Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo-mechanical coupling in plane strain problems

Abstract: In linear elasticity, the concept of reduced integration combined with hourglass stabilization can be directly derived from a mixed method, if certain assumptions are made. Such a derivation is much more difficult when the relation between stress and strain is highly non-linear. Earlier works use the linearized form of a classical multi-field functional in order to derive the hourglass stabilization analytically. In the present contribution, it is shown how such stabilization techniques can be directly derived at the level of the weak form. Crucial to the new concept is a Taylor expansion of the constitutively dependent quantities with respect to the centre of the element. The approach is suitable for various kinds of inelastic material models and thermo-mechanical coupling. One of the important features of the new element technology is its computational efficiency which is especially visible when the numerical effort at the element level is very high. Copyright © 2003 John Wiley & Sons, Ltd.

Finite Element Investigation of Quasi-Static Crack Growth in Functionally Graded Materials Using a Novel Cohesive Zone Fracture Model

Abstract: This work studies mode I crack growth in ceramic/metal functionally graded materials (FGMs) using three-dimensional interface-cohesive elements based upon a new phenomenological cohesive fracture model. The local separation energies and peak tractions for the metal and ceramic constituents govern the cohesive fracture process. The model formulation introduces two cohesive gradation parameters to control the transition of fracture behavior between the constituents. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with standard isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive fracture model and computational scheme to analyze crack growth in compact tension, C(T), and single-edge notch bend, SE(B), specimens with material properties characteristic of a TiB/Ti FGM. Young's modulus and Poisson's ratio of the background solid material are determined using a self-consistent method (the background material remains linear elastic). The numerical studies demonstrate that the load to cause crack extension in the FGM compares to that for the metal and that crack growth response varies strongly with values of the cohesive gradation parameter for the metal. These results suggest the potential to calibrate the value of this parameter by matching the predicted and measured crack growth response in standard fracture mechanics specimens. ©2002 ASME

R-curve modeling of rate and size effects in quasibrittle fracture

Abstract: The equivalent linear elastic fracture model based on an R-curve (a curve characterizing the variation of the critical energy release rate with the crack propagation length) is generalized to describe both the rate effect and size effect observed in concrete, rock or other quasibrittle materials. It is assumed that the crack propagation velocity depends on the ratio of the stress intensity factor to its critical value based on the R-curve and that this dependence has the form of a power function with an exponent much larger than 1. The shape of the R-curve is determined as the envelope of the fracture equilibrium curves corresponding to the maximum load values for geometrically similar specimens of different sizes. The creep in the bulk of a concrete specimen must be taken into account, which is done by replacing the elastic constants in the linear elastic fracture mechanics (LEFM) formulas with a linear viscoelastic operator in time (for rocks, which do not creep, this is omitted). The experimental observation that the brittleness of concrete increases as the loading rate decreases (i.e. the response shifts in the size effect plot closer to LEFM) can be approximately described by assuming that stress relaxation causes the effective process zone lenght in the R-curve expression to decrease with a decreasing loading rate. Another power function is used to describe this. Good fits of test data for which the times to peak range from 1 sec to 250000 sec are demonstrated. Furthermore, the theory also describes the recently conducted relaxation tests, as well as the recently observed response to a sudden change of loading rate (both increase and decrease), and particularly the fact that a sufficient rate increase in the post-peak range can produce a load-displacement response of positive slope leading to a second peak.