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Stefanie Reese - One of the best experts on this subject based on the ideXlab platform.
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a single Gauss Point continuum finite element formulation for gradient extended damage at large deformations
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Oliver Barfusz, Tim Brepols, Tim Van Der Velden, Jan Frischkorn, Stefanie ReeseAbstract:Abstract Some years ago, a family of large deformation continuum finite elements based on reduced integration was investigated by Reese (2005), Schwarze and Reese (2011) and Frischkorn and Reese (2015). Many structural components with different kinds of elastic and inelastic material behavior were considered and these elements showed accurate results while being more efficient than similar three-dimensional formulations based on full integration. The objective of the present contribution is to extend the analysis to non-local damage and fracture. To this end, the incorporation of the gradient-extended damage plasticity model for large deformations of Brepols et al. (2020) into the framework of reduced integration-based continuum elements is presented. For the sake of brevity, the present work is restricted to solids with only one integration (Gauss) Point in the center of the element. The weak form of the formulation, which is based on a two-field variational functional closely related to the enhanced-assumed strain (EAS) method is extended by the weak form of the micromorphic balance equation. The steps required in order to transform the extended formulation into a stable, robust and efficient single Gauss Point concept are described in detail. Due to the analogy to fully-coupled thermomechanical problems, the derivation of a novel micromorphic hourglass stabilization is based on earlier contributions of the research group. Therein, the Taylor series expansion of all constitutively dependent quantities plays a crucial role. Representative numerical examples of quasi-brittle and ductile fracture reveal the accuracy and efficiency of the proposed approach. Besides the ability to deliver mesh-independent results, the framework is especially suitable for constrained situations in which conventional low-order finite elements suffer from well-known locking phenomena.
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a large deformation solid shell concept based on reduced integration with hourglass stabilization
International Journal for Numerical Methods in Engineering, 2007Co-Authors: Stefanie ReeseAbstract:In this paper a new eight-node (brick) solid-shell finite element formulation based on the concept of reduced integration with hourglass stabilization is presented. The work focuses on static problems. The starting Point of the derivation is the three-field variational functional upon which meanwhile established 3D enhanced strain concepts are based. Important additional assumptions are made to transfer the approach into a powerful solid-shell. First of all, a Taylor expansion of the first Piola–Kirchhoff stress tensor with respect to the normal through the centre of the element is carried out. In this way the stress becomes a linear function of the shell surface co-ordinates whereas the dependence on the thickness co-ordinate remains non-linear. Secondly, the Jacobian matrix is replaced by its value in the centre of the element. These two assumptions lead to a computationally efficient shell element which requires only two Gauss Points in the thickness direction (and one Gauss Point in the plane of the shell element). Additionally three internal element degrees-of-freedom have to be determined to avoid thickness locking. One important advantage of the element is the fact that a fully three-dimensional stress state can be modelled without any modification of the constitutive law. The formulation has only displacement degrees-of-freedom and the geometry in the thickness direction is correctly displayed. Copyright © 2006 John Wiley & Sons, Ltd.
Antonio Huerta - One of the best experts on this subject based on the ideXlab platform.
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numerical differentiation for non trivial consistent tangent matrices an application to the mrs lade model
International Journal for Numerical Methods in Engineering, 2000Co-Authors: Agusti Perezfoguet, Antonio Rodriguezferran, Antonio HuertaAbstract:In Reference [1] the authors have shown that numerical differentiation is a competitive alternative to analytical derivatives for the computation of consistent tangent matrices. Relatively simple models were treated in that reference. The approach is extended here to a complex model: the MRS-Lade model [2,3]. This plastic model has a cone-cap yield surface and exhibits strong coupling between the flow vector and the hardening moduli. Because of this, derivating these quantities with respect to stresses and internal variables —the crucial step in obtaining consistent tangent matrices— is rather involved. Numerical differentiation is used here to approximate thesederivatives.Theapproximatedderivativesarethenused1)tocomputeconsistenttangentmatrices(globalproblem)and2)tointegratetheconstitutiveequation at each Gauss Point (local problem) with the Newton-Raphson method. The choice of the stepsize (i.e. the perturbation in the approximation schemes), based on the concept of relative stepsize, poses no difficulties. In contrast to previous approaches for the MRS-Lade model, quadratic convergence is achieved, for both the local and the global problems. The computational efficiency (CPU time) and robustness of the proposed approach is illustrated by means of several numerical examples, where the major relevant topics are discussed in detail.
