A mathematical model for fitting and predicting relaxation modulus and simulating viscoelastic responses

Area of Science:

• Materials Science
• Continuum Mechanics
• Computational Mechanics

Background:

• Existing polymer models often rely on complex molecular-chain structures, requiring numerous parameters.
• Accurate modeling of material relaxation modulus is crucial for predicting behavior under various loading conditions.
• There is a need for simpler, yet accurate, models for general solid materials.

Purpose of the Study:

• To propose a novel mathematical model for relaxation modulus with a simplified parameter set.
• To develop a robust finite-element (FE) framework for numerical implementation.
• To validate the model's accuracy and stability against experimental data and existing methods.

Main Methods:

• Extended a sigmoidal function to incorporate nonlinear strain hardening for the relaxation modulus model.
• Developed a finite-element (FE) framework with a robust numerical algorithm for static and dynamic simulations.
• Validated the model using experimental data from asphalt concrete, polymers, spider silk, hydrogels, agar, and bone.

Main Results:

• The proposed five-parameter model accurately fits experimental data for diverse materials.
• The model demonstrates improved prediction stability outside the experimental range compared to Prony series.
• Satisfies the second law of thermodynamics, enabling simulation of creep, sinusoidal deformation, and energy dissipation.

Conclusions:

• The novel mathematical model offers a simplified and accurate approach to representing relaxation modulus in general solid materials.
• The developed FE framework provides a stable and efficient tool for simulating material responses.
• This model presents a competitive alternative to traditional methods like the Prony series, with enhanced accuracy and predictive capabilities.