Linear elasticity

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

Intersonic shear crack growth along weak planes

Abstract: Classical dynamic fracture theories predict the Rayleigh surface wave speed (cR) to be the limiting speed of propagation for mode-I cracks in constitutively homogeneous, isotropic, linear elastic m...

Mixed finite element methods with continuous stresses

Abstract: We present a modified mixed formulation for second order elliptic equations and linear elasticity problems which automatically satisfies the “ellipticity on the kernel” condition, i.e., one of the two compatibility conditions necessary to ensure stability and optimal error bounds (the other being the Inf-Sup condition). This modification differs from similar ones introduced by other authors in that it is independent of the mesh size. Moreover, it allows the use of continuous stresses.

Nonconforming mixed finite element methods for linear elasticity using rectangular elements in two and three dimensions

Abstract: We present nonconforming, rectangular mixed finite element methods based on the Hellinger-Reissner variational principle in both two and three dimensions and show stability and convergence An optimal error estimate of $\mathcal{O}(h^2)$ is obtained for the displacement, along with a suboptimal, $\mathcal{O}(h)$ , error estimate for the stress, in both dimensions

Micromechanics characterization of sublaminate damage

Abstract: A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.