A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

Abstract

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

Integration efficiency for model reduction in micro-mechanical analyses

“…Due to the nonlinear character of the internal force, the integral in equation (13) can not be precomputed. This procedure remains computationally expensive since the material model needs to be resolved on each integration point to compute the integral of the internal force.…”

“…More recently, computational homogenization has been used in various fields to analyze the material behavior, such as acoustics [10], composites [11] among many other fields. A detailed overview of the advances in computational homogenization is presented by Geers et al [12] and Matouš et al [13].…”

A framework for implementation of RVE‐based multiscale models in computational homogenization using isogeometric analysis

“…Moreover, the emergence of new material classes such as architectured materials() and metamaterials,() which derive their outstanding capabilities not from the intrinsic properties of their components (which are comparatively inferior) but from complex and highly heterogeneous hierarchical topologies that can span a multitude of length scales, means that ever more advanced simulation tools are needed. These tools should capture the intricate geometrical details and nonlinear physical phenomena present at microscales so as to quantify how material properties emerge from the complex interplay between constituent phases and topological arrangement …”

An algorithmically consistent macroscopic tangent operator for FFT‐based computational homogenization

“…As a result of the strongly increasing computational power, associated numerical schemes become more and more viable even for highly complex and large structures. In general, we may distinguish computational methods based on finite differences (FD), finite elements (FE), fast Fourier transforms (FFT), and many more; see, for example, the recent review by Matouš et al…”