Gradient plasticity theory with a variable length scale parameter

Voyiadjis, George Z.; Al‐Rub, Rashid K. Abu

doi:10.1016/j.ijsolstr.2004.12.010

Cited by 238 publications

(120 citation statements)

References 82 publications

Supporting

Mentioning

118

Contrasting

Order By: Relevance

“…Averaging these local plastic shear strains over the entire ASB will lead to the nonlocal plastic shear strain, as can be easily confirmed through integrating (1) with respect to the coordinate y 2 ( w/2 −w/2 γ p (y 2 )dy 2 ), and then divided by the ASB width. For two and three-dimensional cases, the Laplacian will appear in GDP [Askes et al 2000;Peerlings et al 2001;Simone et al 2004;Voyiadjis and Abu Al-Rub 2005;Peerlings 2007;Poh et al 2011]. GDP can be derived from the nonlocal theory [Askes et al 2000;Peerlings et al 2001] by expanding the plastic strain into a Taylor series, and by neglecting gradient terms of order four and higher.…”

Section: Shear Displacement Distribution Of a Flow Linementioning

confidence: 99%

“…The phenomenon of the same shear stress corresponding to different shear strains cannot be uniquely described by classical continuum models where no internal length parameter is included, so that the nonuniform strain distribution and nonlinear displacement distribution in the localized zone, as well as the zone size, cannot be accurately obtained. Among the enriched continuum models, nonlocal and gradient continua have been widely used to avoid pathological localization in numerical simulation [De Borst and Mühlhaus 1992;Pamin and De Borst 1995;Askes et al 2000;Menzel and Steinmann 2000;Peerlings et al 2001;Simone et al 2004;Voyiadjis and Abu Al-Rub 2005;Peerlings 2007;Poh et al 2011], as have the Cosserat continuum and viscoplastic theories [Bažant and Pijaudier-Cabot 1988;Shawki and Clifton 1989]. In gradient continua, second-order gradient-dependent plasticity (GDP) is usually adopted, and a few analytical solutions of the strain and strain rate distribution in the localized band have been derived in the one-dimensional tensile and shear cases [De Borst and Mühlhaus 1992;Pamin and De Borst 1995;Menzel and Steinmann 2000].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A model for the shear displacement distribution of a flow line in the adiabatic shear band based on gradient-dependent plasticity

Wang¹,

Ma²

2012

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

Based on second-order gradient-dependent plasticity (GDP), we establish the shear displacement distribution of material points of a flow line beyond the occurrence of the adiabatic shear band (ASB) at a position on a thin-walled tubular specimen in dynamic torsion. In the ASB, the shear displacements of a material point include two parts caused by homogeneous and inhomogeneous strain components, respectively. The former is assumed to be a linear function of the material point coordinate, while the latter is found to be a sinusoidal function of the coordinate due to the microstructural effect. For the Ti-6Al-4V alloy and two kinds of steels, the coefficients of the constant, linear, and nonlinear terms in the expression for the shear displacement distribution are determined by least-squares fitting for different widths and positions of the ASB. During the localized shear process, the coefficients of the linear and nonlinear terms are found to have increasing tendencies, while the deformed ASB width (which is larger than the width of the ASB central region) is slightly decreased. This investigation shows that secondorder GDP may be successfully applied in simulation of the shear displacement distribution of material points at flow lines in the ASBs.

show abstract

Section: Shear Displacement Distribution Of a Flow Linementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A model for the shear displacement distribution of a flow line in the adiabatic shear band based on gradient-dependent plasticity

Wang¹,

Ma²

2012

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

show abstract

“…Comparisons of the theoretical predictions and the experimental results are shown in Fig. 7 under the assumption that the intrinsic length keeps a constant for beams with different thicknesses, though Voyiadjis and Abu Al-Rub [64] thought the length scale parameter as a function of the course of deformation and the material micro-structural features. From Fig.…”

