Maximum‐Entropy‐Based Meshless Modeling of Surface‐Tension‐Driven Large Deformation

Soft material modeling is challenging due, among others, to the substantial structural changes these materials undergo. In this context, meshless methods offer a promising alternative to overcome the limitations of established mesh‐based approximations such as finite elements. However, they introduce new challenges. One of these is the incorporation of surface effects, such as cohesive surface behavior or deformation induced by surface tension, which are important in soft materials such as hydrogels and biological tissues but remain difficult to account for in meshfree settings. In this work, we present and benchmark an enhanced local maximum‐entropy (max‐ent) framework for surface modeling, thereby extending max‐ent to problems simultaneously involving surface tension and large deformation. We propose alternatives to identify boundary orientation in the presence of diffuse boundaries, consistently using 3D surface max‐ent interpolants, and to prevent cross‐coupling errors in irregular domains. We assess the performance of the framework by means of surface‐tension‐driven benchmarks involving strong volumetric contraction, near‐incompressibility, and complex geometries. The results show that the proposed framework yields accurate and robust predictions under severe structural changes, making it a promising tool for the modeling of polymers and soft biological systems in applications involving surface tension, membrane permeability, traction and pressure loading, and interfacial chemical interactions.