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Finite-deformation phase-field chemomechanics for multiphase, multicomponent inelastic solids

By Bob Svendsen (Material Mechanics/RWTH Aachen)
Co-authors: Pratheek Shanthraj (Max Planck Institute für Eisenforschung GmbH)

The purpose of this work is the development of a framework for the formulation of geometrically non-linear chemomechanical models for generally inelastic solids containing multiple (i.e., more than two) chemical components diffusing among multiple (i.e., more than two) transforming solid phases. In particular, solid phase modeling is based on a chemomechanical free energy and stress relaxation via the evolution of phase-specific concentration fields, order-parameter fields, and internal variables. At the mixture level, differences or contrasts in phase composition and phase local deformation in phase interface regions are treated as mixture internal variables whose evolution toward equilibrium is relaxational. In this context, three different interface models are considered. Besides a simple "thick" or "bulk" interface case, these include two models for "thin" interfaces. In the equilibrium limit, the corresponding "relaxed" values of phase contrasts in composition and local deformation in the interface region are determined via (bulk) energy minimization. On the chemical side, the equilibrium limit of the current model formulation reduces to a multiple component, multiple phase generalization of the two-phase binary alloy interface equilibrium conditions of Kim et al.~(Phys.~Rev.~E 60, 7186, 1999). On the mechanical side, the equilibrium limit of the bulk interface model represents a multiple-component, multiple-phase generalization of Reuss-Sachs conditions from mechanical homogenization theory (i.e., equal phase stresses:~e.g., Steinbach and Apel, Physica D, 153, 2006). Analogously, those of the "thin" interface models represent multiple-component, multiple-phase generalizations of interface equilibrium conditions consistent with interface kinematic compatibility and mechanical equilibrium (e.g., Mosler et al., J.~Mech.~Phys.~Sols.~68, 251, 2014; Durga et al., Comp.~Mat.~Sci.~99, 81, 2015, Schneider et al., Comp.~Mech., online, 2017). Examples will be given.

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