scholarly journals Effective strain gradient continuum model of metamaterials and size effects analysis

2020 ◽  
Author(s):  
Hua Yang ◽  
Dmitry Timofeev ◽  
Ivan Giorgio ◽  
Wolfgang H. Müller
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Continuum Model ◽  
Effective Strain

scholarly journals Size effects of mechanical metamaterials: a computational study based on a second-order asymptotic homogenization method

2020 ◽  
Author(s):  
Hua Yang ◽  
Wolfgang H. Müller
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Effective Strain ◽  
Homogenization Method ◽  
Second Order ◽  
Strain Gradient Theory ◽  
Asymptotic Homogenization ◽  
Aspect Ratios ◽  
Mechanical Metamaterials ◽  
Asymptotic Homogenization Method

Abstract In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient theory is used. By this method, the metamaterials are homogenized and become effective strain gradient continua. The effective metamaterial parameters including the classical and strain gradient stiffness tensors are calculated. Comparisons between a detailed finite element analysis and the effective strain gradient continua model have been made for metamaterials under different boundary conditions, different aspect ratios, different unit cells (closed or open cells) and different topologies. It shows that both stiffening and softening size effects can be captured by using the effective strain gradient continua models.

Scale-Dependent Crack Modeling for Investigation the Effect of Geometrically Necessary Dislocations in Micro/Nano Grain Size of Copper

2016 ◽  
Vol 15 ◽  
pp. 1-16 ◽  
Author(s):  
Amin Zaami ◽  
Ali Shokuhfar
Keyword(s):  
Grain Size ◽  
Stress Concentration ◽  
Strain Gradient ◽  
Stress Concentration Factor ◽  
Size Effects ◽  
Crack Tip ◽  
Length Scale ◽  
State Variables ◽  
Dependent Model ◽  
Homogeneous Strain

In this study, a scale-dependent model is employed to investigate the size effects of copper on the behavior of the crack-tip. This model includes the homogeneous and non-homogeneous strain hardening based on the wavelet interpretation of size effect. Introducing additional micro/nano structural considerations together with decreasing grain size, different size effects can be obtained. As the size dependency is not taken into account in conventional plasticity, an enhanced theory which is related to the strain gradient introduces a length scale will give more realistic representations of state variables near the crack-tip. Accordingly, the contribution of geometrically necessary dislocations (GNDs) activity on strengthening and stress concentration factor is identified in the crack-tip. Finally, the affected zone which is dominated by presence of GNDs is identified

Material-length-scale-controlled nanoindentation size effects due to strain-gradient plasticity

2003 ◽  
Vol 51 (15) ◽  
pp. 4461-4469 ◽  
Author(s):  
Minhua Zhao ◽  
William S. Slaughter ◽  
Ming Li ◽  
Scott X. Mao
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Material Length Scale ◽  
Material Length

FREQUENCY SPECTRA OF FREE LATTICES AND PARTICLE SIZE EFFECTS ON THE HEAT CAPACITY OF SOLIDS

1955 ◽  
Vol 33 (6) ◽  
pp. 1079-1087 ◽  
Author(s):  
D. Patterson
Keyword(s):  
Particle Size ◽  
Heat Capacity ◽  
Low Temperature ◽  
Temperature Effect ◽  
Size Effects ◽  
Continuum Model ◽  
Free Boundaries ◽  
Frequency Spectra ◽  
Optical Modes ◽  
Effect Of Particle Size

The effect of particle size on the heat capacity of solids has been investigated using lattices with free boundaries as models. A monatomic lattice shows a low temperature effect associated with the acoustic modes. This can be compared with results obtained from a continuum model. With a diatomic lattice, however, an effect is also associated with the optical modes and is apparent at higher temperatures. The possibility that this latter effect can explain some recent experimental results is examined.

Strain gradient and wavelet interpretation of size effects in yield and strength

2003 ◽  
Vol 35 (8) ◽  
pp. 733-745 ◽  
Author(s):  
I. Tsagrakis ◽  
A. Konstantinidis ◽  
E.C. Aifantis
Keyword(s):  
Strain Gradient ◽  
Size Effects
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