OpenSG: An Open-Source Multiscale Constitutive Modeling Code for Composite Structures and Materials

Abstract

Mechanics of Structure Genome (MSG) represents a revolutionary approach to multiscale modeling drastically different from the conventional bottom-up multiscale modeling approaches. The principle of minimum information loss (PMIL) is used to avoid a priori assumptions in kinematics and kinetics. MSG confines all approximations to the constitutive modeling for all types of structures including 3D solids, 2D plates/shells, and 1D beams, directly linking the structural properties with microstructural details. MSG allows one to choose the starting scale and ending scale and capture details as needed and affordable without invalid scale separation and assumptions within scales. MSG has been proven to be much faster than the popular alternative, RVE analysis. MSG was implemented in a commercial code called Swift- Comp as a general-purpose constitutive modeling software that can be used by itself for virtual testing of structures and materials or as a plugin for conventional FEA packages. However, to assemble all the talents the world has to offer to realize the ICME vision, we are motivated to develop an open-source implementation of MSG so that others can easily leverage the efficient MSG theory to develop other multiscale models. In this paper, we will show how we implement MSG using FEniCS, an opensource, general-purpose FEA package. FEniCS is a popular open-source computing platform for solving partial differential equations (PDEs). FEniCS enables users to quickly translate scientific models into efficient finite element codes. Formulating the MSG theory using a variational statement suitable for FEniCS along with proper constraints, we developed OpenSG, an open-source implementation of MSG, using FEniCS. OpenSG will be used to perform homogenization and dehomogenization for heterogeneous solids, plates/shells, and beams. Applications of OpenSG to composites, 3D printed materials, metamaterials, biomaterials, and auxetic materials will be demonstrated. The performance in terms of accuracy and efficiency of OpenSG will be compared to SwiftComp. After extensive verification and validation, OpenSG will be made available globally through github.