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On apparent properties of nonlinear heterogeneous bodies smaller than the representative volume

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Summary

Huet's model for overall properties of specimens smaller than the representative volume is generalized on nonlinear heterogeneous elastic materials with imperfect interfaces. A modified definition for the apparent properties of heterogeneous nonlinear elastic bodies is given. The size effect relationships are established between experimental results obtained on a big specimen and on an appropriate set of smaller specimens. Hierarchies between the apparent properties of the families of specimens of different sizes are constructed.

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Abbreviations

D :

domain occupied in space by a material body

∂D :

boundary ofD

x :

position of a material point at timet

n :

outward normal

Γ:

internal interface of a heterogeneous body

[a]=a +−a− :

jump bracket ofa on an interface in the direction of the outward normal

σ:

stress tensor

ε:

strain tensor

ξ:

displacement vector

P :

traction vector density on a surface

〈a〉:

spatial average of the variablea on a domainD

x:

tensor product (dyadic)

∶:

twice contracted tensor product

syma :

symmetric part 1/2(a+a T) of the tensora

F ε,F σ :

potential energy and complementary energy functionals, respectively

S eff,C eff :

effective compliance and modulus tensors, respectively

S ε,C ε :

kinematic apparent compliance and modulus tensors, respectively

S σ,C σ :

static apparent compliance and modulus tensors, respectively

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  1. S. Hazanov (H-Consultants)

    Present address: , 29, rte Malagnov, CH-1208, Geneva, Switzerland

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    Hazanov, S. On apparent properties of nonlinear heterogeneous bodies smaller than the representative volume. Acta Mechanica 134, 123–134 (1999). https://doi.org/10.1007/BF01312651

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    • DOI: https://doi.org/10.1007/BF01312651

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