A one-dimensional theory of strain-gradient plasticity: Formulation, analysis, numerical results

Anand, Lallit; Gurtin, Morton E.; Lele, Suvrat P.; Gething, C.

doi:10.1016/j.jmps.2005.03.003

Cited by 154 publications

(152 citation statements)

References 17 publications

Supporting

Mentioning

136

Contrasting

Order By: Relevance

“…Based on the static theory of strain-gradient viscoplasticity proposed by Anand (2005) and Lele (2008a)'s work, in this section, first we derive a variational formulation for the dynamic analysis. Then, the principle of virtual power is introduced taking into account inertia and body forces in order to obtain the macroscopicand microsopic-force balances.…”

Section: Governing Equationsmentioning

confidence: 99%

“…With such the constitutive theory, the free energy depends on the gradient of plastic strains and strain hardening depends on the plastic strain and a scalar measure to the accumulation of geometrically necessary dislocation as well as a dissipative part of a vector microstress to depend on the gradient of the plastic strain rate. Based on Gurtin's work, Anand et al (2005), Lele and Anand (2008a, 2008b) developed the strain gradient theory for isotropic viscoplastic materials for small and large deformations.…”

Section: Introductionmentioning

confidence: 99%

“…Among the strain-gradient theories mentioned above, the static approaches developed by Gurtin (2000Gurtin ( , 2002Gurtin ( , 2003, Anand (2005) and Lele (2008aLele ( , 2008bLele ( , 2009) are particularly interesting for our study since they can be extended easily to dynamic analysis with integrating strain-gradient viscoplasticity law. Therefore, as the first attempt, this paper presents a one-dimensional dynamic analysis based on the static theory of strain-gradient plasticity proposed by Anand et al (2005), Lele (2008a).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, as the first attempt, this paper presents a one-dimensional dynamic analysis based on the static theory of strain-gradient plasticity proposed by Anand et al (2005), Lele (2008a). We will establish the equation of motion and variational formulation for finite element computation of isotropic hardening materials.…”

Section: Introductionmentioning

confidence: 99%

“…Dynamic effects such as microscopic inertia effects, artificial damping are discussed. Besides, we investigated the effects of hard boundary conditions proposed by Anand (2005) for the dynamic cases to find out more suitable boundary conditions such that the obtained results without length scales are close to that of the conventional plasticity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A one-dimensional dynamic analysis of strain-gradient viscoplasticity

Nguyen¹,

Stoffel²,

Weichert³

2010

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A one-dimensional dynamic analysis of strain-gradient viscoplasticity

Nguyen¹,

Stoffel²,

Weichert³

2010

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

Analysis and comparison of two finite element algorithms for dislocation density based crystal plasticity

2013

View full text Add to dashboard Cite

The purpose of the current work is the formulation and comparison of two finite element algorithms for a dislocation density based crystal plasticity model. We study multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The work is an extension of the first investigation in Klusemann et al. [1] which was limited to a one-dimensional bar. In the γ -algorithm, the displacement u and glide system slips γα are global unknowns and determined via weak field relations. The non-dimensional densities of geometrically necessary dislocations ρ̄α are local quantities and solved for via a strong field relation. In the Q -algorithm, both the displacement uand dislocation densities ρ̄α are modeled as global, and the glide system slips γα as local. As it turns out, both algorithms generally predict the same microstructural behavior on a single crystal level. However, for a polycrystal the two solution strategies predict different material behaviors due to the formulation-dependent representation of the boundary conditions. The introduction of a boundary layer in the model leads to good agreement between both algorithms for single and polycrystal simulations. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

show abstract

A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

et al. 2019

View full text Add to dashboard Cite

Motivated by the increasing interest of the biomechanical community towards the employment of strain‐gradient theories for solving biological problems, we study the growth and remodeling of a biological tissue on the basis of a strain‐gradient formulation of remodeling. Our scope is to evaluate the impact of such an approach on the principal physical quantities that determine the growth of the tissue. For our purposes, we assume that remodeling is characterized by a coarse and a fine length scale and, taking inspiration from a work by Anand, Aslan, and Chester, we introduce a kinematic variable that resolves the fine scale inhomogeneities induced by remodeling. With respect to this variable, a strain‐gradient framework of remodeling is developed. We adopt this formulation in order to investigate how a tumor tissue grows and how it remodels in response to growth. In particular, we focus on a type of remodeling that manifests itself in two different, but complementary, ways: on the one hand, it finds its expression in a stress‐induced reorganization of the adhesion bonds among the tumor cells, and, on the other hand, it leads to a change of shape of the cells and of the tissue, which is generally not recovered when external loads are removed. To address this situation, we resort to a generalized Bilby‐Kröner‐Lee decomposition of the deformation gradient tensor. We test our model on a benchmark problem taken from the literature, which we rephrase in two ways: microscale remodeling is disregarded in the first case, and accounted for in the second one. Finally, we compare and discuss the obtained numerical results.

show abstract

A one-dimensional theory of strain-gradient plasticity: Formulation, analysis, numerical results

Cited by 154 publications

References 17 publications

A one-dimensional dynamic analysis of strain-gradient viscoplasticity

A one-dimensional dynamic analysis of strain-gradient viscoplasticity

Analysis and comparison of two finite element algorithms for dislocation density based crystal plasticity

A study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

Contact Info

Product

Resources

About