"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.
"In the first half of the 20th century, many problems have been solved analytically using complex analytic potentials, Muskhelishvili (1953); England (1971). In the case of fracture configurations, the popular Westergaard approach, Westergaard (1939); Sih (1966); Sanford (1979); Tada et al. (2000); Sanford (2003) provides convenient expressions for instance for mode-I stress state: [ ] [ ] "
[Show abstract][Hide abstract] ABSTRACT: Williams series appear to be the most favored analytical tool for the description of mechanical fields near crack-tips in planar domains. For practical use, these series are generally truncated. A common belief is to consider that the more terms are kept, the more accurate the representation will be. Based on closed-form series expressions, this belief is shown to be only partially true. Asymptotic expansions converge within series convergence disks as expected, but truncated series can also provide exact values for the stress field. This property can be easily observed with the map of relative error comparing truncated series solutions for stress with complex exact ones. The series remainder appears to be equal to zero on curves emanating from the crack-tip. Their number and their initial angles are shown to be related to the zeros of a Williams eigen-function that depends on the number of terms kept in the truncated series.
"Elastic–plastic contact (Liu and Yang, 2013a; Liu and Yang, 2013b) can be investigated more accurately by finite element approach (Kucharski et al., 1994; Etsion et al., 2005b; Eid et al., 2011) owing to the inherent shortcomings of theoretical approaches (e.g. small deformation Hill et al., 1989; Hill, 1992; Storåker et al., 1997 and discontinuous pressure gradient at contact edges Westergaard, 1939). Difference between finite element models and theoretical models can be remarkable (Kucharski et al., 1994; Buczkowski and Kleiber, 2006). "
[Show abstract][Hide abstract] ABSTRACT: A series of finite element simulations of frictionless contact deformations between a sinusoidal asperity and a rigid flat are presented. Explicit expressions of critical variables at plastic inception including interference, contact radius, depth of first yielding, and pressures are obtained from curve fitting of simulation results as a function of material and the geometrical parameters. It is found Hertz solution is not applicable to the critical contact variables at plastic inception for sinusoidal contact, although contact responses of initially plastic deformation follow the same trend as that of purely elastic deformation. The contact pressure at incipient plasticity, which is defined as yield strength, is dependent on Poisson’s ratio, yield stress, and geometrical parameters, but independent of elastic modulus. It is not yield stress, but yield strength that correlates with indentation hardness. The results yield the insight into the specification of material properties to realize elastic contact. A larger ratio of yield stress to elastic modulus is beneficial to sustain a larger load before plastic deformation.
Mechanics of Materials 10/2014; 77. DOI:10.1016/j.mechmat.2014.06.009 · 2.33 Impact Factor
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