Finite Element studies on indentation size effect using a higher order strain gradient theory

Guha, Suman; Sangal, S.; Basu, S.

doi:10.1016/j.ijsolstr.2012.10.017

Cited by 24 publications

(8 citation statements)

References 38 publications

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“…It will be shown in Section 6 that these simplifying assumptions do not significantly degrade the predictive capability and accuracy of the homogenized solutions. From (34), (43), (46), and (47), the macro dissipation rate can be written as…”

Section: Homogenization Of Dissipationmentioning

confidence: 99%

“…This approximation renders the thermodynamic stress R in (47) redundant because the higher order flow rule is now neglected. Note, however, that r f H p still has to be resolved for in the numerical implementation so as to compute the higher order stress B in (46), which enters the homogenized force balance in (38).…”

Section: Homogenization Of Dissipationmentioning

confidence: 99%

“…The variations of plasticity kinematic fields are related to those of basic variables through (C.8) and (C.10) (see derivations in Appendix C), which are next substituted into the linearized stresses in (72) based on their constitutive relations in (46). The numerical framework is thus assembled as Ä K 11 K 12 following the indicial notations in (C.1).…”

Section: Consistent Linearizationmentioning

confidence: 99%

“…The constitutive relations in (46) and (47) capture the effects arising from the non-uniform intra-granular deformation through variables (44) and (45). In general, the exact fluctuation functions in (40) and (41) are not known a priori.…”

Section: Appendix A: Fluctuation Functions For Plane Deformationmentioning

confidence: 99%

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Numerical implementation and validation of a consistently homogenized higher order plasticity model

Poh

Phan

2015

Numerical Meth Engineering

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Summary A homogenization theory was developed earlier that starts with a meso‐scale gradient plasticity model at the bottom and recovers a macroscopically continuous micromorphic model at the top. Through the scale transition framework, the granular mechanics are smeared consistently over a single grain such that the fine scale properties, microstructural length scale (l), and grain size (L) manifest themselves naturally in the homogenized relations, a point of departure from many continuous higher order theories that assume the constitutive relations a priori. This paper elaborates on the numerical implementation of the homogenized model and benchmark its performance through a plane indentation example against detailed numerical simulations. For the two limiting cases of microfree and microhard condition at grain boundaries, the excellent predictive capability of the homogenized model is demonstrated for a range of l/L ratios, at a significantly lower computational cost. It is furthermore highlighted that a more realistic response at grain boundaries can be achieved easily in the homogenized model, by changing the interfacial resistance parameter. In contrast, a non‐trivial numerical treatment is required at the grain boundaries with meso‐scale models. Finally, the homogenized model is shown to perform well even in the absence of a strong scale separation between meso and macro. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Homogenization Of Dissipationmentioning

confidence: 99%

Section: Homogenization Of Dissipationmentioning

confidence: 99%

Section: Consistent Linearizationmentioning

confidence: 99%

Section: Appendix A: Fluctuation Functions For Plane Deformationmentioning

confidence: 99%

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Numerical implementation and validation of a consistently homogenized higher order plasticity model

Poh

Phan

2015

Numerical Meth Engineering

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“…The first one involves high-order stresses as the work-conjugate to the strain gradient with high-order boundary conditions. Typical examples include Fleck et al (1994), Fleck and Hutchinson (1997), Gao et al (1999), Hwang et al (2003), Yi et al (2010) and Guha et al (2013). Another framework retains the essential structure of the classical plasticity without any high-order stress, in which the strain gradient comes into play through the incremental plastic hardening modulus or a yield criterion.…”

Section: Introductionmentioning

confidence: 99%

The coupling effect of size and damage in micro-scale metallic materials

Ban

Yao

Chen

et al. 2017

International Journal of Plasticity

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a b s t r a c tIn order to characterize the deformation behavior accompanying damage of microstructures in micro-scale metallic materials, a new theoretical model is developed based on a low order strain gradient plasticity theory. Not only the size effect induced by strain gradient plasticity but also the one of microstructure damage induced by deformation is considered. The feature of the new theory includes two aspects: the strain gradient is taken as an internal variable to affect the tangential hardening modulus without the introduction of high-order stress or high-order boundary condition; both the elastic modulus and the involved intrinsic length are influenced by the microstructural damage. Two commonly used samples with size effect in micro-scales, i.e., the thin wire torsion and the ultra-thin beam bending, are re-analyzed with the new model. It is found that stiffness of the micro-scale material is gradually reduced along with the increasing deformation and the theoretical prediction is consistent well with the existing experimental data. All the results demonstrate that the present theory should be a promising way for predicting the mechanical behavior of a more complex system, for example, the micro-particle reinforced metal matrix composite and the recent-hot-studied nano-crystallized gradient materials.

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Size-dependent stress intensity factors in a gradient elastic double cantilever beam with surface effects

2018

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Finite Element studies on indentation size effect using a higher order strain gradient theory

Cited by 24 publications

References 38 publications

Numerical implementation and validation of a consistently homogenized higher order plasticity model

Numerical implementation and validation of a consistently homogenized higher order plasticity model

The coupling effect of size and damage in micro-scale metallic materials

Size-dependent stress intensity factors in a gradient elastic double cantilever beam with surface effects

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