A GENERAL RETURN-MAPPING FRAMEWORK FOR FRACTIONAL VISCO-ELASTO-PLASTICITY.

Area of Science:

• Computational mechanics
• Fractional calculus
• Viscoelasticity and plasticity

Background:

• Modeling complex material behaviors like viscoelasticity and plasticity is crucial in engineering.
• Fractional calculus offers a powerful tool for describing materials with memory and power-law characteristics.
• Existing models often face limitations in computational efficiency and flexibility.

Purpose of the Study:

• To develop a novel fractional return-mapping framework for power-law visco-elasto-plasticity.
• To integrate fractional viscoelastic models (Kelvin-Voigt, Maxwell, etc.) with fractional viscoplasticity.
• To enhance computational tractability and flexibility for complex material modeling.

Main Methods:

• Utilized canonical combinations of Scott-Blair elements for fractional viscoelasticity.
• Incorporated a fractional quasi-linear Fung model for nonlinearity.
• Developed a general, fully or semi-implicit return-mapping procedure.
• Conducted numerical experiments with analytical and reference solutions.

Main Results:

• The discrete stress projection and plastic slip exhibit a unified form across models.
• The framework demonstrates at least first-order accuracy for general loading.
• Achieved a 50% reduction in CPU time compared to existing approaches.
• Preserved numerical accuracy while increasing computational tractability.

Conclusions:

• The proposed fractional return-mapping framework is flexible and computationally efficient.
• It accurately models power-law visco-elasto-plastic materials.
• The formulation is particularly suitable for fractional calculus applications in bio-tissues.