Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity...

Area of Science:

• Continuum Mechanics
• Materials Science
• Computational Mechanics

Background:

• Micromorphic and strain/damage gradient theories regularize continuum mechanics models.
• The Helmholtz operator, derived from quadratic potentials, smooths discontinuities and defines localization bands.

Approach:

• Introduced strain or damage micromorphic degrees of freedom into the Helmholtz free energy.
• Developed a new balance equation for generalized stresses coupled with micromorphic constitutive equations.
• Proposed nonlinear extensions considering nonlinear stress-strain relations and finite deformation formulations.

Key Points:

• The generic approach is applicable to elastoviscoplastic and damage models, including anisothermal and multiphysics coupling.
• Combined standard large strain extensions with the micromorphic approach using additive strain splitting or objective rotating frames.
• Derived three distinct operators using multiplicative deformation gradient decomposition.

Conclusions:

• Nonlinear micromorphic and strain/damage gradient models are proposed for enhanced regularization.
• A novel free energy function leads to additional kinematic hardening induced by micromorphic variable gradients.
• The developed framework offers a versatile approach for advanced material modeling.