Micromorphic vs. Phase-Field Approaches for Gradient Viscoplasticity and Phase Transformations

Abstract

Abstract. Strain gradient models and generalized continua are increasingly used to introduce characteristic lengths in the mechanical behavior of materials with microstructure. On the other hand, phase-field models have proved to be efficient tools to simulate microstructure evolution due to thermodynamical processes in the presence of mechanical deformation. It is shown that both methods have strong connections from the point of view of thermomechanical field theory. A general formulation of thermomechanics with additional degrees of freedom is presented that encompasses both applications as special cases. It is based on the introduction of additional power of internal forces introducing generalized stresses. The current knowledge in the formulation of physically non-linear constitutive equations is used to develop strongly coupled elastoviscoplastic material models involving phase transformation and moving boundaries.

A multi-mechanism model for cutting simulations based on the concept of generalized stresses

“…Based on the concept of generalized stresses in Forest et al [4], we extended a multimechanism model developed in our previous work [9] with a gradient term. This general model has been specialized to the scenario of a cutting process in steel production.…”

“…Based on additional degrees of freedom and generalized stresses, Forest et al [4] describe a thermodynamic consistent phase field model, which is extended with gradient terms. It is demonstrated, that there are strong links between generalized continuum mechanics and phase field models which are striving in modern field theories of materials.…”

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

“…In the isotropic case, the previous expression specializes to 12) where the direction N is the direction of the gradient of the scalar microstrain, according to equation (A 1). In the previous hardening law (3.12), the usual Laplace term is complemented by a non-linear contribution that vanishes for m = 2.…”

“…As an example, the following free energy potential is proposed: 12) where ψ α is the appropriate free energy contribution associated with usual work-hardening (not specified here) and 2E ∼ e = C ∼ e − 1 ∼ is the Green-Lagrange elastic strain measure. The microstrain variable is compared to the cumulative plastic strain variable p defined aṡ…”

“…Diffusion-like operators are used in phase field models in the form of Ginzburg-Landau or Allen-Cahn equations. Close relations exist between regularization operators used in continuum damage mechanics and in phase field theory, as recognized recently [12][13][14][15].…”