Inelastic Material Models Research Articles

Delamination growth analysis in laminated structures with continuum-based 3D-shell elements and a viscoplastic softening model

In this paper we consider the simulation of delaminations in composite structures. For this purpose we discuss two aspects of a numerical treatment. The first one is the formulation of an accurate 3D-shell element to describe the global as well as the local behaviour in laminates in a proper way. Here a refined eight-node brick element is presented. The modifications of the element are based on assumed natural strain – and enhanced assumed strain methods. This element is used in the second part of the paper to describe delamination within an interface element with a small but non-vanishing thickness. Thus, strains, stresses and the delamination criterion are calculated in a standard manner from the displacement field and the material law. We introduce – based on an extension of the delamination criterion of Hashin (J. Appl. Mech. 47 (1980) 329–334) – an inelastic material model with softening. Here, the critical energy-release rate G c is the crucial parameter to describe the damage behaviour. Furthermore, a viscoplastic regularization with strain rates according to an approach of Duvaut and Lions is used to prevent negative stiffness parameters in the consistent tangent operators. Numerical calculations show the successful application of the 3D-shell element and the delamination concept.

Application of an extrapolation method in thermocyclic failure analysis

Applying of modern inelastic material models requires much computer resources. This especially is a decisive problem for simulating cyclic loadings of components having a high number of cycles lifetime. To overcome this problem, we extrapolate the complete set of internal variables over a certain number of cycles. The reduction of computer time amounts to a factor of 10–1000. To demonstrate the capabilities of our new scheme, a failure analysis has been carried out for a ring combustor of a gas turbine. The material model used for this investigation is based on the well-known Chaboche model in combination with the damage model by Kachanov/Rabotnov.

Nonlocking Beam Finite Elements for Use with Inelastic Material Models

A locking-assessment procedure for shear-deforming beam elements is proposed that is suitable for inelastic material behavior. By way of example, the procedure is used to motivate the formulation of a nonlocking element in the context of an isotropic but inelastic (e.g., J2-flow theory with isotropic hardening) constitutive model. In particular, constraints among the nodal degrees of freedom (dof) are introduced to ensure uniform, non-shear-locking element behavior. The locking-assessment procedure distinguishes between locking, stiffening, and uniform element behavior in the thin-beam limit by comparing the dimensions of the function spaces containing the bending strains, both in the presence and absence of the thin-beam constraints. Inter-dof constraints that lead to uniform behavior are seen to arise naturally from this element-assessment procedure. Also, a novel cross-sectional numerical integration scheme is presented that is highly accurate in relation to the number of stress-sampling points on the cross section.

Numerical Integrators for Elastic-Secondary Creep

A method has been developed for building error maps to present the accuracy of time-dependent inelastic material models similar to the error maps used for time-independent plasticity. The elastic-secondary creep constitutive model with a Norton creep behavior is used throughout the paper to illustrate the method. It is noted that this is very simple unified creep-plasticity model with no internal state variables, i.e., no back stress or change in the drag stress. The error maps for nine integrators, which are used or have been proposed to be used for creep or unified creep-plasticity models, are then presented. Included are an explicit Euler integrator, explicit Runge-Kutta methods of second, third, and fourth orders, three implicit integrators, and two integrators, which have been specially designed for this equation. A quantitative measure of the accuracy of an integrator is also defined and applied to the nine integrators. A special integrator for the equation was found to be best and the Euler method ranked sixth. Other considerations for choosing an optimum integrator is also discussed.

A unified approach for parameter identification of inelastic material models in the frame of the finite element method

This work is concerned with identification of parameters for inelastic material models. In order to account for possible non-uniformness of stress and strain distributions, the identification is performed in the frame of the finite element method. In particular, linearization procedures are described in a systematic manner for the case of complex material models within a geometric linear theory. This unified approach allows one to apply the Newton method for solving the associated direct problem and to apply gradient based methods for solving the associated inverse problem, which is considered as an optimization problem. Two numerical examples demonstrate the versatility of our approach: firstly, we consider Cooks membrane problem based on simulated data for re-identification of material parameters for a viscoplastic power law. Furthermore, material data for J 2-flow theory are determined, based on experimental data obtained by a grating method for a compact specimen, and we will investigate the results by using different starting values and stochastic perturbation of the experimental data.

