failure modes using the commonly accepted Hashin's failure criteria, (3) Recursive degradation of the material stiffness, and (4) Non-linear incremental finite element analysis to obtain stress redistribution until global failure. The validity of this approach is established by considering the published test data and predictions for (1) strength of laminates under various off-axis loading, (2) strength of laminates with a hole under compression, and (3) strength of laminates with a hole under tension.
Barut, Atila↗
Global-Local Finite Element Analysis of Bonded Single-Lap Joints
Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the finite element method is well suited to model the bonded lap joints, traditional finite elements are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a finite element technique utilizing a global (special) element coupled with traditional elements. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.
Kilic, Bahattin↗
Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element
This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.
Barut, A.↗
Global-Local Finite Element Analysis for Thermo-Mechanical Stresses in Bonded Joints
An analysis of adhesively bonded joints using conventional finite elements does not capture the singular behavior of the stress field in regions where two or three dissimilar materials form a junction with or without free edges. However, these regions are characteristic of the bonded joints and are prone to failure initiation. This study presents a method to capture the singular stress field arising from the geometric and material discontinuities in bonded composites. It is achieved by coupling the local (conventional) elements with global (special) elements whose interpolation functions are constructed from the asymptotic solution.
Shkarayev, S.↗
Residual strength of thin panels with cracks
The previous design philosophies involving safe life, fail-safe and damage tolerance concepts become inadequate for assuring the safety of aging aircraft structures. For example, the failure mechanism for the Aloha Airline accident involved the coalescence of undetected small cracks at the rivet holes causing a section of the fuselage to peel open during flight. Therefore, the fuselage structure should be designed to have sufficient residual strength under worst case crack configurations and in-flight load conditions. Residual strength is interpreted as the maximum load carrying capacity prior to unstable crack growth. Internal pressure and bending moment constitute the two major components of the external loads on the fuselage section during flight. Although the stiffeners in the form of stringers, frames and tear straps sustain part of the external loads, the significant portion of the load is taken up by the skin. In the presence of a large crack in the skin, the crack lips bulge out with considerable yielding; thus, the geometric and material nonlinearities must be included in the analysis for predicting residual strength. Also, these nonlinearities do not permit the decoupling of in-plane and out-of-plane bending deformations. The failure criterion combining the concepts of absorbed specific energy and strain energy density addresses the aforementioned concerns. The critical absorbed specific energy (local toughness) for the material is determined from the global specimen response and deformation geometry based on the uniaxial tensile test data and detailed finite element modeling of the specimen response. The use of the local toughness and stress-strain response at the continuum level eliminates the size effect. With this critical parameter and stress-strain response, the finite element analysis of the component by using STAGS along with the application of this failure criterion provides the stable crack growth calculations for residual strength predictions.
Madenci, Erdogan↗
Mechanically fastened composite laminates subjected to combined bearing-bypass and shear loading
Bolts and rivets provide a means of load transfer in the construction of aircraft. However, they give rise to stress concentrations and are often the source and location of static and fatigue failures. Furthermore, fastener holes are prone to cracks during take-off and landing. These cracks present the most common origin of structural failures in aircraft. Therefore, accurate determination of the contact stresses associated with such loaded holes in mechanically fastened joints is essential to reliable strength evaluation and failure prediction. As the laminate is subjected to loading, the contact region, whose extent is not known, develops between the fastener and the hole boundary through this contact region, which consists of slip and no-slip zones due to friction. The presence of the unknown contact stress distribution over the contact region between the pin and the composite laminate, material anisotropy, friction between the pin and the laminate, pin-hole clearance, combined bearing-bypass and shear loading, and finite geometry of the laminate result in a complex non-linear problem. In the case of bearing-bypass loading in compression, this non-linear problem is further complicated by the presence of dual contact regions. Previous research concerning the analysis of mechanical joints subjected to combined bearing-bypass and shear loading is non-existent. In the case of bearing-bypass loading only, except for the study conducted by Naik and Crews (1991), others employed the concept of superposition which is not valid for this non-linear problem. Naik and Crews applied a linear finite element analysis with conditions along the pin-hole contact region specified as displacement constraint equations. The major shortcoming of this method is that the variation of the contract region as a function of the applied load should be known a priori. Also, their analysis is limited to symmetric geometry and material systems, and frictionless boundary conditions. Since the contact stress distribution and the contact region are not known a priori, they did not directly impose the boundary conditions appropriate for modelling the contact and on-contact regions between the fastener and the hole. Furthermore, finite element analysis is not suitable for iterative design calculations for optimizing laminate construction in the presence of fasteners under complex loading conditions. In this study, the solution method developed by Madenci and Ileri (1992a,b) has been extended to determine the contact stresses in mechanical joints under combined bearing-bypass and shear loading, and bearing-bypass loading in compression resulting in dual contact regions.
Madenci, Erdogan↗