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Equilibrium 3d software4/29/2023 ![]() Thus, the crack propagation of the material can be naturally simulated and the damage rate of the material from the cracks can be obtained simultaneously. If the distance between two particles exceeds the extreme distance, then a crack is generated between them and their interaction force would be interrupted. In this study, the interaction force is expressed by a function, and different functions are established to describe the mechanical properties of elastic and plastic materials. This interaction force appears as a repulsion when two particles are relatively near each other and as attraction when the distance between two particles is far. The concept of “element” is used in this method to record the relative position relationship between particles and their surrounding particles. This method begins by discretizing the problem domain as a set of particles, which interact solely with their surrounding particles through an interaction force. The present study proposes an approach for modeling structural responses to external loads, especially for simulating the crack growth phenomenon in brittle materials. These methods have improved the solution for the problem. Consequently, interpolation meshless methods, such as nature element method (NEM), point interpolation method (PIM), radial PIM (RPIM), and nature neighbor RPIM, have been developed. Although these meshless methods have been widely used, they have difficulty in imposing essential and natural boundary conditions. Approximation meshless methods were proposed first, including smooth particle hydrodynamics (SPH), diffuse element method (DEM), and element-free Galerkin method (EFG). Meshless methods that commonly use the weak form of Galerkin can be classified as approximation meshless methods and interpolation meshless methods. This feature makes the meshless method suitable for modeling fracture propagation. In contrast to the “element” concept of the FEM, nodal connectivity in meshless methods is enforced with the “influence-domain” concept. Meshless methods discretize the problem domain only with a set of unstructured points or nodes without using a predefined element mesh. Thus, several meshless methods have been developed. However, these FEM versions are mesh-based approximation methods and have certain inherent limitations. To improve the FEM in terms of fracture simulation, extended finite element method (XFEM), fractal finite element method, node-based smoothed extended finite element method (NS-XFEM), and edge-based smoothed finite element method (ESFEM) were proposed. However, FEM requires several remeshing processes of the finite element model to represent arbitrary and complex crack paths, which is slightly difficult moreover, automatic remeshing can result in highly distorted elements, which worsens the performance of the FEM. The finite element method (FEM) is a well-known numerical analysis method that has been extensively used in predicting crack paths. Thus, crack propagation simulation is of great significance, and several methods have been applied to address this problem. IntroductionĬrack propagation is one of the most common phenomena in structures, and this remarkable feature is consistently associated with the damage or destruction of structures. A calculation program is developed based on the proposed method’s theory and is applied to three numerical examples with reliable calculation results. The calculated structure attains its final state to the external load when all the particles reach the equilibrium condition of force. The function of interaction force describes the mechanical response of elastic and plastic materials. Once the distance between two particles exceeds the extreme distance, a permanent crack will emerge between them. PEM is based on the idealization of the problem domain as an assemblage of distinct particles, which release interaction forces to their surrounding particles. This study presents the particle equilibrium method (PEM) to achieve this goal. Crack propagation simulation is constantly of great significance.
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