A Unified Determinant-Preserving Formulation for Compressible/Incompressible Finite Viscoelasticity.

Area of Science:

• Computational Mechanics
• Materials Science
• Viscoelasticity

Background:

• Modeling the mechanical response of viscoelastic materials is complex, especially for soft organic materials with varying compressibility.
• Existing formulations may lack a unified approach for diverse material behaviors and numerical tractability.

Purpose of the Study:

• To develop a unified formulation and numerical algorithm for simulating quasistatic finite deformations in a broad class of viscoelastic materials.
• To ensure numerical tractability and stability for highly compressible to fully incompressible materials.

Main Methods:

• A Lagrangian two-potential mixed formulation is employed, treating deformation, pressure, and an internal state variable as independent fields.
• A finite-element (FE) discretization of space and finite-difference discretization of time are used.
• A novel time integration scheme is introduced to handle the non-convex constraint det(F_v) = 1 for the internal variable.

Main Results:

• The proposed formulation successfully models the mechanical response of various viscoelastic materials under large deformations.
• The numerical algorithm, incorporating a Variational Multiscale FE method, demonstrates stability and preserves the volume-preserving constraint for viscous deformation.
• Test cases confirm the formulation's capability in handling diverse material properties and deformation scenarios.

Conclusions:

• The developed unified formulation and numerical algorithm provide a robust and efficient tool for analyzing viscoelastic materials.
• The new time integration scheme effectively addresses the challenge of the non-convex constraint, enhancing simulation accuracy and stability.
• This work offers a significant advancement in the computational modeling of soft matter mechanics.