TY - JOUR
T1 - Scale effects in materials with random distributions of needles and cracks
AU - Ostoja-Starzewski, Martin
N1 - Funding Information:
Extensive comments of Prof. C. Huet (Ecole Polytechnique Fédérale de Lausanne) on the research reported here are gratefully acknowledged. We also benefited from the discussions with Prof. I. Jasiuk (Georgia Tech) and Mr. R. Muzzolini (Ecole des Mines de Paris). This research was made possible by the grant CMS-9713764 from the National Science Foundation.
PY - 1999/12/1
Y1 - 1999/12/1
N2 - According to a classical prescription of micromechanics, a representative volume element (RVE) is well defined when the response under uniform displacement (Dirichlet) boundary condition becomes the same as that under uniform stress (Neumann) boundary condition. We study the convergence of both responses in anti-plane elasticity of sheets with non-periodic, random distributions of thin needle-shaped inclusions. By lowering the stiffness of inclusions and increasing their aspect ratio (up to 100), we approach the situation of cracks embedded in a matrix. We show that, with the needles' stiffness decreasing and their slenderness growing, the RVE tends to be very large. The statistics of the first and second invariants of both response tensors are very well modeled by a Beta probability distribution. For moderate aspect ratio needles, the coefficient of variation of the second invariant is found to stay at about 0.5 irrespective of the window size, the mismatch in stiffness between the inclusions and the matrix, and the needle aspect ratio.
AB - According to a classical prescription of micromechanics, a representative volume element (RVE) is well defined when the response under uniform displacement (Dirichlet) boundary condition becomes the same as that under uniform stress (Neumann) boundary condition. We study the convergence of both responses in anti-plane elasticity of sheets with non-periodic, random distributions of thin needle-shaped inclusions. By lowering the stiffness of inclusions and increasing their aspect ratio (up to 100), we approach the situation of cracks embedded in a matrix. We show that, with the needles' stiffness decreasing and their slenderness growing, the RVE tends to be very large. The statistics of the first and second invariants of both response tensors are very well modeled by a Beta probability distribution. For moderate aspect ratio needles, the coefficient of variation of the second invariant is found to stay at about 0.5 irrespective of the window size, the mismatch in stiffness between the inclusions and the matrix, and the needle aspect ratio.
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U2 - 10.1016/S0167-6636(99)00039-3
DO - 10.1016/S0167-6636(99)00039-3
M3 - Article
AN - SCOPUS:0033340049
SN - 0167-6636
VL - 31
SP - 883
EP - 893
JO - Mechanics of Materials
JF - Mechanics of Materials
IS - 12
ER -