On boundary conditions and plastic strain-gradient discontinuity in lower-order gradient plasticity

2004 ◽  
Vol 52 (8) ◽  
pp. 1793-1826 ◽  
Author(s):  
Amit Acharya ◽  
Huang Tang ◽  
Sunil Saigal ◽  
John L. Bassani
Keyword(s):  
Plastic Strain ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Lower Order ◽  
Gradient Plasticity ◽  
Plastic Strain Gradient

Gradient of Soil Constitutive Model

2010 ◽  
Vol 168-170 ◽  
pp. 1126-1129
Author(s):  
Wen Xu Ma ◽  
Ying Guang Fang
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Soil Analysis ◽  
Natural Material ◽  
Flow Rule ◽  
The Finite Element Method ◽  
Gradient Effect ◽  
Non Local ◽  
Associated Flow Rule ◽  
Plastic Strain Gradient

For the soil is a very complex natural material, significant strain gradient effect exist in soil analysis. Based on the "gradient" phenomenon, we add the plastic strain gradient hardening item into the traditional Cambridge yield surface. By using the consistency conditions and associated flow rule, we get the explicit expression of plastic strain gradient stiffness matrix. And the finite element method of plastic strain gradient is also shown in this article. Plastic strain gradient is actually a phenomenological non-local model containing microstructure information of the material. It may overcome the difficulties in simulating the gradient phenomenon by traditional mechanical model.

scholarly journals Equivalent plastic strain gradient enhancement of single crystal plasticity: theory and numerics

2012 ◽  
Vol 468 (2145) ◽  
pp. 2682-2703 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Thomas Böhlke
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Equivalent Plastic Strain ◽  
Plasticity Theory ◽  
Strain Gradient Theory ◽  
Local Algorithm ◽  
Alternative Formulation ◽  
Element Discretization ◽  
Gradient Enhancement ◽  
Plastic Strain Gradient

We propose a visco-plastic strain gradient plasticity theory for single crystals. The gradient enhancement is based on an equivalent plastic strain measure. Two physically equivalent variational settings for the problem are discussed: a direct formulation and an alternative version with an additional micromorphic-like field variable, which is coupled to the equivalent plastic strain by a Lagrange multiplier. The alternative formulation implies a significant reduction of nodal degrees of freedom. The local algorithm and element stiffness matrices of the finite-element discretization are discussed. Numerical examples illustrate the advantages of the alternative formulation in three-dimensional simulations of oligo-crystals. By means of the suggested formulation, complex boundary value problems of the proposed plastic strain gradient theory can be solved numerically very efficiently.

A new strain-gradient theory for an isotropic plastically deformed polycrystalline solid body

2017 ◽  
Vol 23 (9) ◽  
pp. 1333-1344 ◽  
Author(s):  
AS Borokinni ◽  
AP Akinola ◽  
OP Layeni ◽  
OO Fadodun
Keyword(s):  
Plastic Strain ◽  
Solid Body ◽  
Strain Gradient ◽  
Plasticity Theory ◽  
Flow Rule ◽  
Gradient Plasticity ◽  
Polycrystalline Solid ◽  
Work Done ◽  
Strain Gradient Plasticity Theory ◽  
Internal Microstresses

This study considers strain-gradient plasticity theory in the context of small deformations for an isotropic solid body with a view to investigating the distortion effects associated with the divergence of plastic strain through the Burgers tensor. The principle of virtual power is employed and the constraint of irrotationality is imposed on the plastic component of the gradient of the displacement vector. It is obtained that the gradient, curl, and divergence of the plastic strain in the body are mutually related. This relation establishes the existence of work done through the divergence of plastic strain as distinct from the work done through the gradient of the plastic strain. Consequently, a polycrystalline solid body undergoing distortion associated with the divergence of plastic strain exhibits new internal microstresses; and the obtained model, consisting of the microforce balance, constitutive relations, and plastic flow rule, extends the known Gurtin–Anand model in a natural fashion. Furthermore, in the governing flow rule, it is revealed that the internal microstresses associated with the divergence of plastic strain act as opposing agents to the internal microstresses associated with the gradient of the plastic strain via the length scales Q, L, and the gradient of the divergence of the plastic strain. This work shows the distortion effects associated with the divergence of plastic strain which the Gurtin–Anand strain-gradient plasticity theory in literature does not apprehend.

Microscopy and microindentation mechanics of single crystal Fe−3 wt. % Si: Part II. TEM of the indentation plastic zone

1993 ◽  
Vol 8 (6) ◽  
pp. 1300-1310 ◽  
Author(s):  
W. Zielinski ◽  
H. Huang ◽  
W.W. Gerberich
Keyword(s):  
Plastic Strain ◽  
Plastic Zone ◽  
Single Crystal ◽  
Strain Gradient ◽  
Continuum Models ◽  
Large Loop ◽  
Direct Observations ◽  
Small Loop ◽  
Secondary Reactions ◽  
Plastic Strain Gradient

Direct observations of dislocation arrangements about a range of microindentations into the [100] face of an Fe−3 wt. % Si single crystal have been accomplished. Dislocations of both large loop character initiated from the indenter and small loop character initiated as secondary reactions are found. Analysis of these allows the various contributions to the plastic strain gradient around the indentation to be assessed, with the experimental observations being reasonably consistent with continuum models.

scholarly journals The combined effect of size, inertia and porosity on the indentation response of ductile materials

2020 ◽  
Author(s):  
Jose Rodriguez-Martinez ◽  
Tiago dos Santos ◽  
Ankit Srivastava
Keyword(s):  
Plastic Strain ◽  
Size Effect ◽  
Porous Materials ◽  
Strain Gradient ◽  
Cavity Expansion ◽  
Material Hardness ◽  
Parametric Analyses ◽  
Expansion Model ◽  
Indentation Response ◽  
Plastic Strain Gradient

Herein, we present a self-similar cavity expansion model that follows from the work of Cohen and Durban (2013b) to analyze the dynamic indentation response of elasto-plastic porous materials while accounting for the plastic strain gradient induced size effect. The incorporation of the plastic strain gradient induced size effect in the dynamic cavity expansion model for elasto-plastic porous materials is the key novelty of our model. The predictions of the cavity expansion model for the material hardness, for different indentation depths and speeds, are compared against the available experimental results for OFHC copper, for strain rates varying from 10−4 s−1 to 108 s−1. We note that despite several simplifying assumptions, the predictions of our cavity expansion model show a reasonable agreement with the experimentally measured material hardness over a wide range of indentation depths and speeds. In addition, we have also carried out parametric analyses to elucidate the specific roles of indentation speed, size effect and initial porosity, on the material hardness and cavitation fields that develop during the indentation process. In particular, our parametric analyses show that there exists a critical value of the indentation speed beyond which the contribution of inertial effect becomes extremely important and the material hardness increases rapidly. While the influence of the initial porosity on the material hardness is found to increase with increasing indentation speed and decrease with increasing size effect.

scholarly journals An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems

2018 ◽  
Vol 45 (2) ◽  
pp. 177-188
Author(s):  
Adebowale Borokinni ◽  
Odunayo Fadodun ◽  
Adegbola Akinola
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Plane Strain ◽  
Strain Gradient ◽  
Dissipative Process ◽  
Strain Gradient Plasticity ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Gradient Plasticity ◽  
Plane Strain Problem

This article considers a plane strain gradient plasticity theory of the Gurtin?Anand model [M. Gurtin, L. Anand, A theory of strain gradient plasticity for isotropic, plastically irrotational materials Part I: Small deformations, J. Mech. Phys. Solids 53 (2005), 1624?1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin?Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.

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