Tuning mechanical behaviors of highly entangled hydrogels with the random distribution of mobile entanglements

Abstract

Highly entangled hydrogels exhibit excellent mechanical properties, including high toughness, high stretchability, and low hysteresis. By considering the evolution of randomly distributed entanglements within the polymer network upon mechanical stretches, we develop a constitutive theory to describe the large stretch behaviors of these hydrogels. In the theory, we utilize a representative volume element (RVE) in the shape of a cube, within which there exists an averaged chain segment along each edge and a mobile entanglement at each corner. By employing an explicit method, we decouple the elasticity of the hydrogels from the sliding motion of their entanglements, and derive the stress-stretch relations for these hydrogels. The present theoretical analysis is in agreement with experiment, and highlights the significant influence of the entanglement distribution within the hydrogels on their elasticity. We also implement the present developed constitutive theory into a commercial finite element software, and the subsequent simulations demonstrate that the exact distribution of entanglements strongly affects the mechanical behaviors of the structures of these hydrogels. Overall, the present theory provides valuable insights into the deformation mechanism of highly entangled hydrogels, and can aid in the design of these hydrogels with enhanced performance.