Exponential Softening

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Željana Nikolić - One of the best experts on this subject based on the ideXlab platform.

  • Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model
    Computer Methods in Applied Mechanics and Engineering, 2018
    Co-Authors: Mijo Nikolić, Adnan Ibrahimbegovic, Željana Nikolić
    Abstract:

    In this work we propose and compare the two models for crack propagation in dynamics. Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms. The first one is based on discrete lattice approach, where the domain is discretized with Voronoi cells held together prior to crack occurrence by cohesive links represented in terms of Timoshenko beams. The second one is based on constant strain triangular solid element. In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities. The latter remain localized inside the element, regulated by the localized traction separation behavior defined through Exponential Softening law. Thus, the both models provide the result that remain mesh-independent, with fracture energy as the model parameter. We show that implementation in dynamics framework can be obtained by adding inertial effects without modifying the existing quasi-statics models. In order to provide reliable results, classical implicit Newmark algorithm can be used for time integration. The two presented models are subjected to dynamic crack propagation benchmarks, where detailed analysis on strain, kinetic, plastic free and dissipated energy during simulation is verified by comparison to the amount of total work which is introduced into the system. The main strength of the proposed approach is that cracks initiation, propagation, their coalescence, merging and branching are automatically obtained without any tracking algorithms. In addition, since the discontinuities remain localized inside elements, accurate results can be obtained even with coarser grids, leading to efficient methodology capable of capturing complex crack patterns in dynamics.

Agelet C De Saracibar - One of the best experts on this subject based on the ideXlab platform.

  • Softening localization and stabilization capture of discontinuous solutions in j2 plasticity
    International Journal for Numerical and Analytical Methods in Geomechanics, 2004
    Co-Authors: Miguel Cervera, Michele Chiumenti, Agelet C De Saracibar
    Abstract:

    This paper exploits the concept of stabilization techniques to improve the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible or nearly incompressible situations. Elasto-J2-plastic constitutive behaviour has been considered with linear and Exponential Softening. Two different stabilization methods are used to attain global stability of the corresponding discrete finite element formulation. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the formulation derived is free of volumetric locking and spurious oscillations of the pressure. The results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with the standard, non-stabilized, approaches. Copyright © 2004 John Wiley & Sons, Ltd.

  • shear band localization via local j2 continuum damage mechanics
    Computer Methods in Applied Mechanics and Engineering, 2004
    Co-Authors: Miguel Cervera, Michele Chiumenti, Agelet C De Saracibar
    Abstract:

    This paper describes a novel formulation for the solution of problems involving shear band localization using a local isotropic J2 continuum damage model and mixed linear simplex (triangles and tetrahedra). Stabilization methods are used to ensure existence and uniqueness of the solution, attaining global and local stability of the corresponding discrete finite element formulation. Consistent residual viscosity is used to enhance robustness and convergence of the formulation. Implementation and computational aspects are also discussed. A simple isotropic local J2 damage constitutive model is considered, either with linear or Exponential Softening. The Softening modulus is regularized according to the material mode II fracture energy and the element size. Numerical examples show that the formulation derived is fully stable and remarkably robust, totally free of volumetric locking and spurious oscillations of the pressure. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with the ill-posed standard approaches. � 2004 Elsevier B.V. All rights reserved.

J Botsis - One of the best experts on this subject based on the ideXlab platform.

  • intralaminar fracture of unidirectional carbon epoxy composite experimental results and numerical analysis
    International Journal of Solids and Structures, 2016
    Co-Authors: G Pappas, J Botsis
    Abstract:

    Abstract Fracture of carbon fiber reinforced polymers (CFRPs) is dominated by large scale fiber bridging which acts as a very important toughening mechanism. The objective of this paper is to investigate the intralaminar Mode I fracture in a unidirectional CFRP composite in double cantilever beam specimens with thickness H  = 6, 10 and 14 mm with a symmetric intralaminar precrack introduced by a thin diamond wire saw. Optical fibers with 10 multiplexed Bragg grating sensors are glued onto the upper surface of selected specimens of H  = 6 and 10 mm, to measure the axial strain profile during fracture. The bridging tractions are expressed as a function of the maximum bridging stress, the bridging zone length and Exponential Softening parameter. The measured strains are input to an inverse parametric numerical model to obtain the traction separation relation due to bridging. The optimized strain distribution corresponds to a bridging traction profile, with a maximum bridging traction of ∼8.3 MPa. This stress is 6 times larger than the corresponding in interlaminar fracture value. The resultant resistance-curves increase with sample thickness in corresponding steps of 20%. The plateau energy release rate is ∼2.3 times higher than the corresponding interlaminar one, although having the same initial fracture toughness. The calculated energy contribution of bridging agrees very well with the produced resistance-curves. The resultant bridging law is applied over a cohesive element model to reproduce the load-displacement curves.

Mijo Nikolić - One of the best experts on this subject based on the ideXlab platform.

  • Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model
    Computer Methods in Applied Mechanics and Engineering, 2018
    Co-Authors: Mijo Nikolić, Adnan Ibrahimbegovic, Željana Nikolić
    Abstract:

    In this work we propose and compare the two models for crack propagation in dynamics. Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms. The first one is based on discrete lattice approach, where the domain is discretized with Voronoi cells held together prior to crack occurrence by cohesive links represented in terms of Timoshenko beams. The second one is based on constant strain triangular solid element. In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities. The latter remain localized inside the element, regulated by the localized traction separation behavior defined through Exponential Softening law. Thus, the both models provide the result that remain mesh-independent, with fracture energy as the model parameter. We show that implementation in dynamics framework can be obtained by adding inertial effects without modifying the existing quasi-statics models. In order to provide reliable results, classical implicit Newmark algorithm can be used for time integration. The two presented models are subjected to dynamic crack propagation benchmarks, where detailed analysis on strain, kinetic, plastic free and dissipated energy during simulation is verified by comparison to the amount of total work which is introduced into the system. The main strength of the proposed approach is that cracks initiation, propagation, their coalescence, merging and branching are automatically obtained without any tracking algorithms. In addition, since the discontinuities remain localized inside elements, accurate results can be obtained even with coarser grids, leading to efficient methodology capable of capturing complex crack patterns in dynamics.

R D S G Campilho - One of the best experts on this subject based on the ideXlab platform.

  • a cohesive zone element for mode i modelling of adhesives degraded by humidity and fatigue
    International Journal of Fatigue, 2018
    Co-Authors: M Costa, G Viana, Romain Creachcadec, L F M Da Silva, R D S G Campilho
    Abstract:

    Abstract A finite element is proposed, based on the cohesive zone model approach and implemented as a user element, for the modelling of adhesively bonded joints subjected to degradation by humidity and fatigue using software ABAQUS®. Functionality included in this element that is not available using standard cohesive zone elements includes: (a) various types of traction-separation laws, such as triangular with Exponential Softening, trapezoidal and Exponential, (b) an intuitive and easy to use graphical interface built in MATLAB that helps visualize all traction-separation laws, create the mesh, run the simulation and visualize the results, (c) custom degradation laws for both humidity and fatigue which allow the user to easily model the effects of said degrading parameters. It is shown that the trapezoidal traction-separation law is the most appropriate to model the experimental data in both unaged and aged specimens. The proposed fatigue degradation approach correctly predicts the number of cycles until failure of all unaged and aged conditions, thus proving itself as a very useful tool capable of modelling a vast array of experimental conditions and details that adhesive joints are subjected to in real world applications.