Q3T Prisms: A Linear-Quadratic Solid Shell Element for Elastoplastic Surfaces

Abstract

We introduce an approach for simulating elastoplastic surfaces using quadratic through-the-thickness (Q3T) solid shell elements. Modeling the mechanics of deformable surfaces has been a cornerstone of graphics research for decades. Although thin shell models are suitable for many materials and applications, simulation-based planning of plastic forming processes requires attention to deformation in the thickness direction. Building on recent advances in the graphics community, we explore solid shell elements for modeling elastoplastic surfaces. Linear prism elements perform well for compressible materials such as thick cloth and foam mats. However, due to their inability to capture non-constant strain in the thickness direction, they suffer from severe locking artifacts when applied to incompressible and plastic materials. Q3T elements address this limitation with a minimal yet effective modification to linear prisms, resulting in significantly improved performance with only a moderate increase in computational cost. Through various examples, we demonstrate that Q3T elements closely match the qualitative behavior of reference simulations and provide accurate quantitative results compared to real-world deep drawing experiments.