The development and validation of a numerical integration method for non-linear viscoelastic modeling.

Area of Science:

• Biomechanics
• Computational modeling
• Materials science

Background:

• Biological soft tissues exhibit complex strain- and time-dependent mechanical behaviors.
• Accurate modeling of non-linear viscoelasticity is crucial for understanding tissue mechanics under dynamic conditions.
• Existing finite element models face computational challenges due to the history-dependent nature of viscoelastic stress states.

Purpose of the Study:

• To develop a computationally efficient numerical integration approach for capturing non-linear viscoelasticity in biological soft tissues.
• To improve the fitting efficiency and computational tractability of viscoelastic models.
• To validate a new methodology for deriving viscoelastic properties from experimental data.

Main Methods:

• Developed a strain-dependent numerical integration approach.
• Stored only a strain-dependent history state variable from the preceding time step.
• Validated the methodology using simulated stress-relaxation and dynamic cyclic experimental data.

Main Results:

• The new method successfully recovered non-linear viscoelastic coefficients from simulated data.
• Average errors in recovered coefficients were 0.3% for stress-relaxation and 0.1% for cyclic data.
• Demonstrated improved fitting efficiency and computational tractability compared to traditional methods.

Conclusions:

• The presented strain-dependent numerical integration approach effectively captures non-linear viscoelasticity.
• This methodology provides a viable tool for developing viscoelastic models from experimental data of biological soft tissues.
• Supports the creation of linear or non-linear viscoelastic models for diverse tissue types.