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Abstract
In this paper, an asymptotic method is employed to formulate nano- or micro-beams based on strain gradient elasticity. Although a basic theory for the strain gradient elasticity has been well established in literature, a systematic approach is relatively rare because of its complexity and ambiguity of higher-order elasticity coefficients. In order to systematically identify the strain gradient effect, an asymptotic approach is adopted by introducing the small parameter which represents the beam geometric slenderness and/or the internal atomistic characteristic. The approach allows us to systematically split the two-dimensional strain gradient elasticity into the microscopic one-dimensional through-the-thickness analysis and the macroscopic
one-dimensional beam analysis. The first-order beam problem turns out to be different from the classical elasticity in terms of the bending stiffness, which comes from the through-the-thickness strain gradient effect. This subsequently affects the second-order transverse shear stress in which the surface shear stress exists. It is demonstrated that a careful derivation of a first strain gradient elasticity embraces \"Gurtin-Murdoch traction\" as the surface effect of a one-dimensional Euler-Bernoulli-like beam model.
Key Words
strain gradient elasticity; size effect; surface tension; asymptotic method
Address
Jun-Sik Kim: Department of Mechanical System Engineering, Kumoh National Institute of Technology, 61 Daehak-ro, Gumi, Gyeongbuk 730-701, Republic of Korea
Abstract
In this paper, a mixed-mode cohesive law for an interface crack between epoxy and TR (transparent thermoplastic) resin is inversely estimated by the field projection method using numerical solutions and experimentally measured displacements. Displacements in a region far away from the crack tip are measured by digital image correlation technique. An inverse analysis, the field projection method formulated from the interaction J- and M-integrals with numerical auxiliary fields, is carried out to estimate a mixed-mode cohesive law for an interface crack between dissimilar materials. In the present approach, nonlinear deformations and damage near the crack tip are converted into the relationships of tractions and separations on crack surfaces behind the crack tip. The phase angle of mixed-mode singularities of the interface crack is also obtained from measured displacements in this study.
Key Words
cohesive laws; interface crack; mixed-mode singularity; inverse problem; field projection method
Address
Sung-Il Song, Kwang-Soo Kim and Hyun-Gyu Kim: Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul, 139-743, Republic of Korea
Abstract
Amyloid fibrils have recently been considered as an interesting material, since they exhibit the excellent mechanical properties such as elastic modulus in the order of 10 GPa, which is larger than that of other protein materials. Despite recent findings of these excellent mechanical properties for amyloid fibrils, it has not been fully understood how these excellent mechanical properties are achieved. In this work, we
have studied the nanomechanical deformation behaviors and properties of amyloid fibrils such as their elastic modulus as well as fracture strength, by using atomistic simulations, particularly steered molecular dynamics simulations. Our simulation results suggest the important role of the length of amyloid fibrils in their mechanical properties such that the fracture force of amyloid fibril is increased when the fibril length decreases. This length scale effect is attributed to the rupture mechanisms of hydrogen bonds that sustain the
fibril structure. Moreover, we have investigated the effect of boundary condition on the nanomechanical deformation mechanisms of amyloid fibrils. It is found that the fracture force is critically affected by boundary condition. Our study highlights the crucial role of both fibril length and boundary condition in the nanomechanical properties of amyloid fibrils.
Key Words
amyloid fibrils; mechanical deformation mechanisms; molecular dynamics simulation;
fracture property; boundary condition
Address
Bumjoon Choi, Sang Woo Lee: Department of Biomedical Engineering, Yonsei University, Wonju 26493, Republic of Korea
Kilho Eom: Biomechanics Laboratory, College of Sport Science, Sungkyunkwan University,
Suwon 16419, Republic of Korea
Abstract
In this study, an influence of local variation of nanoparticulate volume fraction on the homogenized elastic properties is investigated. It is well known that interface effect is dependent on the radius and volume fraction of reinforced nanofillers. However, there is no study on the multiscale modeling and analysis of polymer nanocomposites including polydispersed nanoparticles with consideration of interphase zone, which is dependent on the volume fraction of corresponding nanoparticles. As results of numerical examples, it is confirmed that an influence of local variation of nanoparticulate volume fraction should be considered for non-dilute system such as cluster of nanoparticles. Therefore representative volume element analysis is conducted by considering local variation of nanoparticle volume fraction in order to analyze the practical size of cell including hundreds of nanoparticles. It is expected that this study could be extended to the multiparticulate nanocomposite systems including polydispersed nanoparticles.
Key Words
volume fraction effect; polymer nanocomposites; multiscale homogenization; molecular dynamics simulation; Interface effect
Address
Hyunseong Shin, Jin-Gyu Han, Seongmin Chang and Maenghyo Cho: Department of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, Shillim-Dong, Kwanak-Ku, Seoul 151-742, Republic of Korea