Virtual element topology optimization with tension compression asymmetrical material constitutive

Structural topology optimization finds extensive application in engineering domains, including aerospace, automotive, and civil engineering, facilitating the development of lightweight, high-performance structures characterized by complex, often organically inspiredgeometries. By integrating finite element analysis with advanced optimization techniques, topology optimization enhances design efficiency, minimizes material usage, and supports the advancement of innovative engineering solutions. In the present work, topology optimization is further developed through the incorporation of computational geometry and material science, offering a robust methodology for designing high-performance, lightweight structures applicable to fields ranging from civil engineering to additive manufacturing. A novel formulation for topology optimization is introduced through the integration of the Virtual Element Method (VEM) with constitutive models for granular materials, aiming to address complex challenges in structural design. The proposed framework capitalizes on the flexibility of VEM in managing arbitrary polygonal meshes, allowing for accurate representation of intricate geometries and material interfaces typical of granular systems. By incorporating a granular material constitutive model that accounts for particle interactions and frictional behavior, the approach effectively captures microscale mechanics that influence macroscale structural performance. The optimization process adopts a density-based approach, in which the virtual element framework discretizes the design domain, while a granular constitutive model characterizes the material behavior within each element. Sensitivity analysis is conducted to direct the iterative redistribution of material, with structural compliance adopted as the objective function. The robustness of the proposed approach is demonstrated through standard topology optimization benchmark problems and further validated via numerical case studies derived from these benchmarks. The topologies generated through this method verify that the proposed mathematical formulation and its related solution algorithm are valid and effective.