ASME 2018 International Mechanical Engineering Congress & Exposition (IMECE)
Prof. Ahmad R. Najafi will present at the ASME 2018 International Mechanical Engineering Congress & Exposition (IMECE), Pittsburgh, Pennsylvania, November 9-15, 2018.
Title:
Multi-scale Design of Periodic Nonlinear Materials Using a Gradient-Based Shape Optimization
Authors:
Ahmad Najafi and Masoud Safdari
Abstract:
There are ever-growing demands for creating high-performance materials that satisfy specific requirements. For instance, there is a critical need for designing novel lightweight structures and materials in the automobiles, aircraft, and spacecraft industries, which enhance vehicle energy efficiency while maintaining the structure crashworthiness. To fulfill these needs and requirements, a reverse engineering design problem should be solved. Here, the main challenge is how to tailor the material microstructure suited for a particular application. In this work, a shape optimization scheme is used to design the structure of periodic architected cellular materials to obtain targeted mechanical properties at the macroscale. This class of materials offers exceptional properties, including light-weight, high mechanical performance, and high-energy absorption. These properties are mainly the function of material geometry and by recent advances in manufacturing techniques and computational analysis, we can tune the material architecture for the desired material behavior. The current study presents a systematic way to design architected material in a multiscale framework by coupling shape optimization and computational homogenization. Following previous works by the author and his co-authors, the optimization employed in this study is a Eulerian-based shape optimization scheme that incorporates the NIGFEM. Similar to G/XFEM approaches, the NIGFEM is formulated on a fixed nonconforming mesh, thereby eliminating the mesh distortion problems associated with Lagrangian shape optimization schemes. In NIGFEM, NURBS are employed as enrichment functions in the IGFEM framework to model the response with nonconforming meshes. The method thus combines the advantages of the Eulerian shape optimization approaches with the accurate NURBS-based representation of the geometry. In this work, an analytic sensitivity is developed, which is simplified by the fact that only the enrichment control points on material interfaces move, appear or disappear during the shape optimization process. The sensitivity analysis is performed using the adjoint method. The proposed analytic sensitivity also avoids the technical difficulties encountered in the finite difference or semi-analytical schemes when the boundary intersects an element very close to a node in a non-conforming mesh. In these situations, the boundary may move to another element during the design perturbation step, resulting in changes of the mesh topology, making the differentiation of the stiffness matrix and load vector problematic. To demonstrate the performance and accuracy of the method, the NIGFEM shape optimization scheme is applied to several 2D structural problems. Using a multiscale approach, the optimized microstructure of a periodic architected material is obtained for several targeted mechanical properties.