Atomistic configurational forces in crystalline fracture - Birang Oskouei, Seyedehelmira; Park, Harold S.; Smith, Ana-Suncana; Steinmann, Paul (Forces in Mechanics, 2021)
Configurational atomistic forces contribute to the configurational mechanics (i.e. non-equilibrium) problem that determines the release of total potential energy of an atomistic system upon variation of the atomistic positions relative to the initial atomic configuration. These forces drive energetically favorable irreversible re-organizations of the material body, and thus characterize the tendency of crystalline defects to propagate. In this work, we provide new expressions for the atomistic configurational forces for two realistic interatomic potentials, i.e. the embedded atom potential (EAM) for metals, and second generation reactive bond order (REBO-II) potential for hydrocarbons. We present a range of numerical examples involving quasistatic fracture for both FCC metals and mono and bi-layer graphene at zero Kelvin that demonstrate the ability to predict defect nucleation and evolution using the proposed atomistic configurational mechanics approach. Furthermore, we provide the contributions for each potential including two-body stretching, three-body mixed-mode stretching-bending, and four-body mixed-mode stretching-bending-twisting terms that make towards defect nucleation and propagation.
Keywords: Atomistic configurational mechanics; Configurational forces; Many-body potentials; Fracture mechanics

Atomistic two-, three- and four-body potentials. Spatial and material settings - Steinmann, Paul; Smith, Ana-Suncana; Birang Oskouei, Seyedehelmira; Birang, E.; McBride, A.; Javili, A. (Journal of the Mechanics and Physics of Solids, 2021)
In molecular dynamics or molecular statics (MD/MS) multi-body potentials empirically capture the energetic interactions in atomistic systems enabling the computation of the corresponding atomistic forces as energetic conjugates to the atomistic positions. We distinguish here between spatial and material atomistic positions and consequently between the corresponding spatial and material atomistic forces. In quasi-statics, i.e. MS, the former, also denoted as deformational atomistic forces, contribute to the classical deformational mechanics (i.e., equilibrium) problem that seeks to minimise the total potential energy of an atomistic system with respect to the atomistic positions relative to the ambient space. The latter, also denoted as configurational atomistic forces, contribute to the configurational mechanics (i.e., non-equilibrium) problem that determines the release of total potential energy of an atomistic system upon variation of the atomistic positions relative to the ambient material, i.e., due to perturbations of the material (initial) atomistic configuration. The importance of material atomistic forces is that they drive energetically favourable re-organisations of the material atomistic configuration, thereby characterising the tendency of generic atomistic defects to propagate. In this contribution we focus on two-, three-, and four-body potentials, whereby we distinguish between novel stretch- and classical angle-based potentials for the two latter cases. Taken together, as the main contribution, we derive expressions for the corresponding spatial and, for the first time, material atomistic forces and highlight their striking formal similarity. The derivations are detailed but the final expression compact and well-suited for numerical implementation.
CRIS-Team Scopus Importer:2021-06-25

Configurational Forces in Bond Order Potentials - Birang Oskouei, Seyedehelmira; Smith, Ana-Suncana; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2021)
In this contribution, a configurational mechanics framework is elaborated to assess the applicability of atomistic configurational forces in fracture of crystalline lattices. To this end, an analytical interatomic potential is reformulated in terms of the material positions occupied by the atoms participating in two- and three-body interactions. It is demonstrated that such a potential satisfies the requirements of invariances i.e., translational, rotational and parity. The focus of this work is developing the configurational setting for the bond order Tersoff potential. Two-dimensional pre-cracked mono-layer graphene modelled with the Tersoff potential is chosen to study the configurational force approach in determining energy release during crack propagation into the lattice.<br

Discrete configurational mechanics for the computational study of atomistic fracture mechanics - Birang Oskouei, Seyedehelmira; Steinmann, Paul (Forces in Mechanics, 2021)
We formulate discrete configurational mechanics in an atomistic setting, discuss the corresponding computational details, and demonstrate its utility via computational analyses of atomistic fracture mechanics problems. To this end, we first propose a novel Configurational-Force-Criterion (CFC) to predict crack propagation into an atomic crystalline lattice. Thereby, specifically, the CFC relies on comparing discrete configurational forces with a corresponding Crack-Propagation-Threshold (CPT) in the quasi-static approximation of atomistic systems at zero Kelvin. Next, based on the CFC, we introduce a quasi-static computational atomistic crack propagation algorithm. Therein, whenever an atomic pair meets the CFC, we modify the lattice connectivity by deleting the corresponding interatomic bond, thus resulting in true irreversibility, i.e. dissipation upon crack extension. Finally, based on different choices for the magnitude of the CPT employed in the CFC, we demonstrate suitability and versatility of discrete configurational mechanics in analyzing atomistic fracture mechanics.<br
Keywords: Atomistic configurational mechanics; Fracture criterion; Crack propagation

Phonon-based thermal configurational forces: Definitions and applications in rupture of semiconductors - Birang Oskouei, Seyedehelmira; Smith, Ana-Suncana; Steinmann, Paul (Engineering Fracture Mechanics, 2021)
A general framework encompassing spatial and material settings of atomistic crystalline systems is presented. Theoretical and computational analysis of configurational forces in the context of atomistic thermomechanics constitutes the central topic of the presented paper. We distinguish between atomistic configurational forces stemming from the changes in static energy density and the changes in vibrational energy density. To this end, we first propose a novel atomistic phonon-based thermal configurational forces rendering infinitesimal changes in vibrational energy density under configurational variations. Next, we employ pair and triplet configurational forces resulting from the changes in static energy density due to two-body stretch and three-body stretch-bending. Using thermal configurational forces, we study numerically the problem of temperature rise, bond stretching and bending occurring at the crack tip induced by brittle crack propagation in crystalline lattices. Energy release caused by large harmonic vibrations and deformations is estimated by the magnitude of configurational forces at the crack tip. The atomistic temperature is shown to be governed by atom-wise frequency through local entropy. Finally, we demonstrate suitability and versatility of atomistic configurational forces in analyzing fracture of silicon diamond lattice subjected to mode-I loading at different finite temperatures.
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Keywords: Atomistic configurational mechanics; Atomistic fracture mechanics; Configurational forces; Effective empirical potential; Spatial and material settings