TY - JOUR
T1 - Bending and fracture properties of small scale elastic beams : a nonlocal analysis
AU - Li, X. F.
AU - Wang, B. L.
PY - 2012
Y1 - 2012
N2 - Using the nonlocal elasticity theory, this paper presents a static analysis of a microbeam according to the Timoshenko beam model. A fourth-order governing differential equation is derived and a general solution is suggested. For a cantilever beam at nanoscale subjected to uniform distributed loading, explicit expressions for deflection, rotation and strain energy are obtained. The nonlocal effect decreases the deflection and maximum stress distribution. With a double cantilever beam model, the strain energy release rate of a cracked beam is evaluated, and the results obtained show that the strain energy release rate is decreased (hence an increased apparent fracture toughness is measured) when the beam thickness is several times the material characteristic length. However, in the absence of a uniformly distributed loading, the nonlocal beam theory fails to account for the size-dependent properties for static analysis. Particularly, the nonlocal Euler-Bernoulli beam can be analytically obtained from the nonlocal Timoshenko beam if the apparent shear modulus is sufficiently large.
AB - Using the nonlocal elasticity theory, this paper presents a static analysis of a microbeam according to the Timoshenko beam model. A fourth-order governing differential equation is derived and a general solution is suggested. For a cantilever beam at nanoscale subjected to uniform distributed loading, explicit expressions for deflection, rotation and strain energy are obtained. The nonlocal effect decreases the deflection and maximum stress distribution. With a double cantilever beam model, the strain energy release rate of a cracked beam is evaluated, and the results obtained show that the strain energy release rate is decreased (hence an increased apparent fracture toughness is measured) when the beam thickness is several times the material characteristic length. However, in the absence of a uniformly distributed loading, the nonlocal beam theory fails to account for the size-dependent properties for static analysis. Particularly, the nonlocal Euler-Bernoulli beam can be analytically obtained from the nonlocal Timoshenko beam if the apparent shear modulus is sufficiently large.
KW - fracture mechanics
KW - nanostructured materials
UR - http://handle.westernsydney.edu.au:8081/1959.7/uws:47014
U2 - 10.4028/www.scientific.net/AMM.152-154.1417
DO - 10.4028/www.scientific.net/AMM.152-154.1417
M3 - Article
SN - 1660-9336
VL - 152-154
SP - 1417
EP - 1426
JO - Applied Mechanics and Materials
JF - Applied Mechanics and Materials
ER -