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Mechanical and interface properties of biominerals: Atomistic to coarse-grained modeling
Published in Elaine DiMasi, Laurie B. Gower, Biomineralization Sourcebook, 2014
Arun K. Nair, Flavia Libonati, Zhao Qin, Leon S. Dimas, Markus J. Buehler
heterogeneous materials at the meso- and macroscale (Hassold and Srolovitz 1989; Curtin and Scher 1990; Gao and Klein 1998). The speci c force extension laws employed in this study are the ones also presented in Figure 21.10d. These behaviors represent the nanoscale deformation characteristics of bulk and nanoporous silica (Sen and Buehler 2010). The choice of silica as the base constituent of our models is motivated by the aim of making our models as general as possible. We seek to improve the mechanical characteristics of an inferior and brittle base constituent simply by tuning the geometrical features. The softer phase also consists solely of silica and achieves its compliance due to the geometry and nanocon nement (Garcia et al. 2011). The goal of this study is to investigate the improved mechanical characteristics achieved through ordering a soft and sti phase in an appropriate con guration. We therefore choose to isolate this mechanism in our models, motivating the simple model described earlier. We exclude other features accounting for other mechanically significant mechanisms (e.g., microcracking, crack-bridging, etc.), which have been comprehensively studied by others (Weiner and Wagner 1998; Aizenberg et al. 2005; Weaver et al. 2007; Meyers et al. 2008), in order to isolate the effect of architecture and recognize the limitations; this enforces on the predictive power of our models. Inspired by natural materials, we investigate two speci c arrangements of the softer and sti er phase, a biocalcite-like geometry and a bone-like geometry, reviewing here what was reported in a recent study (Dimas and Buehler 2012). Further, in an attempt to optimize the strain transfer, we construct and investigate an additional geometry, here named rotated-bone-like geometry. All geometries are presented with appropriate titles in Figure 21.10. In order to study the mechanics of these structures, it is essential to evaluate the local variation of stresses and strains. Although these concepts are somewhat less familiar in the context of discrete particles, well-de ned expressions do exist that have been shown to be equivalent to the continuum measures, under the assumption of validity of the Cauchy–Born rule. To evaluate stresses, we employ the virial stress measure presented in the study of Tsai (1979). For characterization of the local variation of strains, we nd the measure developed by Zimmerman et al. (2009) useful. The strain is de ned through the de nition of the left Cauchy–Green tensor, unique to a particular particle in terms of its nearest neighbors: 1 b=
Effects of void shape and orientation on the elastoplastic properties of spheroidally voided single-crystal and nanotwinned copper
Published in Philosophical Magazine, 2020
During the unidirectional strain loading process, stresses develop on every atom and are measured by the virial stress tensor defined at the atomic level where , and are, respectively, the volume, mass and velocity of atom i. The Greek indices α and β may represent any of the three global coordinate directions. From Equation (8), it is seen that both the instantaneous velocity and interatomic forces contribute to the virial stress acting on atom i. During every temporal step of MD simulations, the virial stress defined by Equation (8) is first calculated for each atom and subsequently summed up and averaged over all atoms within the whole simulation box. The averaged virial stress leads to the definition of macroscopic stress.
Modeling of fracture behavior in polymer composites using concurrent multi-scale coupling approach
Published in Mechanics of Advanced Materials and Structures, 2018
Shibo Li, Samit Roy, Vinu Unnikrishnan
The macroscopic or equivalent continuum stress in molecular scale is commonly evaluated by the virial stress, which was originally proposed by Irving and Kirkwood [19] and derived by Cormier et al. [20] based on the work of Lutsko [21]. The tensor form of the virial stress can be expressed as: where mβ is the mass of the βth molecule in volume Ω, fαβ and xαβ are the force and position vector between particle α and β, respectively, and relative velocity vector is defined as . It has been demonstrated [22] that virial stress including the kinetic contribution is not equivalent to the mechanical Cauchy stress. After removing the kinetic part, the stress tensor becomes: