ABAQUS Plugin Tool for Periodic RVE Homogenisation (EasyPBC)

The use of the representative volume element (RVE) homogenisation method to estimate the stiffness properties of composite and hybrid materials is widely used. Theoretical methods can be used for homogenisation, but they are based on several assumptions that may not represent the material accurately. Given the nature of the assumptions associated with the development of these analytical methods, an average of 15% difference has been observed between the properties estimated using numerical and analytical methods for a typical composite RVE. Therefore, the literature acknowledges that numerical homogenisation methods are more accurate and are becoming the standard approach for composite materials. However, the implementation of this approach in Finite Element Analysis (FEA) software is complex and time-consuming, because they do not have an automated process for finding and generating the required boundary nodal sets (which are over 30 sets for a typical 3D RVE), creating the constraint equations, applying the displacement boundary conditions, or post-processing calculations. Additionally, there are no clear instructions or open-source tools to implement it efficiently. Thus, there was a need to develop a tool that can represent RVEs with various geometrical configurations. Therefore, the authors developed EasyPBC[1], an ABAQUS CAE[2] plugin to estimate the homogenised effective elastic properties of a user-created periodic RVE, all within ABAQUS, without the need to use third-party software. The plugin automatically applies the concepts of the periodic RVE homogenisation method in the software’s user interface by categorising, creating, and linking the sets necessary for achieving deformable periodic boundary surfaces, which can distort and are not fixed to remain plane. Additionally, it allows the user to benefit from finite element analysis data within the ABAQUS CAE interface after calculating homogenised properties. EasyPBC is in high demand for applications of various backgrounds requiring periodic RVE homogenisation, as it meets the needs of a wide range of users. In addition, EasyPBC can accept unlimited configurations of composite and hybrid materials. Currently, there is no other such tool that provides the user with complete control over the process of generating their model, selecting their pre-processing preferences, and accessing the post-processing data to serve specific research topics. As a result, the tool is being used by a large number of students, researchers, and industrial professionals. As it stands, EasyPBC allows the following: • Calculate the effective elastic properties of hybrid and composite materials for 2D and 3D RVEs. • Apply Periodic Boundary Conditions (PBC) for the user without calculating the effective elastic properties. • Calculate the coefficient of thermal expansion (CTE) of hybrid and composite materials for 2D and 3D RVEs. In this study the background theory and implementation of EasyPBC is presented, while highlighting the limitations and future plans for development.

This paper explores the use of optimization to design multifunctional metamaterials, and proposes a methodology for constructing a design envelope of potential properties. A thermal-mechanical metamaterial, proposed by Ai and Gao (2017), is used as the subject of the study. The properties of the metamaterial are computed using finite element-based periodic homogenization, which is implemented in Abaqus utilizing an open-source plugin (EasyPBC). Several optimization problems are solved using a particle swarm-based optimization method from the pyOpt package. A series of constrained optimization problems are used to construct a design envelop of potential properties. The design envelope more fully captures the potential of the metamaterial, compared with the current practice of using parametric studies. This is because the optimizer can change all parameters simultaneously to find the optimal design. This demonstrates the potential of using an optimization-based approach for designing and exploring multifunctional metamaterial properties. This proposed approach is general and can be applied to any metamaterial design, assuming an accurate numerical model exists to evaluate its properties.

This study investigates the effect of micro-scale geometric and material property uncertainties on the elastic properties and reliability of fibre reinforced composite materials. Composite materials are often designed using conservative design factors to account for a limited understanding of how multi-scale uncertainties effect reliability. Structural reliability analysis can produce more efficient designs, but requires an understanding of how all sources uncertainty effect probability of failure. Previous studies have not considered micro-scale geometrical uncertainties and their combinations in a multi-scale probabilistic-based reliability framework. Thus, this study will investigate the effect of numerous combinations of micro-scale material property and geometric uncertainties on the homogenised elastic properties. Furthermore, to account for the effect in a reliability-based framework, a novel surrogate modelling technique is developed to represent the uncertainties efficiently. The study concluded that the geometrical fibre stacking uncertainty is as influential as the widely investigated constituent material stiffness uncertainties. Consequently, representing the micro-scale geometric uncertainties within the developed multi-scale probabilistic-based framework improves the estimated stiffness. Thus probability of failure is reduced, compared with considering material property uncertainties only. Moreover, the framework clarified and highlighted the importance of representing fibre geometrical stacking uncertainty for a deeper understanding of their effect on composite stiffness properties.

This study evaluates the effect and sensitivity of micro-scale geometric and material property uncertainties on the numerically determined effective elastic properties of unidirectional fibre reinforced matrix composite materials. Due to the multi-scale build-up nature of composites many uncertainties occur, mainly material properties and geometric uncertainties. These uncertainties present a challenge in estimating composite material properties. Research has been conducted to understand their effect. However, there are limited studies investigating the effect of geometric random fibre stacking uncertainty. Hence, this study examines the effect of geometric along with seven material property uncertainties on a composite’s effective elastic properties using a developed periodic RVE homogenisation tool. A factorial design method is used to investigate the sensitivity of all possible uncertainty combinations. It is concluded that fibre stacking uncertainty is an influential uncertainty that needs to be represented along with constituent material properties uncertainties in a multi-scale analysis approach. Additionally, concept of a polynomial-based surrogate model is developed to approximate homogenised effective elastic properties under the effect of uncertainties without the need to run numerical homogenisation.

EasyPBC is an ABAQUS CAE plugin developed to estimate the homogenised effective elastic properties of user created periodic representative volume element (RVE), all within ABAQUS without the need to use third-party software. The plugin automatically applies the concepts of the periodic RVE homogenisation method in the software’s user interface by categorising, creating, and linking sets necessary for achieving deformable periodic boundary surfaces, which can distort and no longer remain plane. Additionally, it allows the user to benefit from finite element analysis data within ABAQUS CAE interface after calculating homogenised properties. In this article, the algorithm of the plugin based on periodic RVE homogenisation method is explained, which could be developed for other commercial FE software packages. Furthermore, examples of its implementation and verification are illustrated.