A continuum approach to brittle and fatigue damage: Theory and numerical procedures

Paas, Mhjw Michel; Schreurs, Pjg Piet; Brekelmans, Wam Marcel

doi:10.1016/0020-7683(93)90189-e

Cited by 65 publications

(49 citation statements)

References 15 publications

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“…A large number of purely phenomenological fatigue damage cumulative laws have been proposed since the middle of this century [15] [16]. Within the framework of continuum damage mechanics, several fatigue damage laws for homogeneous materials were developed recently (see, for example, [3] [36]). In [35][42], the application of CDM to the fatigue of heterogeneous media is also explored.…”

Section: Fatigue Damage Cumulative Lawmentioning

confidence: 99%

“…Based on the same concept, two similar fatigue damage cumulative laws have been developed in [35] for homogeneous material and [36] for concrete on macroscopic scale. It has been proved in [36], by assuming constant exponent in the power law, that fatigue damage cumulation law in the form of (33) can be reduced to the modified Palmgreen-Miner's model [16].…”

Section: Figure 2 Comparison Between Static and Fatigue Damage Cumulmentioning

confidence: 99%

“…It has been proved in [36], by assuming constant exponent in the power law, that fatigue damage cumulation law in the form of (33) can be reduced to the modified Palmgreen-Miner's model [16]. More sophisticated fatigue damage model reveals that the exponent is better off defined as a stress dependent parameter, i.e.…”

Section: Figure 2 Comparison Between Static and Fatigue Damage Cumulmentioning

confidence: 99%

“…In recent years several fatigue models have been developed within the framework of continuum damage mechanics (CDM) [10][12] [29][35] [36]. Within this framework, internal state variables are introduced to model the fatigue damage.…”

Section: Introductionmentioning

confidence: 99%

“…An efficient integrator, or the so-called "cycle jump" technique [9], for the integration of fatigue damage cumulative law must be developed for the fully coupled fatigue analysis. Several efforts have been made in this area as reported in [12] and [36].…”

Section: Introductionmentioning

confidence: 99%

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Computational mechanics of fatigue and life predictions for composite materials and structures

Fish

2002

Computer Methods in Applied Mechanics and Engineering

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A multiscale fatigue analysis model is developed for brittle composite materials. The mathematical homogenization theory is generalized to account for multiscale damage effects in heterogeneous media and a closed form expression relating nonlocal microphase fields to the overall strains and damage is derived. The evolution of fatigue damage is approximated by the first order initial value problem with respect to the number of load cycles. An efficient integrator is developed for the numerical integration of the continuum damage based fatigue cumulative law. The accuracy and computational efficiency of the proposed model for both low-cycle and high-cycle fatigue are investigated by numerical experimentation. IntroductionIn recent years several fatigue models have been developed within the framework of continuum damage mechanics (CDM) [10][12] [29][35] [36]. Within this framework, internal state variables are introduced to model the fatigue damage. The degradation of material response under cyclic loading is simulated using constitutive equations which couple damage cumulation and mechanical responses. The microcrack initiation and growth are lumped together in the form of the evolution of damage variables from zero to some critical value. Most of the existing CDM based fatigue damage models are based on the classical (local) continuum damage theory even though it is well known that the accumulation of damage leads to strain softening and loss of ellipticity in quasi-static problems and hyperbolicity in dynamic problems (see, for example, [45] revealed the intrinsic links between the nonlocal CDM theory and fracture mechanics providing a possibility for building a unified framework to simulate crack initiation, propagation and overall structural failure under cyclic loading.When applying the CDM based fatigue model to life prediction of engineering systems, the coupling between mechanical response and damage cumulation poses a major computational challenge. This is because the number of cycles to failure, especially for high-cycle fatigue, is usually as high as tens of millions or more, and therefore, it is practically not feasible to carry out a direct cycle-by-cycle simulation for the fully coupled models even with today's powerful computers. An efficient integrator, or the so-called

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Section: Fatigue Damage Cumulative Lawmentioning

confidence: 99%

Section: Figure 2 Comparison Between Static and Fatigue Damage Cumulmentioning

confidence: 99%

Section: Figure 2 Comparison Between Static and Fatigue Damage Cumulmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational mechanics of fatigue and life predictions for composite materials and structures

Fish

2002

Computer Methods in Applied Mechanics and Engineering

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Gradient-enhanced damage modelling of high-cycle fatigue

Peerlings

Brekelmans

Borst

et al. 2000

Int. J. Numer. Meth. Engng.

155

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Continuum damage mechanics can be used to model the initiation and growth of fatigue cracks. However, finite element analyses using standard fatigue damage formulations exhibit an extreme sensitivity to the spatial discretisation of the problem. The mesh sensitivity is caused by the fact that the underlying continuum model predicts instantaneous, perfectly brittle crack growth as soon as a crack has been initiated. The growth of damage localizes in a vanishing volume during this instantaneous growth. This localization is not so much due to loss of ellipticity of the problem, but is caused by the fact that the damage rate is singular at the crack tip. The damage rate singularity can be removed by the introduction of higher‐order deformation gradients in the constitutive modelling. As a result, crack growth at a finite rate and with a positive amount of energy dissipation is predicted. Finite element analyses converge to this solution and are thus no longer pathologically dependent on the spatial discretization. Copyright © 2000 John Wiley & Sons, Ltd.

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Computational modelling of microcracking effects in polycrystalline piezoelectric ceramics

2008

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MSC (2000) 82D45, 74R20, 74M25Piezoelectric ceramics nowadays are widely commercialised in various fields of engineering technology and related constitutive modelling approaches constitute an active field of research. The physical performance of these materials is often limited by fatigue effects, possibly in combination with micro-cracking phenomena. In this contribution, such micro-crackbased fatigue effects in ferroelectric materials are computationally investigated by applying a cohesive-type approach embedded into a finite element context. The geometry or rather discretisation of a representative specimen elaborated in this work refers to a natural grain structure on the meso-level. Accordingly, the overall response of the underlying grains is approximated by means of coupled continuum elements, while the grain boundaries are discretised with interface elements. Interfacial constitutive relations are chosen to reflect highcycle-fatigue, which finally is demonstrated by a fatigue-motivated benchmark-type boundary value problem.

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A continuum approach to brittle and fatigue damage: Theory and numerical procedures

Cited by 65 publications

References 15 publications

Computational mechanics of fatigue and life predictions for composite materials and structures

Computational mechanics of fatigue and life predictions for composite materials and structures

Gradient-enhanced damage modelling of high-cycle fatigue

Computational modelling of microcracking effects in polycrystalline piezoelectric ceramics

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