Nondeterministic Multiscale Modeling of Biomimetic Crack Self-Healing in Nanocrystalline Solids under Mechanical Loading
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Nondeterministic Multiscale Modeling of Biomimetic Crack Self-Healing in Nanocrystalline Solids under Mechanical Loading Eduard G. Karpov and Mykhailo Grankin Civil & Materials Engineering, University of Illinois, Chicago, IL 60607, U.S.A. ABSTRACT A nondeterministic multiple scale approach based on numerical solution of the MonteCarlo master equation coupled with a standard finite-element formulation of material mechanics is presented. The approach is illustrated in application to the long-term evolutionary processes of self-diffusion, precipitation and crack/void healing in nanocrystalline fcc and bcc solids. Effect of static and dynamic loading patterns on the crack healing rates are investigated. The approach is widely applicable to the modeling and characterization of advanced functional materials with evolutionary internal structure, as well as emerging behavior in materials systems. INTRODUCTION One of the most challenging aspects of multiscale modeling of solids is the coupling of disparate spatial scales or multiphysics behavior associated with the discrete atomistic and continuum representations [1-11]. A significant effort has also been invested into coupling of models arising from different levels of atomistic description, such as quantum mechanics and classical particle dynamics, however, we focus here on the coupling of continuum mechanics with atomic scale models, where individual atoms are non-excitable particles moving in a given potential energy field. Physical and mathematical nature of these approaches is deterministic, where the solution is sought as a unique function of initial conditions and system properties. The atomistic model is imposed on a localized critical region and designed to provide an adequate enrichment for the continuum finite element (FE) model in the form of dynamic constitutive relationships and boundary conditions. This implies that maximal time accessible by the coupled simulation is restricted by maximal time allowed by the atomistic domain, typically, represented by a molecular dynamics (MD) model. Many exciting opportunities have been inspired by the biological world, and lead to a range of “self-healing” materials systems, advanced implant materials for medical applications, and other bio-inspired systems. Individual functional components of such systems are integrated to perform a self-controlled smart action, similar to a living creature able to sense and process the environment and take necessary actions. This smart action is related to a progressive change of material internal structure and chemical composition. The dynamic internal structure then implies varying constitutive properties viewed as an adequate response of the material to the external loading. The slow-rate evolution of internal structure is often owed to the effects of non-elastomechanics nature, such as phase transitions, chemical reactions, diffusion, and other kinetic processes. Besides, the interplay between the mechanical performance and the internal dynamics is two-way. This implies that the mec
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