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Research Papers

Effect of Specimen Size on the Dissipated Energy Density in Compression

[+] Author and Article Information
Giuseppe Ferro1

 Department of Structural Engineering and Geotechnics, Corso Duca degli Abruzzi 24, Politecnico di Torino, 10129 Torino, Italyferro@polito.it

Alberto Carpinteri

 Department of Structural Engineering and Geotechnics, Corso Duca degli Abruzzi 24, Politecnico di Torino, 10129 Torino, Italy

1

Corresponding author.

J. Appl. Mech 75(4), 041003 (May 09, 2008) (8 pages) doi:10.1115/1.2910899 History: Received August 09, 2006; Revised September 11, 2006; Published May 09, 2008

The size effects in compression on drilled cylindrical concrete specimens obtained from a unique concrete block over a large scale range (1:19) are analyzed. The experimental results show scale effects on dissipated energy density rather than on the compressive strength. A theoretical explanation for such a phenomenon is presented, assuming a noninteger physical dimension of the subdomain where dissipation occurs. A comparison between experimental and theoretical values is discussed and a renormalization procedure to obtain a scale-independent constitutive law is presented.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Geometries of the five different concrete specimens; (b) overall view of the five specimen sizes

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Figure 2

Stress-strain curves for four different cylindrical specimen sizes

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Figure 3

Normalized stress versus postpeak displacement for four different cylindrical specimen sizes

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Figure 4

Peak stresses by varying specimen size

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Figure 5

Physical meaning of exponent D; (a) at each step, only one cube is retained, while all the others are divided into 27 equalsized cubes with rn=13rn−1(D=2.93), very close to a volumetric fragmentation; (b) at each step, the eight angular cubes are retained, while all the others 19 are divided into 27 equal-sized cubes with rn=13rn−1(D=2.70); (c) and (d) at each step, the nine cubes are divided into 27 equal-sized cubes with rn=13rn−1, while the others 18 are retained (D=2.00), showing a localization of the dissipation energy

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Figure 6

Cumulative statistics for the proposed fragmentation models

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Figure 7

Size effect on dissipated energy density in compression

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Figure 8

Multifractal scaling law for volumetric energy dissipation versus size scale

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Figure 9

Bilogarithmic diagrams of dissipated energy density versus size: (a) three sizes; (b) four sizes

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Figure 10

Multifractal scaling law for two different material microstructures

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