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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: In this article, the idea of existing hourglass control is carefully examined for its convergence and accuracy, and is extended to include both selective and directional reduced integration methods for anisotropic linear elasticity.
78 citations
TL;DR: In this article, a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation is proposed, where two methods are compared: a graded knot insertion near crack tip; (2) partition of unity enrichment.
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 JkJk integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.
78 citations
TL;DR: In this paper, the optimum direction of in-plane continuous crack advance in functionally graded materials (FGMs) is discussed, and the kink direction is determined as the angle at which either the energy release is maximized (G max ) or at which kink tip is deformed without shear (K II = 0).
78 citations
TL;DR: In this article, a non-linear differential equation for uniaxial viscoplasticity is transformed into an equivalent integral equation, which employs total strain only and is symmetric with respect to the origin and applies for tension and compression.
Abstract: A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.
78 citations
01 Jan 2000
TL;DR: In this article, the authors investigated the effects of rupture directivity at near-fault sites on the ratio of maximum inelastic displacement demand to maximum elastic displacement demand in single-degree-of-freedom systems undergoing different levels of deformation when subjected to 82 earthquake ground motions recorded at distances closer than 15 km from the surface projection of the rupture.
Abstract: The effects of rupture directivity at near-fault sites on the ratio of maximum inelastic displacement demand to maximum elastic displacement demand are investigated. Inelastic displacement ratios are computed for single-degree-of-freedom systems undergoing different levels of inelastic deformation when subjected to 82 earthquake ground motions recorded at distances closer than 15 km from the surface projection of the rupture. It is found that in addition to increments of linear elastic spectral ordinates in the long period spectral region previously identified by seismologists, forward directivity effects can affect the ratio of maximum inelastic displacement demand to maximum elastic displacement demand. Results indicate that inelastic displacement ratios computed from near-fault records are typically larger than those computed from distant records for periods between 0.1 and about 1.3s. Similarly, inelastic displacement ratios corresponding to faultnormal components are, in general, larger than those of fault-parallel components in the same spectral region. From various ground motions parameters investigated that may affect inelastic displacement ratios of structures located in the near field it is found that peak ground velocity and maximum incremental velocity are the most important ones. Results show that structures subjected to ground motions with large velocity pulses may experience maximum inelastic deformations larger than those subjected to ground motions that do not have these pulses, even if linear elastic ordinates in the short period spectral region are similar. Thus, it is concluded that modification of linear elastic design spectra alone may not be enough to adequately control maximum inelastic deformations in structures located near active faults.
78 citations