Peridynamics for bending of beams and plates with transverse shear deformation

Progressive failure analysis of structures is still a major challenge. There exist various predictive techniques to tackle this challenge by using both classical (local) and nonlocal theories. Peridynamic (PD) theory (nonlocal) is very suitable for this challenge, but computationally costly with respect to the finite element method. When analyzing complex structures, it is necessary to utilize structural idealizations to make the computations feasible. Therefore, this study presents the PD equations of motions for structural idealizations as beams and plates while accounting for transverse shear deformation. Also, their PD dispersion relations are presented and compared with those of classical theory

Peridynamic modeling of composite laminates under explosive loading

High velocity impact and shock or blast responses are a critical design characteristic determining sizing of composite parts and, ultimately, weight savings. This study demonstrates the applicability of peridynamics to accurately predict nonlinear transient deformation and damage behavior of composites under shock or blast type s of loadings due to explosions. The peridynamic predictions correlate well with the experimental results available in the literature. Therefore, peridynamics provides the ability to predict residual strength and durability for improving structural designs of composites under such loading conditions

A novel finite element technique for moisture diffusion modeling using ANSYS

This study presents a novel modeling approach for wetness and moisture concentration in the presence of time dependent saturated moisture concentration by employing the traditional ANSYS thermal and surface effect elements. The accuracy of the present approach is established by comparison with those of the existing ANSYS "diffusion" and "coupled field" elements as well as peridynamic theory. The comparison concerns the desorption process in a fully saturated bar made of two different materials with equal and unequal values of solubility activation energy in the presence of time dependent saturated moisture concentration under uniform and nonuniform temperature conditions. The results from the present approach agree well with those of peridynamics and ANSYS "coupled field" elements if the diffusivity is specified as time dependent. Significant deviation occurs if the diffusivity is specified as temperature dependent. The ANSYS "diffusion" element is applicable only for uniform temperature, and deviation becomes significant especially for unequal values of solubility activation energy

Determination of horizon size in state-based peridynamics

Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems

Peridynamic wetness approach for moisture concentration analysis in electronic packages

Within the finite element framework, a commonly accepted indirect approach employs the concept of normalized concentration to compute moisture concentration. It is referred to as “wetness” approach. If the saturated concentration value is not dependent on temperature or time, the wetness equation is analogous to the standard diffusion equation whose solution can be constructed by using any commercial finite element analysis software such as ANSYS. However, the time dependency of saturated concentration requires special treatment under temperature dependent environmental conditions such as reflow process. As a result, the wetness equation is not directly analogous to the standard diffusion equation. This study presents the peridynamic wetness modeling for time dependent saturated concentration for computation of moisture concentration in electronic packages. It is computationally efficient as well as easy to implement without any iterations in each time step. Numerical results concerning the one-dimensional analysis illustrate the accuracy of this approach. Moisture concentration calculation in a three-dimensional electronic package configuration with many different material layers demonstrates its robustness

Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate

A peridynamic based machine learning model for one-dimensional and two-dimensional structures

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics based machine learning model for one and two-dimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a pre-existing crack, a two-dimensional representation of a three-point bending test, and a plate subjected to dynamic load are simulated

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model

A computational framework for underwater shock response of marine structures

Composite structures have extensive area of practice in engineering disciplines. One of the application areas is to use them under extreme loading conditions. However, our understanding of their behaviour under shock loading is rather limited. As a result of this, current designs of composite structures are very conservative which significantly reduce the weight saving advantage. In order to improve our understanding, experimental studies are essential but they can be prohibitively costly. On the other hand, computer simulations can be a good alternative. Hence, the main objective of this study is to investigate underwater shock response of marine composite structures by using a new theory called peridynamics. Numerical approach based on peridynamics is used to predict the failure modes in marine composite structures. The evaluated results are validated by comparing against the available data in literature which demonstrates the capability of peridynamics for such complex problems

Fracture modes, damage tolerance and failure mitigation in marine composites

The fracture behaviour of composite materials and structures is quite complex with respect to metals and it is difficult to predict fracture modes intuitively. In addition to the failure modes which are commonly observed in composite structures, the marine environment can introduce new failure mechanisms such as blistering. During the design process of composite structures, it is important to determine the load-carrying capability of a structure once it has been damaged by service loads; this is known as damage tolerance. The repair process can be done based on the severity of the damage. For major damage, the bonded patch repair technique can be an effective technique for composites