B W Golley - One of the best experts on this subject based on the ideXlab platform.
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a time stepping procedure for structural dynamics using Gauss Point collocation
International Journal for Numerical Methods in Engineering, 1996Co-Authors: B W GolleyAbstract:When a cubic function is interpolated between the prescribed initial displacement and velocity and the exact displacement and velocity at the end of a time step for a single degree of freedom system, the error, or residual, in the governing equation is zero at a number of times. It is shown that for a general undamped system, in the limit as the time step approaches zero these times correspond to Gauss Points. This observation is verified by considering a general collocation procedure in which the displacement in any time step is approximated as a cubic function of time, with two coefficients chosen to satisfy the displacement and velocity at the beginning of the time step with the other two coefficients being chosen to satisfy the governing differential equation at any two times. It is shown that optimum accuracy is obtained if these Points are the Gauss Points. Detailed expressions are then presented for this particular case, and stability of the algorithm is investigated showing that the procedure is conditionally stable. For time steps which are a small proportion of the least period of vibration of the structure, the algorithm is considered to be the most accurate possible procedure based on cubic approximation of the displacement.
Khemais Saanouni - One of the best experts on this subject based on the ideXlab platform.
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Thermomechanical modeling of distortional hardening fully coupled with ductile damage under non-proportional loading paths
International Journal of Solids and Structures, 2018Co-Authors: Kai Zhang, Houssem Badreddine, Khemais SaanouniAbstract:In order to capture, as accurately as possible, the complex physical effects during texture evolution of high strength materials subject to non-proportional loading paths at high temperature, a macroscale thermo-mechanical model is developed. This model accounts, in the framework of large inelastic strains, for anisotropic thermo-elasto-viscoplasticity with isotropic, kinematic and distortional hardenings strongly coupled with isotropic ductile damage. Following the footsteps of François (2001), induced anisotropy is modeled to predict the behavior under complex non-proportional loading paths. The initial plastic anisotropy and tension-compression asymmetry are considered through two different temperature dependent fourth-rank tensors. The full coupling of thermo-mechanical model with ductile damage is considered based on the total energy equivalence assumption. The proposed constitutive equations are implemented into finite element code ABAQUS/Explicit using appropriate user subroutine VUMAT. The local integration algorithm (at each Gauss Point) of the developed model is based on a fully-implicit scheme. Applications have been made to three different materials (aluminum alloy AU4G T4 (2024), titanium alloy Ti-6Al-4V and magnesium alloy AZ31) to demonstrate the predictive capabilities of the proposed model.
Chloé Arson - One of the best experts on this subject based on the ideXlab platform.
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Anisotropic nonlocal damage model for materials with intrinsic transverse isotropy
International Journal of Solids and Structures, 2018Co-Authors: Jin Wencheng, Chloé ArsonAbstract:Abstract This paper presents the theoretical formulation and numerical implementation of an anisotropic damage model for materials with intrinsic transverse isotropy. Crack initiation and propagation are modeled by phenomenological damage evolution laws, controlled by four equivalent strain measures. The latter are constructed so as to distinguish the mechanical response of the material in tension and compression, along the direction perpendicular to the bedding plane and within the bedding plane. To avoid mesh dependency induced by softening, equivalent strains are replaced by nonlocal counterparts, defined as weighted averages over a neighborhood scaled by two internal length parameters. Finite Element equations are solved with a normal plane arc length control algorithm, which allows passing limit Points in case of snap back or snap through. The model is calibrated against triaxial compression tests performed on shale, for different confinements and loading orientations relative to the bedding plane. Gauss Point simulations confirm that the model successfully captures the variation of uniaxial tensile strength with respect to the bedding orientation. Finite Element simulations of three-Point bending tests and compression splitting tests show that nonlocal enhancement indeed avoids mesh dependency, and that the axial and transverse dimensions of the damage process zone are scaled by the two characteristic lengths. Results further show that the damage process zone is direction dependent both in tension and compression. The model can be used for any type of textured brittle material; it allows representing several concurrent damage mechanisms in the macroscopic response and interpreting the failure mechanisms that control the damage process zone.