Efficient multiscale modeling of heterogeneous materials using deep neural networks

Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element RVE . The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model

An introduction to computational micromechanics

In this, its second corrected printing, Zohdi and Wriggers' illuminating text presents a comprehensive introduction to the subject. The authors include in their scope basic homogenization theory, microstructural optimization and multifield analysis of heterogeneous materials. This volume is ideal for researchers and engineers, and can be used in a first-year course for graduate students with an interest in the computational micromechanical analysis of new materials

A finite element primer for beginners: the basics

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for t

Electromagnetic Properties of Multiphase Dielectrics: A Primer on Modeling, Theory and Computation

Recently, several applications, primarily driven by microtechnology, have emerged where the use of materials with  tailored  electromagnetic  (dielectric) properties are necessary for a successful  overall design.  The ``tailored'' aggregate properties are achieved by combining an easily moldable  base matrix with particles  having dielectric properties that are chosen to deliver (desired) effective properties. In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response,  which can be important to determine possible failures in ``hot spots.'' This necessitates   a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well.   A central  objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers: (1) The foundations of  Maxwell's equations, (2) Basic homogenization theory, (3) Coupled systems (electromagnetic, thermal, mechanical and chemical), (4) Numerical methods and (5) An introduction to select biological problems. The text can be viewed as a research monograph  suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials

Dynamics of Charged Particulate Systems: Modeling, Theory and Computation

The objective of this monograph is to provide a concise introduction to the dynamics of systems comprised of charged small-scale particles. Flowing, small-scale, particles ("particulates'') are ubiquitous in industrial processes and in the natural sciences. Applications include electrostatic copiers, inkjet printers, powder coating machines, etc., and a variety of manufacturing processes. Due to their small-scale size, external electromagnetic fields can be utilized to manipulate and control charged particulates in industrial processes in order to achieve results that are not possible by purely mechanical means alone. A unique feature of small-scale particulate flows is that they exhibit a strong sensitivity to interparticle near-field forces, leading to nonstandard particulate dynamics, agglomeration and cluster formation, which can strongly affect manufactured product quality. This monograph also provides an introduction to the mathematically-related topic of the dynamics of swarms of interacting objects, which has gained the attention of a number of scientific communities. In summary, the following topics are discussed in detail: (1) Dynamics of an individual charged particle,  (2) Dynamics of rigid clusters of charged particles, (3) Dynamics of flowing charged particles, (4) Dynamics of charged particle impact with electrified surfaces and (5) An introduction to the mechanistic modeling of swarms. The text can be viewed as a research monograph suitable for use in an upper division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials

Application of the Particle Finite Element Method in Machining Simulation Discussion of the Alpha-Shape Method in the Context of Strength of Materials

In particle finite element simulations, a continuous body is represented by a set of particles that carry all physical information of the body, such as the deformation. In order to form this body, the boundary of the particle set needs to be determined. This is accomplished by the α-shape method, where the crucial parameter α controls the level of detail of the detected shape. However, in solid mechanics, it can be observed that α has an influence on the structural integrity as well. In this paper, we study a single boundary segment of a body during a deformation and it is shown that α can be interpreted as the maximum stretch of this segment. On the continuum level, a relation between α and the eigenvalues of the right Cauchy–Green tensor is presented