Multiscale analysis of solids with a spaces of functions blending method

Resumo

Many engineering problems deal with localized effects in a larger domain, such as cracked solids,
localized plastic strains and discontinuities like holes or stiffeners. The proper analysis of such problems require
techniques that allow to accurately represent the mechanical fields of the problem at different scales. In this study, a
space of functions blending technique is applied for two-dimensional solids, under a position-based finite element
formulation for large displacements dynamic and static problems. The multiscale analysis consists of overlapping
a local finite element discretization, able to capture the localized effects, to an isogeometric global discretization.
In a region of the local discretization, close to its outer boundaries (blending zone), the fem and isogeometric
spaces of shape functions are weighted by functions specially designed to avoid a linear combination and added
generating the blended space of functions. With this approach, no additional degrees of freedom are introduced to
enforce continuity between models. Numerical examples are simulated, considering plane strain and plane stress,
with results compared to the literature in order to verify the proposed method and assess its accuracy and efficiency.