Introduction to Continuum Damage Mechanics

Kachanov, L. M.; Krajčinović, Dušan

doi:10.1115/1.3173053

Cited by 122 publications

(106 citation statements)

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“…In general, damage accumulation can occur under elastic deformation (fatigue), elastic-plastic deformation (ductile plastic damage), or under creep conditions (creep damage). In more complex cases, d can assume the form of a vector function or fourth order tensor (Kachanov, 1986). Here, we assume the simple case where d is a scalar function of the equivalent plastic strains.…”

Section: Resultsmentioning

confidence: 99%

Characterization of indentation response and stiffness reduction of bone using a continuum damage model

Zhang¹,

Michalenko²,

Kuhl³

et al. 2010

Journal of the Mechanical Behavior of Biomedical Materials

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Indentation tests can be used to characterize the mechanical properties of bone at small load/length scales offering the possibility of utilizing very small test specimens, which can be excised using minimally-invasive procedures. In addition, the need for mechanical property data from bone may be a requirement for fundamental multi-scale experiments, changes in nano-and micro-mechanical properties (e.g., as affected by changes in bone mineral density) due to drug therapies, and/or the development of computational models. Load vs. indentation depth data, however, is more complex than those obtained from typical macro-scale experiments, primarily due to the mixed state of stress, and thus interpretation of the data and extraction of mechanical properties is more challenging. Previous studies have shown that cortical bone exhibits a visco-elastic response combined with permanent deformation during indentation tests, and that the load vs. indentation depth response can be simulated using a visco-elastic/plastic material model. The model successfully captures the loading and creep displacement behavior, however, it does not adequately reproduce the unloading response near the end of the unloading cycle, where a pronounced decrease in contact stiffness is observed. It is proposed that the stiffness reduction observed in bone results from an increase in damage; therefore, a plastic-damage model was investigated and shown capable of simulating a typical bone indentation response through an axisymmetric finite element simulation. The plasticdamage model was able to reproduce the full indentation response, especially the reduced stiffness behavior exhibited during the latter stages of unloading. The results suggest that the plastic-damage model is suitable for describing the complex indentation response of bone and may provide further insight into the relationship between model parameters and mechanical/physical properties.

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Section: Resultsmentioning

confidence: 99%

Characterization of indentation response and stiffness reduction of bone using a continuum damage model

Zhang¹,

Michalenko²,

Kuhl³

et al. 2010

Journal of the Mechanical Behavior of Biomedical Materials

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“…In anisotropic cases of non-random crack orientations, it should be changed to a symmetric second rank crack density tensor [10]:…”

Section: Spherical Pores and Circular Or Elliptical Cracksmentioning

confidence: 99%

Quantitative characterization of microstructures of plasma-sprayed coatings and their conductive and elastic properties

Sevostianov

Kachanov

Ruud

et al. 2004

Materials Science and Engineering: A

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“…Based on basic damage mechanics (Kachanov, 1986, Lemaitre, 1996), the microdamage density ( D ) can be simply defined as follows:

D = 1 - \frac{E_{i}}{E_{0}}

where E i is the instantaneous modulus and E 0 is the original modulus.…”

Section: Empirical Constitutive Relationshipsmentioning

confidence: 99%

“…Kachanov’s damage model states that damage evolves as a power law function of the effective stress (Kachanov, 1986). Krajcinovic et al (Krajcinovic, et al, 1987) proposed a linear elastic damage model using a simple statistical mode of fiber pull-out.…”

Section: Introductionmentioning

confidence: 99%

Constitutive relationship of tissue behavior with damage accumulation of human cortical bone

Luo¹,

Leng²,

Acuna³

et al. 2010

Journal of Biomechanics

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Microdamage accumulation has been identified as a major conduit for bone tissues to absorb fracture energy. Due to the poor understanding of its underlying mechanism, however, an adequate constitutive relationship between damage accumulation and the mechanical behavior of bone has not yet been established. In this study, the constitutive relationship between the damage accumulation induced by overload and the evolution of mechanical properties of bone with incremental deformation was established based on the experimental results obtained from a novel progressive loading protocol developed in our laboratory. First, a decayed exponential model was proposed to capture the damage accumulation (modulus loss) with increasing applied strain. Next, a power law function was proposed to represent the progression of plastic deformation with damage accumulation. Finally, a linear combination of the Kohlrausch-Williams-Watts (KWW) function and Debye function was used to depict the viscoelastic behavior of bone associated with damage accumulation. The results of this study may help develop a constitutive model for predicting the mechanical behavior of cortical bone tissues.

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Introduction to Continuum Damage Mechanics

Cited by 122 publications

References 0 publications

Characterization of indentation response and stiffness reduction of bone using a continuum damage model

Characterization of indentation response and stiffness reduction of bone using a continuum damage model

Quantitative characterization of microstructures of plasma-sprayed coatings and their conductive and elastic properties

Constitutive relationship of tissue behavior with damage accumulation of human cortical bone

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