Plane Asymptotic Interface Crack Solutions in Gradient Elasticity Theory

2016 ◽  
Vol 713 ◽  
pp. 151-154
Author(s):  
Michal Kotoul ◽  
Tomáš Profant ◽  
Petr Padělek
Keyword(s):  
Fracture Mechanics ◽  
Elasticity Theory ◽  
Plane Strain ◽  
Interface Crack ◽  
Strain Gradient ◽  
Special Form ◽  
Gradient Elasticity ◽  
Strain Gradient Elasticity ◽  
The Past ◽  
Gradient Elasticity Theory

The goal of the contribution is to develop an asymptotic interface crack-tip solution under conditions of plane strain for a bi-material that obeys a special form of linear isotropic gradient elasticity. Several fracture mechanics problems have been solved in the past within the framework of strain gradient elasticity which is capable to capture additional length/size parameters. However to our best knowledge no solution concerning an interface crack is available in the literature.

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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