Measurement of apparent young's modulus in the bending of cantilever beam by heterodyne holographic interferometry

Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity

“…On the contrary, generalized continuum theories intend to capture effects of microstructure extending the range of applicability of the 'continuum' concept in an effort to bridge the gap between classical continuum theories and atomiclattice theories. Notable examples appearing in relatively recent studies include the strengthening effects observed in bending and torsion (Kakunai et al 1985;Fleck et al, 1994;Stolken and Evans, 1998), the buckling of elastic fibers in composites (Fleck and Shu, 1995), micro-indentation experiments where the measured indentation hardness increases as the width of the indent decreases (Ma and Clarke, 1995;Poole et al, 1996), fracture of cellular materials , and scale effects in simple structural components (Giannakopoulos and Stamoulis, 2006). An interesting review on experiments in generalized continua is also given by Lakes (1995).…”

Measuring the nonlocal effects of a micro/nanobeam by the shifts of resonant frequencies

“…If the number of unknown parameters is more than one, such one-to-one relation does not exist. For example, the nonlocal effect due to the strain gradient elasticity theory ( l 2 ) concludes that "smaller is stiffer" ( Ellis and Smith, 1966;Gauthier and Jahsman, 1975;Kakunai et al, 1985;McFarland and Colton, 2005;Schijve, 1966 ). In contrast, the nonlocal effect due to the nonlocal elasticity theory says the opposite: "smaller is more compliant" ( Zhang et al, 2005 ).…”

“…However, the torsion test of aluminum-epoxy composite ( Gauthier and Jahsman, 1975 ), the bending tests of aluminum alloy ( Schijve, 1966 ), aluminum and low-carbon steel ( Ellis and Smith, 1966 ) all failed to detect the nonlocal effects of strain gradient elasticity. The failure reason was thought to be the measurement accuracy by Kakunai et al (1985) and by adopting a measurement method with much higher accuracy, their bending tests of high purity aluminum show that l 2 is one fifth of the grain size. As discussed later, besides the measurement accuracy, there are more reasons for the failure of detecting the nonlocal effects.…”

“…The above error sources can be significant and thus dramatically influence how we interpret the experimental data and thus bending rigidity. In the above experiments ( Ellis and Smith, 1966;Gauthier and Jahsman, 1975;Kakunai et al, 1985;McFarland and Colton, 2005;Schijve, 1966 ) and simulations ( Eringen, 1983;Wang and Hu, 2005;Zhang et al, 2005 ), there is only one unknown parameter: l 1 or l 2 . By matching the result of nonlocal theories with that of experiment or simulation, there is an one-to-one relation, which can uniquely determine l 1 or l 2 .…”

“…Similarly, Yang and Lakes (1982) bending tests of human bones conclude that l 2 in each specimen is different and its distribution ranges from 0.16 mm to 0.84 mm though the unit cell diameter of osteon keeps unchanged as 0.25 mm. In all of the above experiments ( Ellis and Smith, 1966;Gauthier and Jahsman, 1975;Kakunai et al, 1985;McFarland and Colton, 2005;Perkins and Thompson, 1973;Schijve, 1966;Yang and Lakes, 1981 ), there are multiple specimens are used to obtain l 2 by curve-fitting. There is a potential problem of using multiple specimens to determine the characteristic lengths for one material.…”