A three-dimensional element-free framework for coupled mechanical-diffusion induced nonlinear deformation of polymeric gels using the IMLS-Ritz method

A generalized decoupling numerical framework for polymeric gels and its element‐free implementation

“…Different conceptual frameworks were invoked to account two, three, or multiphases as well as physical fields in gels according to material specific . For a system of the gel with surrounding solutions, most of these studies focused their attention on gel region only excluding the surrounding solution for effective simplification . A few others covered both gel and solution to enhance authenticity .…”

“…A few others covered both gel and solution to enhance authenticity . Some studies concerned the transient swelling/deswelling process, and others conducted steady state analysis . The problem dimensions vary from one‐dimensional, two‐dimensional to three‐dimensional (3D) …”

“…Among these models, a monophase model developed by Hong et al for the coupled large deformation and diffusion of gel at equilibrium state gained a lot of attentions . In this model, mainly three kinds of triggers, that is, the external mechanical loads, the geometric constrains, and the diffusion of the solvents, are considered.…”

“…The issues of the complexly interacted multiphase (solid, solution, ion, and so on), the strongly coupled multifield (mechanical, diffusional, chemical, electrical, thermal, magnetical, and so on), the extreme large deformation (both large volumetric deformation and local instable large strain), the incompressibility of polymers and solution and the moving boundary, interface or sharp discontinuity (including gel‐solution interface, diffusional frontier in gel region, and cracks), are basic numerical challenges in gel modeling. Most researchers employed finite element codes (including XFEM and mixed FEM) or software (mainly ABAQUS and COMSOL) in numerical modelling of gels.…”

“…Most researchers employed finite element codes (including XFEM and mixed FEM) or software (mainly ABAQUS and COMSOL) in numerical modelling of gels. With regard to taking advantages of the meshless method when applied to these numerical challenges, especially for problems involving large deformation, moving boundary, interface and sharp discontinuity, however, only a limited amount of literatures can be identified …”