Strain gradient plasticity

By Huajian Gao. 2001

695 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8f25cfd27456c0949bf4bb2306e487ebeebc5f6e

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Multi-scale micromorphic theory for hierarchical materials (2007, methodology): “(7) for N ¼ 1, we have: dPint ¼ Z O r : dDþ b̄1 : ½dL1 dL þ b 1.. . dL1 r ( dO ¼ Z O r : dDþ b 1.. . dLr ( dO. ð25Þ This corresponds to the form of internal power used in the framework for strain gradient plasticity laid out by Fleck et al. (1994) and Fleck and Hutchinson (1997).”
Generalizing J2 flow theory: Fundamental issues in strain gradient plasticity (2012, background): “Here, following Fleck and Hutchinson [2,10], a strain gradient version of deformation theory will be introduced at the start.”
Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme (2002, methodology): “A selection of examples in the eld of metal–matrix composites has been collected, for example, in Reference [7].”
Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity (2001, methodology): “Their theory is built on the earlier work of Fleck and Hutchinson (1997), but involves making a number of additional constitutive assumptions, including an inhomogeneous coupling between strain and strain gradient in the definition of overall effective strain.”
Thin Film Materials: Stress, Defect Formation and Surface Evolution (2004, background): “(1994) and Fleck and Hutchinson (1997). The structure of the theory will not be discussed further here.”
Size effects in manufacturing of metallic components (2009, methodology): “Nix et al. [41] give a good introduction to the development of the strain gradient model by Ashby [42], Fleck and Hutchinson [43,44], while Bazant et al. published a comprehensive review on the development of the strain gradient models [45].”
On the origin of size effects in small-strain elasticity of solid polymers (vol 44, pg 1582, 2007) (2007, background): “In the following, we explore the link between xij,k, which is a third-order tensor, and the second-order curvature tensor, vij, related to rotational gradients, and defined, for example, in Fleck and Hutchinson (1997), Yang et al. (2002) and Lam et al. (2003).”
On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals (2004, background): “…has been developed that incorporate a length scale dependence in the constitutive response of the material through functional dependencies on the plastic strain gradient (MMulhaus and Aifantis, 1991; Fleck and Hutchinson, 1997; Shu and Fleck, 1999; Gao et al., 1999; Acharya and Bassani, 2000).”
Experiments and theory in strain gradient elasticity (2003, neutral): “Inthe derivations of Mindlin (1965) and Fleck and Hutchinson (1997), the Cauchy stress tensor, (cid:7) ij , and double stress tensor, (cid:16) ijk , are conjugated with the strain tensor and the second-order deformation gradient tensor via The variation of the total strain energy in the volume V of…”
Computational homogenization of cellular materials (2014, neutral): “[53]).”
Mixed finite element formulations of strain-gradient elasticity problems (2002, methodology): “An extensive summary of this experimental evidence is given in a recent review article by Fleck and Hutchinson [13].”
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications (2010, background): “Size effects can be introduced into CPFE frameworks by using phenomenological strain gradient theories which were developed by Fleck et al. [229], Fleck and Hutchinson [230], and Nix and Gao [231].”
Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension (2004, positive): “This leaves an intermediate region where strain gradient plasticity theory has been proposed to describe material behavior (Aifantis, 1992; Fleck and Hutchinson, 1993, 1997; Fleck et al., 1994; Gao et al., 1999a, b; Huang et al., 2000; Hutchinson, 2000; Bazant and Guo, 2001).”
Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity (2001, background): “A particular strain gradient plasticity formulation is advocated by Fleck and Hutchinson [18].”
A physically based gradient plasticity theory (2006, background): “The first framework involves higher-order stresses and higher-order (or additional) governing equations and therefore requires extra boundary conditions, such as the couple stress theory (e.g., Fleck and Hutchinson, 1993, 1997, 2001; Gurtin, 2002, 2003), and MSG theory.”
Metal forming progress since 2000 (2008, background): “An explanation for this phenomenon is given by the theory of strain gradient plasticity [26].”
Three-dimensional X-ray structural microscopy with submicrometre resolution (2002, neutral): “, and fundamental plastic deformation investigation”
Mechanism-based strain gradient plasticity—II. Analysis (2000, methodology): “4 , and the ratio b of mesoscale cell size l E to dislocation spacing at plastic yielding is 1 for solid lines and 10 for dashed lines . by stresses and higher - order stresses in the wire and external virtual work done by the torque , as detailed in Fleck and Hutchinson ( 1997 ) .”