Inelastic Large Displacement Behavior and Buckling of Cooling Tower

Inelastic, large displacement behavior of reinforced concrete hyperbolic cooling towers is studied using a finite-element program developed on the Cray Y-MP supercomputer. The large displacement effects are formulated based on the Lagrangian approach in which the displacements are measured from the original configuration of the structure. The concrete cracking is modeled using the rotating smeared crack approach and the bending deformation is represented using the layering technique. The concrete constitutive behavior is represented by a biaxial inelastic material model. The tension stiffening of concrete is modeled using gradual linear unloading of the stress strain curve of concrete. Several nonlinear analyses of the Grand Gulf cooling tower are performed. Unlike the results of previous investigations that attribute the failure of the cooling tower to the yielding of the meridional reinforcement, the results of this investigation show that the failure occurs due to the circumferential buckling in the vicinity of the throat triggered by the reduction of the stiffness due to concrete cracking.

Cyclic stress-strain response of polycrystalline copper in a wide range of plastic strain amplitudes: Polak, J., Obrtlik, K., Hajek, M. and Vasek, A. Mater Sci Eng AA151 1 (15 Apr 1992) pp 19–27

Applying of modern inelastic material models requires much computer resources. This especially is a decisive problem for simulating cyclic loadings of components having a high number of cycles lifetime. To overcome this problem, we extrapolate the complete set of internal variables over a certain number of cycles. The reduction of computer time amounts to a factor of 10–1000. To demonstrate the capabilities of our new scheme, a failure analysis has been carried out for a ring combustor of a gas turbine. The material model used for this investigation is based on the well-known Chaboche model in combination with the damage model by Kachanov/Rabotnov.

Experimental data and calculated results about the fatigue endurance limit of metals under multiaxial alternating load (Versuchs- und Rechendaten zur Dauerschwingfestigkeit von Metallischen Werkstoffen Unter Mehrachsiger Beanspruchung): Troost, A., Akin, O., and Klubberg, F. Materialwissenchaft und Werkstofftechnik23 1 (Jan 1992) pp 1–12 (in German)

Applying of modern inelastic material models requires much computer resources. This especially is a decisive problem for simulating cyclic loadings of components having a high number of cycles lifetime. To overcome this problem, we extrapolate the complete set of internal variables over a certain number of cycles. The reduction of computer time amounts to a factor of 10–1000. To demonstrate the capabilities of our new scheme, a failure analysis has been carried out for a ring combustor of a gas turbine. The material model used for this investigation is based on the well-known Chaboche model in combination with the damage model by Kachanov/Rabotnov.

Dynamic response sensitivity of inelastic structures

A general finite element solution method for the dynamic response sensitivity of inelastic structures is developed. Employing a direct differentiation method, the gradient equation of motion is solved without iteration and by taking advantage of the available solution of the response. Special attention is given to sensitivities with respect to inelastic material parameters and detailed derivations are made for the J 2 plasticity model with a linear hardening rule. The method can be applied to any other inelastic material model that has an analytically defined yield function and flow rule. The formulation is easily incorporated in existing finite element codes. Numerical examples demonstrate the accuracy and efficiency of the method.

Validation of Inelastic Analysis by Full-Scale Component Testing

This paper compares theoretical and experimental results for full-scale, prototypical components tested at elevated-temperatures to provide validation for inelastic analysis methods, material models, and design limits. Results are discussed for piping elbow plastic and creep buckling, creep ratcheting, and creep relaxation; nozzle creep ratcheting and weld cracking; and thermal striping fatigue. Comparisons between theory and test confirm the adequacy of components to meet design requirements, but identify specific areas where life prediction methods could be made more precise.

Nonlinear structural and life analyses of a combustor linear

Three dimensional, nonlinear finite-element structural analyses were performed for a simulated combustor liner specimen to asses the capability of nonlinear analyses using classical inelastic material models to represent the thermoplastic-creep response of the one-half scale component. The structural analysis results indicated continued cyclic hardening and ratcheting while experimental data suggested a stable stress-strain response after only a few loading cycles. In addition, the computed stress-strain response after only a few loading cycles. In addition, the computed stress-strain history at the critical location was input into two lilfe prediction methods, Strainrange Partitioning and a Pratt and Whitney Combustor Life Prediction Method, to evaluate their ability to predict cyclic crack initiation. The life prediction analyses overpredicted the observed cyclic crack initiation life.