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"illustrates the chosen edge crack problem. we use the rst-term asymptotic solution of a crack problem  (refer to the auxiliary displacements in Appendix B), which we prescribe as Dirichlet boundary condition on the outer boundaries, while keeping crack faces traction free. The parameters E = 1, ν = 0.3, a = 1, L = 2. "
[Show abstract][Hide abstract] ABSTRACT: We propose a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation. To capture the stress singularity around the crack tip, two methods are compared: (1) a graded knot insertion near crack tip; (2) partition of unity enrichment. A well-established CAD algorithm is adopted to generate smooth crack surfaces as the crack grows. The M integral and J k integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.
"Despite achievement of significant milestones in the development of continuum mechanics of fracture (Griffith 1921, Irwin 1948, Irwin 1956, Dugdale 1960, Irwin 1957, McClintock 1968, Rice and Rosengren 1968, Corresponding author, Ph.D., E-mail: firstname.lastname@example.org Vijay Kumar Sutrakar, N. Subramanya and D. Roy Mahapatra Westergaard 1939, Williams 1957) the complex fracture mechanism occurring at atomistic level is not completely understood. However, it is well known that the observable fracture phenomenon at macroscopic level is an outcome of various events occurring at micro-and nano-scale. "
[Show abstract][Hide abstract] ABSTRACT: Initiation of crack and its growth simulation requires accurate model of traction – separation law. Accurate modeling of traction-separation law remains always a great challenge. Atomistic simulations based prediction has great potential in arriving at accurate traction-separation law. The present paper is aimed at establishing a method to address the above problem. A method for traction-separation law prediction via utilizing atomistic simulations data has been proposed. In this direction, firstly, a simpler approach of common neighbor analysis (CNA) for the prediction of crack growth has been proposed and results have been compared with previously used approach of threshold potential energy. Next, a scheme for prediction of crack speed has been demonstrated based on the stable crack growth criteria. Also, an algorithm has been proposed that utilizes a variable relaxation time period for the computation of crack growth, accurate stress behavior, and traction-separation atomistic law. An understanding has been established for the generation of smoother traction-separation law (including the effect of free surface) from a huge amount of raw atomistic data. A new curve fit has also been proposed for predicting traction-separation data generated from the molecular dynamics simulations. The proposed traction-separation law has also been compared with the polynomial and exponential model used earlier for the prediction of traction-separation law for the bulk materials.
"触においては，上述した A r と W の比例関係は必ずしも成立しない (Westergaard, 1939, Johnson, et al., 1985, G Manners, 2000, Hyun, et al., 2004, Yang and Persson, 2008, Persson, et al., 2002)．一般的には，λ が十分に小さい低荷重 域では A r /W の値はほぼ一定であるものの，荷重が増加して全面接触状態（A r = A a ）に近づくにつれて A r / W の値 は著しく減少する (Hyun, et al., 2004)．これは，λ が大きい場合では，真実接触点間の距離が小さくなり（もしく は合一して）接触点同士の相互干渉により真実接触面積の増加が鈍化することに起因する (Persson, et al., 2002)． "
[Show abstract][Hide abstract] ABSTRACT: In this study, in-situ observations of a contact interface between a transparent rubber hemisphere made of PDMS (poly dimethyl siloxane) and a smooth plate made of PMMA (polymethyl methacry- late) were performed. Using a reflective optics, the space distribution of real contact regions formed in the apparent contact region was visualized. Additionally, the normal load dependence of friction force that acts on the contact interface was also investigated. As a result, it was found that the classical Amontons' friction law breaks down in this system; friction coefficient gradually decreased with increasing normal load. Based on Persson's contact theory, we discussed the mechanism of the normal load dependence of real contact area and friction coefficient. Finally, a novel method for estimating the real contact area and shear strength in sliding friction of a rubber like material was developed. The use of this method allows to estimate the real contact area and shear strength without any optical measurements of contact interfaces.