Mechanokinetic coupled Modeling of Self-Healing Behavior in Materials
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Many inspiration in biological science world strike exciting opportunities in material science and led to a range of biomimetic and other advanced functional materials for engineering and medical applications. The self-controlled smart behavior of these systems make their individual functional components sense and process the environment and take necessary actions, similar to a living creature. This smart action is referred to a progressive change of material internal structure and chemical composition at a macroscopic interval of time. The dynamic internal structure results in varying constitutive properties and viewed as an adequate response of the material to external loading. The slow-rate evolution of constitutive properties of the materials is often affected by non-elastomechanical nature, such as phase transitions, chemical reactions, diffusion and other kinetic processes at the atomic scale. Additionally, the interplay between the mechanical performance and the internal structure dynamics can be two-way. This indicates that mechanical stress or strain in such material may trigger or affect kinetic processes responsible for its internal structure evolution; in turn, the changed internal structure may influence bulk properties and therefore mechanical response of the material to the external loading. In this study, a nondeterministic multiple scale approach based on numerical solution of the Monte-Carlo master equation on atomic lattices solved together with a standard vi ￼Finite-Element formulation of solid mechanics is investigated. This approach is applicable to long-term evolutionary processes such as precipitation, volume diffusion and creep cavity self-healing in nano-crystalline austenite (Fe fcc) samples. A two-way mechanokinetic coupling is achieved through implementation of strain- dependent diffusion rates and dynamic update of the finite element model based on atomic structure evolution. This study also discusses the effect of macroscopic static loading and cavity geometry on the total healing time. The approach is used in application of modeling and characterization of advanced functional materials with evolutionary internal structures, and emerging behavior in material systems. In the current research we are studying a nondeterministic multiple scale approach based on numerical solution of the Monte-Carlo master equation on atomic lattices which is solved together with a standard Finite-Element formulation of solid mechanics. This approach is applicable to long-term evolutionary processes such as precipitation, volume diffusion and creep cavity self-healing in nanocrystalline austenite (Fe fcc) samples. A two-way mechanokinetic coupling is achieved through implementation of strain-dependent diffusion rates and dynamic update of the finite element model based on atomi structure evolution. This study also discusses the effect of macroscopic static loading and cavity geometry on the total healing time. The approach is used in application of modeling and characterization of advanced functional materials with evolutionary internal structures, and emerging behavior in material systems. In this work, we also demonstrate one possible probabilistic approach for modeling slow-rate vii ￼evolutionary processes in materials at the atomic scale coupled with their bulk mechanical behavior at a continuum level. For this purpose, we consider the slow-rate process as an outcome of multiple random transitions of individual atoms in a host potential field that require time intervals many orders of magnitude shorter than a mean time between two successive transitions. Such processes can generally be described by the Monte-Carlo master equation (Fichthorn et al., 1991; Gardiner et al., 1985). We demonstrate coupling of numerical solution to this equation with a standard finite element solver for the purpose of a unified mechanokinetic modeling approach. Detailed information about atomic trajectories is not preserved within Monte-Carlo methodologies, however material properties, morphological and geometric parameters are still available as time-dependent system observables. These macroscopic parameters form a time-parameterized family of ensemble average quantities, whose temporal evolution is governed by stochastic processes at the atomic scale. A specific algorithm is proposed here to perform a two-way coupling of the Monte-Carlo (MC) and finite element (FE) solution techniques. An effort has been made to keep the two modules as separate as possible by sharing a minimal set of basic parameters; that makes the approach usable for a wide range of practical problems. Generic physical framework of the Monte-Carlo to solid mechanics coupling, where the stochastic process takes place within the solid body itself, were recently outlined by these authors in (Liu et al., 2010) and (Liu et al., 2006.). Another group (Qian et al., 2008, 2009) discussed a stochastic-elastic approach to cell adhesion problems where the viii random process of receptor-ligand bond breakage to determine traction is occurring at the interface between two elastic bodies (cells). The present work unfolds the approach (Liu et al., 2010) in application to the phenomenon of self-healing in nanocrystalline austenite structures by interstitial diffusion and surface precipitation processes under mechanical loading.