Section: Elastic Casementioning

confidence: 99%

“…This issue has attracted many researchers' interests, among which Gao et al [33] and Huang et al [36] introduced the intrinsic material length into their MSG theory based on the Taylor dislocation and identified the intrinsic length as (μ/σ Y ) 2 b, where μ is the shear modulus, σ Y the yield stress, and b the Burgers vector. Voyiadjis and Abu Al-Rub [64] discussed in detail the length scale parameter and proposed a physically based relationship for the length scale parameters as functions of the course of deformation and the material micro-structural features. As for the phenomenological strain gradient theories, such as Chen and Wang [2,53,54], Fleck and Hutchinson [1,29,30], and Hu et al [65], the intrinsic length can be obtained from the calibration of experimental data.…”

Section: Introductionmentioning

confidence: 99%

Size effect in micro-scale cantilever beam bending

Chen

Feng

2011

Acta Mech

View full text Add to dashboard Cite

When the thickness of metallic cantilever beams reduces to the order of micron, a strong size effect of mechanical behavior has been found. In order to explain the size effect in a micro-cantilever beam, the couple-stress theory (Fleck and Hutchinson, J Mech Phys Solids 41:1825-1857, 1993) and the C-W strain gradient theory (Chen and Wang, Acta Mater 48:3997-4005, 2000) are used with the help of the BernoulliEuler beam model. The cantilever beam is considered as the linear elastic and rigid-plastic one, respectively. Analytical results of the cantilever beam deflection under strain gradient effects by applying these two kinds of theories are obtained, from which we find an explicit relationship between the intrinsic lengths introduced in the two kinds of theories. The theoretical results are further used to analyze the experimental observations, and predictions by both theories are further compared. The results in the present paper should be useful for the design of micro-cantilever beams in MEMS and NEMS.

show abstract

“…This form is used for simplicity, motivated by analogy to linear elasticity theory, and also is used to provide a back stress dependent on the density of dislocations [60,64] or its gradient [51,53]. Remaining open issues pertaining to continuum modeling of dislocation defects in the context of gradient plasticity are quantification of the length scale parameter(s) required to normalize the energy [65] and proper selection of the metric tensor used to collapse the GND tensor to scalar form [55,66].…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Point and Line Defects in Cubic Lattices

Chung

Clayton

2007

Int J Mult Comp Eng

View full text Add to dashboard Cite

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 2008 REPORT TYPE Reprint DATES COVERED (From SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESA reprint from the International Journal for Multiscale Computational Engineering, vol. 5, nos. 3 and 4, pp. 203-226, 2007. 14. ABSTRACT A multilength scale method based on asymptotic expansion homogenization (AEH) is developed to compute minimum energy configurations of ensembles of atoms at the fine length scale and the corresponding mechanical response of the material at the coarse length scale. This multiscale theory explicitly captures heterogeneity in microscopic atomic motion in crystalline materials, attributed, for example, to the presence of various point and line lattice defects. The formulation accounts for large deformations of nominally hyperelastic, monocrystalline solids. Unit cell calculations are performed to determine minimum energy configurations of ensembles of atoms of body-centered cubic tungsten in the presence of periodic arrays of vacancies and screw dislocations of line orientations [111] or [100]. Results of the theory and numerical implementation are verified versus molecular statics calculations based on conjugate gradient minimization (CGM) and are also compared with predictions from the local Cauchy-Born rule. For vacancy defects, the AEH method predicts the lowest system energy among the three methods, while computed energies are comparable between AEH and CGM for screw dislocations. Computed strain energies and defect energies (e.g., energies arising from local internal stresses and strains near defects) are used to construct and evaluate continuum energy functions for defective crystals parameterized via the vacancy density, the dislocation density tensor, and the generally incompatible lattice deformation gradient. For crystals with vacancies, a defect energy increasing linearly with vacancy density and applied elastic deformation is suggested, while for crystals with screw d...

show abstract

Gradient plasticity theory with a variable length scale parameter

Cited by 238 publications

References 82 publications

A model for the shear displacement distribution of a flow line in the adiabatic shear band based on gradient-dependent plasticity

A model for the shear displacement distribution of a flow line in the adiabatic shear band based on gradient-dependent plasticity

Size effect in micro-scale cantilever beam bending

Multiscale Modeling of Point and Line Defects in Cubic Lattices

Contact Info

Product

Resources

About