Topic
Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, both stress-based and stress resultant-based elastoplastic formulations of GBT-based beam finite elements were developed to analyze the physically non-linear (plastic zone) behaviour of thin-walled metal members.
Abstract: This paper addresses the formulation and validation of GBT-based beam finite elements, intended to analyse the physically non-linear (plastic zone) behaviour of thin-walled metal members. Both stress-based and stress resultant-based elastoplastic formulations are developed. The stress-based formulation is generally more accurate, but the stress resultant-based formulation, which employs the Ilyushin yield function, leads to significant computational savings, namely (i) numeric integration in the through-thickness direction is not required and (ii) constraints to the stress resultant and work-conjugate strain field, typical of linear elastic GBT-type formulations, are straightforwardly enforced. The choice of interpolation functions and the cross-section discretization procedure are also discussed. In order to illustrate the application, provide validation and demonstrate the capabilities of the proposed finite elements, several numerical results are presented and discussed. These results are compared with those obtained with standard 2D-solid and shell finite element analyses.
63 citations
••
TL;DR: In this paper, a new quadrilateral shell element with 5/6 nodal degrees of freedom is presented, assuming linear isotropic elasticity a Hellinger-Reissner functional with independent displacements, rotations and stress resultants is used.
63 citations
••
TL;DR: Chambon et al. as discussed by the authors proposed a two-component local/non-local constitutive model for inhomogeneous linear elastic materials, in which the stress is the sum of the local stress and a nonlocal-type stress expressed in terms of the strain difference field, hence identically vanishing in the case of uniform strain.
63 citations
••
TL;DR: In this paper, a simple and direct derivation of balance laws for linear dynamic elasticity including nonhomogeneities, thermal effects, anisotropy, and body forces is presented.
Abstract: A simple and direct derivation of certain balance (or conservation) laws for linear dynamic elasticity is presented including nonhomogeneities, thermal effects, anisotropy, and body forces. Additionally, the connection between the balance laws and energy release rates for defect motions is established.
63 citations
••
TL;DR: In this paper, a two-dimensional theory for predicting arbitrary paths of ultra-high-speed cracks was developed, which incorporates elastic nonlinearity without extraneous criteria, and showed that cracks undergo an oscillatory instability controlled by small-scale, near crack-tip, elastic non-linearity.
Abstract: Understanding crack formation is important for improving the mechanical performance of materials. A new theory is now presented for the description of cracks propagating at high speeds, with elastic nonlinearity as the underlying principle. Cracks, the major vehicle for material failure1, undergo a micro-branching instability at ∼40% of their sonic limiting velocity in three dimensions2,3,4,5,6. Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an oscillatory instability7,8. Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks1, which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths9. We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an oscillatory instability controlled by small-scale, near crack-tip, elastic nonlinearity. This instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics.
63 citations