Modeling and Analysis of Size-Dependent Structural Problems by Using Low-Order Finite Elements with Strain Gradient Plasticity

2011 ◽  
Vol 35 (9) ◽  
pp. 1041-1050 ◽  
Author(s):  
Moon-Shik Park ◽  
Yeong-Sung Suh ◽  
Seung Song
Keyword(s):  
Finite Elements ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Modeling And Analysis ◽  
Size Dependent ◽  
Structural Problems ◽  
Low Order

scholarly journals A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190258 ◽  
Author(s):  
Andrea Panteghini ◽  
Lorenzo Bardella ◽  
Christian F. Niordson
Keyword(s):  
Strain Gradient ◽  
Free Energy Density ◽  
Higher Order ◽  
Strain Gradient Plasticity ◽  
Threshold Values ◽  
Gradient Plasticity ◽  
Proportional Loading ◽  
Size Dependent ◽  
Plastic Potential ◽  
Dislocation Density Tensor

We propose a plastic potential for higher-order (HO) phenomenological strain gradient plasticity (SGP), predicting reliable size-dependent response for general loading histories. By constructing the free energy density as a sum of quadratic plastic strain gradient contributions that each transitions into linear terms at different threshold values, we show that we can predict the expected micron-scale behaviour, including increase of strain hardening and strengthening-like behaviour with diminishing size. Furthermore, the anomalous behaviour predicted by most HO theories under non-proportional loading is avoided. Though we demonstrate our findings on the basis of Gurtin (Gurtin 2004 J. Mech. Phys. Solids 52 , 2545–2568, doi:10.1016/j.jmps.2003.11.002 ) distortion gradient plasticity, adopting Nye's dislocation density tensor as primal HO variable, we expect our results to hold qualitatively for any HO SGP theory, including crystal plasticity.

Length Scale in Solder Joints Materials

2006 ◽  
Author(s):  
Juan Gomez ◽  
Cemal Basaran
Keyword(s):  
Strain Gradient ◽  
Constitutive Models ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Additional Material ◽  
Size Dependent ◽  
Dependent Behavior ◽  
Material Length Scale ◽  
Material Length

Strain gradient plasticity theories that have emerged during recent years to provide an explanation for size dependent behavior exhibited by some materials have also created a need for additional material parameters. In this study on Pb/Sn solder alloys the material length scale, which is needed for use in strain gradient plasticity type constitutive models, is determined. The value of length scale is in agreement with values available in the literature for different materials like copper, nickel and aluminum.

Low Order Finite Element Modeling of Size Effects in Micro Structured Materials Based on Strain Gradient Plasticity

2011 ◽  
Author(s):  
Moon Shik Park ◽  
Yeong Sung Suh ◽  
Seung Song
Keyword(s):  
Finite Element ◽  
Strain Gradient ◽  
Size Effects ◽  
Strain Gradient Plasticity ◽  
Dislocation Model ◽  
Gradient Plasticity ◽  
Structured Materials ◽  
Close Proximity ◽  
Micro Indentation ◽  
Low Order

A low order finite element method using theory of strain gradient plasticity along with Taylor dislocation model was developed to evaluate size effects occurring in micro structured materials. The gradient is evaluated in the framework of nonlinear incremental analysis where plastic strains are calculated and averaged at nodes then interpolated and differentiated. The proposed method was verified by solving typical size effect problems such as micro-bending, micro-indentation, and tensile test of a particle-reinforced metal matrix composite. The predicted results show clear length scale effect and close proximity to the respective experimental results.

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