Meshfree Models Research Articles

Review on modeling techniques for powder bed fusion processes based on physical principles

Powder bed fusion is one of the most common types of additive manufacturing processes using granular materials. In this field, improvements in the processing of materials and process repeatability with desired part quality are needed to allow the implementation of powder bed fusion process at full scale across various industrial sectors. The microstructure and the thermo-mechanical properties of the components vary according to the process parameters adopted in the manufacturing process. Physically accurate modeling of the powder bed fusion process can play a vital role in the qualification of components and materials and also can help in predicting the experimental observations. This paper aims to provide a comprehensive review on the state of the art referred to numerical simulation of powder bed fusion, by covering both mesh based approaches such as finite element modeling, finite volume modeling and mesh free methods such as the discrete element modeling, the lattice Boltzmann method, the optimal transportation method and the smoothed particle hydrodynamics approach. Combined approaches of different methods are discussed as well. A case study comparing two different types of models for a similar type of problem has been provided. Moreover, means of experimental techniques used to validate the numerical models are briefly discussed. • Review on various types of mesh based and mesh free models used in powder bed fusion process of additive manufacturing. • Advantages, disadvantages and uses of various models to study different phenomena are discussed. • A comparative case study of mesh based and mesh-free models is provided. • The influence of various process parameters on the mechanical characteristics of the specimen is given.

Angular particle impact on ductile materials using the Lagrangian gradient smoothing method

The impacts of single angular particles on ductile materials can result in large deformations and material chip separation, which cannot be effectively simulated using conventional mesh-based numerical methods. In this study, a novel particle-based mesh-free method called the Lagrangian gradient smoothing method (L-GSM) is first applied to simulate the dynamic process of single diamond-shaped particles impact on metallic surfaces. Based on the theory of L-GSM, a numerical model is established by incorporating the Johnson–Cook plasticity and failure models. Oxygen-free high-conductivity (OFHC) copper which is represented by a series of discrete particles, is selected as the material of the target block. Simulation results show that the L-GSM model can reproduce the typical erosion mechanisms such as cutting, micro-machining and ploughing. The large deformation of plastic craters and material removal are successfully simulated without using any additional techniques to handle the distorted domain. In addition, the computational accuracy and efficiency of the L-GSM are discussed by comparison with different mesh-free models. This study provides an effective numerical model with better accuracy and efficiency, helping to reveal the fundamental erosion mechanisms resulting from the impacts of angular particles.

FEA-AI and AI-AI: Two-Way Deepnets for Real-Time Computations for Both Forward and Inverse Mechanics Problems

Recent breakthroughs in deep-learning algorithms enable dreams of artificial intelligence (AI) getting close to reality. AI-based technologies are now being developed rapidly, including service and industrial robots, autonomous and self-driving vehicles. This work proposes Two-Way Deepnets (TW-Deepnets) trained using the physics-law-based models such as finite element method (FEM), smoothed FEM (S-FEM), and meshfree models, for real-time computations of both forward and inverse mechanics problems of materials and structures. First, unique features of physics-law-based models and data-based models are analyzed in theory. The training characteristics of deepnets for forward problems governed by physics-laws are then investigated, when an FEM (or S-FEM) model is used as the trainer. The training convergence rates of such an FEM-AI model are examined in relation to the property of the system matrix of the FEM model for deepnets. Next, a study on the training characteristics of deepnets for inverse problems, when the forward FEM-trained AI Deepnets are used as the trainer to train an AI model for inverse analyses. Next, a discussion is conducted on the roles of regularization techniques to overcome the ill-posedness of inverse problems in deepnet structures for noisy data. Finally, TW-Deepnets (FEM-AI and AI-AI models) are presented for real-time analyses of both forward and inverse problems of materials and structures with high-dimensional parameter space. The major finding of this study is as follows: (1) The understandings on the fundamental features of both data-based and physics-based methods is critical for creations of novel game-changing computational methods, which take advantages of both types of methods; (2) The good property of the system matrix of FEM allows effective training of FEM-AI deepnets for forward mechanics problems; (3) Our new technique to training inverse deepnets using FEM-AI deepnets as a surrogate model offers an innovative means, to effectively train deepnets for solving inverse mechanics problems; (4) The TW-Deepnets is capable of performing real-time analysis of both forward and inverse problems of materials and structures with high-dimensional parameter spaces; (5) Such TW-Deepnets can be easily utilized by the mass: a transformative new concept of AI-enabling democratization of complicated computational technology in modeling and simulation.

Evaluation of effective elastic properties of 3D printable interpenetrating phase composites using the meshfree radial point interpolation method

ABSTRACTInterpenetrating phase composites (IPCs) have recently been fabricated using three-dimensional (3D) printing methods. In a two-phase IPC, the two phases are topologically interconnected and mutually reinforced in the three dimensions. As a result, such IPCs exhibit higher stiffness, strength, and toughness than particle- or fiber-reinforced composites. In the current study, three unit cell models for the IPCs with the simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC) microstructures are developed using the meshfree radial point interpolation method. Radial basis functions with polynomial reproduction are applied to construct shape functions, and the Galerkin method is employed to formulate discretized equations. These unit cell-based meshfree models are used to evaluate effective elastic properties of 3D printable IPCs. The simulation results are compared with those based on the finite element (FE) method and various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. It is found that all of the simulation results for the effective Young's modulus and shear modulus fall between the Voigt–Reuss upper and lower bounds for each IPC considered, with the FE models predicting higher values than the meshfree models. In addition, it is seen that the SC microstructure leads to higher effective Young's modulus than the BCC and FCC microstructures. Furthermore, the numerical results reveal that the IPCs with the SC, BCC, and FCC microstructures can be approximated as isotropic materials (with the Zener anisotropic ratio varying between 0.9 and 1.0), with the BCC IPC being the most isotropic one, and the SC IPC being the least isotropic one among the three types of IPCs.

Soil Models and Vehicle System Dynamics

The mechanical behavior of soils may be approximated using different models that depend on particular soil characteristics and simplifying assumptions. For this reason, researchers have proposed and expounded upon a large number of constitutive models and approaches that describe various aspects of soil behavior. However, there are few material models capable of predicting the behavior of soils for engineering applications and are at the same time appropriate for implementation into finite element (FE) and multibody system (MBS) algorithms. This paper presents a survey of some of the commonly used continuum-based soil models. The aim is to provide a summary of continuum-based soil models and examine their suitability for integration with the large-displacement FE absolute nodal coordinate formulation (ANCF) and MBS algorithms. Special emphasis is placed on the formulation of soils used in conjunction with vehicle dynamics models. The implementation of these soil models in MBS algorithms used in the analysis of complex vehicle systems is also discussed. Because semiempirical terramechanics soil models are currently the most widely used to study vehicle/soil interaction, a review of classical terramechanics models is presented in order to be able to explain the modes of displacements that are not captured by these simpler models. Other methods such as the particle-based and mesh-free models are also briefly reviewed. A Cam–Clay soil model is used in this paper to explain how such continuum-mechanics based soil models can be implemented in FE/MBS algorithms.

Algorithms for interpolation and localization in irregular 2D meshes

In numerical simulations of power systems; discrete models and mesh-free models are very often used simultaneously, for example, in particle-in-cell (PIC) codes. The aim of this paper is to introduce new techniques for interpolation as well as for localization in irregular fourpoint meshes. These algorithms extend the existing, methods for regular grids to grids consisting of non-equidistant convex four-point meshes. They were developed in order to obtain short CPU times and possible vectorization.