Topic
Tangent stiffness matrix
About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors developed a general consistent and systematic framework for the analysis of heterogeneous media that assesses a strong coupling between rate-dependent plasticity and anisotropic ratedependent damage for dynamic problems within the framework of thermodynamic laws and gradient theories.
212 citations
TL;DR: In this paper, a numerical integration method for the non-linear viscoelastic behavior of isotropic materials and structures is presented, where the Schapery's 3D nonlinear material model is integrated within a displacement-based finite element (FE) environment.
Abstract: This study presents a numerical integration method for the non-linear viscoelastic behaviour of isotropic materials and structures. The Schapery's three-dimensional (3D) non-linear viscoelastic material model is integrated within a displacement-based finite element (FE) environment. The deviatoric and volumetric responses are decoupled and the strain vector is decomposed into instantaneous and hereditary parts. The hereditary strains are updated at the end of each time increment using a recursive formulation. The constitutive equations are expressed in an incremental form for each time step, assuming a constant incremental strain rate. A new iterative procedure with predictor–corrector type steps is combined with the recursive integration method. A general polynomial form for the parameters of the non-linear Schapery model is proposed. The consistent algorithmic tangent stiffness matrix is realized and used to enhance convergence and help achieve a correct convergent state. Verifications of the proposed numerical formulation are performed and compared with a previous work using experimental data for a glassy amorphous polymer PMMA. Copyright © 2003 John Wiley & Sons, Ltd.
209 citations
TL;DR: In this paper, a multiscale simulation of plastic deformation of metallic specimens using physically-based models that take into account their polycrystalline microstructure and the directionality of deformation mechanisms acting at single-crystal level is presented.
202 citations
TL;DR: In this paper, the perturbed Lagrangian function is introduced for the discrete description of the contact problem, where the perturbation of the Lagrangians is expressed as a perturbed Gaussian function.
Abstract: SUMMARY In the numerical solution of geometrically nonlinear contact problems by the finite element method, it is often assumed that the modification to the tangent stiffness takes the form of the single rank-one-update characteristic of the linear theory. It is shown that due to the kinematic nonlinearity such a simple structure no longer holds. Within the context of the discrete problem arising from a finite element formulation, explicit expressions for the residual and the tangent stiffness matrix are obtained for both penalty and Lagrangian parameter procedures. FORMULATION OF THE DISCRETE PROBLEM By introducing the perturbed Lagrangian functional, both penalty and Lagrange parameter procedures may be presented in a unified manner. For the discrete description of the contact problem, the perturbed Lagrangian function, re, may be expressed as
197 citations
TL;DR: In this article, a two-node catenary cable element, derived using exact analytical expressions for the elastic catenary, is proposed for the modeling of cables, and the cable element tangent stiffness matrix and internal force vector are evaluated accurately and efficiently using an iterative procedure.
196 citations