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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 authors presented a generalization to a three-dimensional (3D) case of a mechanically-based approach to non-local elasticity theory, recently proposed by the authors in a 1D case, by assuming that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range forces exerted by nonadjacent elements.
58 citations
TL;DR: In this paper, a finite element program was developed in which the material is treated as elastic-viscoplastic, based on a theory by P. P erzyna.
Abstract: I n order to investigate rapid Mode I crack propagation in steel under large scale yielding conditions a finite element program was developed in which the material is treated as elastic-viscoplastic, based on a theory by P. P erzyna . In this model, rate effects in the plastic deformation process are accounted for. The parameters of the constitutive model were determined from ordinary tensile tests on small specimens by varying the loading rate. It was found that the strain rate can satisfactorily be related to the increase of the inelastic stress-strain relation raised to some power n . The FEM-program was applied to a number of crack propagation experiments on highly loaded SEN specimens of a high strength steel. For comparison some experiments were also analysed assuming linear elastic and simulated elastic-plastic material behaviour with no rate sensitivity. It was found that combined plastic and viscous effects are of great importance for an adequate description of rapid crack growth when large scale yielding is at hand. The energy flow to the crack tip region in the viscoplastic case, which is used as a fracture parameter, seems to converge to finite and non-trivial values for sufficiently small values of the element size along the crack tip. This may be due to the asymptotic dominance of the elastic field at the crack-tip for the particular rate-dependent model used. Geometry effects, which are present in a linear elastic analysis, are shown to be negligible in the present elastic-viscoplastic analysis with respect to different specimen heights.
58 citations
TL;DR: In this article, a new state-based peridynamic model is proposed to quantitatively analyze fracture behavior (crack initiation and propagation) of materials, and the general relationship of the critical stretch and the critical energy release rate is for the first time obtained for linear elastic brittle materials.
Abstract: A new state-based peridynamic model is proposed to quantitatively analyze fracture behavior (crack initiation and propagation) of materials. In this model, the general relationship of the critical stretch and the critical energy release rate is for the first time obtained for the state-based peridynamic model of linear elastic brittle materials, and the released energy density is defined to quantitatively track the energy released during crack propagation. The three-dimensional (3D) and two-dimensional (2D) (for both plane stress and plane strain) cases are all considered. As illustrations, the compact tension and double cantilever beam tests are analyzed using the proposed model, which is capable of successfully capturing fracture behaviors (e.g., crack path and concentration of strain energy density) of the considered fracture tests. The characteristic parameters (i.e., critical load, critical energy release rate, etc.) are calculated and compared with available experimental and numerical data in the literature to demonstrate validity of the proposed model.
58 citations
TL;DR: In this paper, the complex frequency spectrum of axisymmetric wave modes in a circular cylindrical shell containing various viscoelastic media is measured by combining a high-resolution laser interferometer with modern spectrum estimation methods.
Abstract: The complex frequency spectrum of axisymmetric wave modes in a circular cylindrical shell containing various viscoelastic media is measured. A new measurement technique has been developed for this purpose by combining a high-resolution laser interferometer with modern spectrum estimation methods. To decompose the complex wave-number dependence, a complex spectrum estimation method has been implemented. Up to 40 dispersion curves of traveling, axisymmetric modes are decomposed simultaneously in a frequency range between 1 kHz and 2 MHz. The guided structural waves are excited by piezoelectric transducers. Linear elasticity can be considered as an extreme case of viscoelasticity (long relaxation times compared with the deformation periods). To ascertain the validity of the theory, dispersion curves are calculated for a shell containing a viscoelastic material behaving like the elastic shell and are compared with the measured curves of an isotropic aluminium rod. The phenomenon of “backward wave propagation,...
58 citations
TL;DR: With group-representation theory all quadratic invariants and the expressions of elastic energy have been derived for quasicrystals with cubic point-group symmetry and the generalized Hooke's law and equilibrium for cubic quasICrystals are obtained.
Abstract: With group-representation theory all quadratic invariants and the expressions of elastic energy have been derived for quasicrystals with cubic point-group symmetry Using the generalized elasticity theory of quasicrystals, we have also obtained the expressions of the generalized Hooke's law and equilibrium for cubic quasicrystals
58 citations