A phase field model for fracture based on the strain gradient elasticity theory with hybrid formulation

2021 ◽  
Vol 256 ◽  
pp. 107975
Author(s):  
Baiwei Zhang ◽  
Jun Luo
Keyword(s):  
Elasticity Theory ◽  
Phase Field ◽  
Strain Gradient ◽  
Field Model ◽  
Phase Field Model ◽  
Gradient Elasticity ◽  
Strain Gradient Elasticity ◽  
Strain Gradient Elasticity Theory ◽  
Hybrid Formulation ◽  
Gradient Elasticity Theory

Size Dependent Vibration Behavior of an AFM with Sidewall and Top-Surface Probes Based on the Strain Gradient Elasticity Theory

2015 ◽  
Vol 07 (03) ◽  
pp. 1550046 ◽  
Author(s):  
Mohammad Abbasi
Keyword(s):  
Elasticity Theory ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Strain Gradient Theory ◽  
Strain Gradient Elasticity ◽  
Size Dependent ◽  
Vibration Behavior ◽  
Vertical Extension ◽  
Strain Gradient Elasticity Theory ◽  
Gradient Elasticity Theory

In this paper, the size-dependent vibration behavior of an atomic force microscope with assembled cantilever probe (ACP) is analyzed utilizing the modified strain gradient elasticity theory. The proposed ACP comprises a horizontal cantilever, a vertical extension and two tips located at the free ends of the cantilever and extension. Because the vertical extension is located between the clamped and free ends of the microcantilever, the cantilever is modeled as two beams. The results of the current model are compared to those evaluated by both modified couple stress and classical beam theories. The results indicate that the resonant frequency and sensitivity of the proposed ACP is strongly size-dependent especially when the contact stiffness is very low or it is very high. The results also declare that utilizing the strain gradient theory is essential in the analysis of the vibration behavior of the proposed ACP.

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