Solving fracture problems using an asymptotic numerical method

Daridon, Loïc; Wattrisse, Bertrand; Chrysochoos, André; Potier‐Ferry, Michel

doi:10.1016/j.compstruc.2010.12.001

Cited by 6 publications

(4 citation statements)

References 27 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to solve Equation ( 6), the ANM is used, which is a continuation technique where the non-linear problem is transformed into a sequence of linear ones. This method has been successfully used in different fields, such as in fluid mechanics (Cadou, Cochelin, Damil, & Potier-Ferry, 2001) or recently to solve the fracture problem (Daridon, Wattrisse, Chrysochoos, & Potier-Ferry, 2011).…”

Section: Problem Formulationmentioning

confidence: 99%

Numerical comparison of reduced order models for non-linear vibrations of damped plates

Boumediene

Duigou

Miloudi

et al. 2012

TECM

View full text Add to dashboard Cite

This work deals with the computation of the non-linear solutions of the vibration of damped plates by coupling a harmonic balance method and the asymptotic numerical method. These computations can lead to lengthy central processing unit (CPU) times if the solution sought contains an important number of harmonics. In this study, we propose two reduced order models which can be applied to solve this type of problem. Both reduced methods are based on a first computation carried out with a small number of harmonics (here two). Numerical examples of plate vibration show that these algorithms help save a great deal of computational time and can be applied to problems involving numerous harmonics.

show abstract

Section: Problem Formulationmentioning

confidence: 99%

Numerical comparison of reduced order models for non-linear vibrations of damped plates

Boumediene

Duigou

Miloudi

et al. 2012

TECM

View full text Add to dashboard Cite

show abstract

“…Study of large strain plasticity in 2D problems (El Kihal et al, 2022a has recently been carried out using ANM. ANM has also been reported for fracture mechanics applications using cohesive zone model (Daridon et al, 2011) for 1D problems, where an elastic damage behavior is considered. Application of ANM, however, has not been attempted for the solution of viscoplasticity problems of steam turbine applications using the unified constitutive models.…”

Section: Introductionmentioning

confidence: 99%

Continuum damage mechanics of cyclic viscoplasticity using asymptotic numerical method

Sen,

Patel

2023

International Journal of Damage Mechanics

View full text Add to dashboard Cite

Conscious efforts on reduction of greenhouse gas emissions have led to an energy transition to renewable energy, however uncertainties of renewable energy production have resulted in higher thermal cycling demands from conventional power plants. Thermal load cycling at high temperature regions of steam turbine components leads to enhanced creep-fatigue damage accumulation. It is well established that such damage mechanism is numerically best predicted by unified constitutive modeling including damage as a variable as per the formalism of continuum damage mechanics at an expense of considerable computational efforts using finite element analysis. In this paper, the non-iterative Asymptotic Numerical Method (ANM), currently limited to partial cycle analysis with linear hardening plasticity model, is proposed for the first time to address cyclic viscoplasticity problems including damage capable of handling multiple cycles and most generalized loading conditions. Regularization techniques additionally necessary to implement loading-unloading-reloading criteria and advanced constitutive models etc. are presented. The constitutive model chosen for the formulation includes the non-linear multiple back stress variable modified Chaboche model to include damage combined with modified Chaboche-Rousselier isotropic hardening model to include damage, power law for viscoplasticity, Lemaitre’s damage potential and Kachanov-Rabotnov’s creep damage law. The method is verified with defined error measures and then applied to two high pressure steam turbine rotors, one with and another without thermal stress relief groove (TSRG) at the inlet under service type loading conditions to study the beneficial effect of the TSRG on creep-fatigue damage evolution. The accumulated errors of the proposed ANM and computational time are compared to a conventional Newton-Raphson solution.

show abstract

“…However, for sake of simplicity, only isothermal transformations are considered in the following sections, and the chosen state variables are the displacement jump vector u and a scalar damage variable, denoted by 𝑢 d . This damage variable 𝑢 d is the maximum of the equivalent opening displacement as used in many papers such as (Ortiz and Pandolfi 1999;van den Bosch et al 2006;Park et al 2009;Daridon et al 2011;Blal et al 2011) for example.…”

Section: Introductionmentioning

confidence: 99%

A damage criterion based on energy balance for isotropic cohesive zone model

Chrysochoos

Daridon

Renouf

2022

Journal of Theoretical, Computational and Applied Mechanics

View full text Add to dashboard Cite

The objective of this paper is to present an energy damage criterion for cohesive zone models (CZM) within the framework of the non-linear thermodynamics of irreversible processes (TIP). An isotropic elastic damageable material is considered for isothermal transformations. Damage is then the only irreversible effect accompanying the deformation process and this mechanism is supposed to be fully dissipative. Once a separation law and a damage state variable have been chosen, the paper shows that the damage criterion can be automatically derived from the energy balance. From this observation, a CZM is derived for a given choice of traction-separation law and damage state variable and the quality of its numerical predictions is analyzed using an experimental benchmark bending test extracted from literature. Finally, damage, elastic and dissipated energy fields around the crack path are shown during this rupture test.

show abstract

Solving fracture problems using an asymptotic numerical method

Cited by 6 publications

References 27 publications

Numerical comparison of reduced order models for non-linear vibrations of damped plates

Numerical comparison of reduced order models for non-linear vibrations of damped plates

Continuum damage mechanics of cyclic viscoplasticity using asymptotic numerical method

A damage criterion based on energy balance for isotropic cohesive zone model

Contact Info

Product

Resources

About