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(1)
(2)
Where f t and _/£ are the dynamic tensile and compressive strengths respectively; f ts and f cs are the
static tensile and compressive strengths respectively; £ r and £ c are the tensile and compressive strain
rates respectively;^and£ cs are the static strain rates in tension and in compression respectively
(f tt = €„ = 10" 5 j' 1 ). Test results indicate that the dynamic modulus of elasticity increases with the
strain rate. A slightly decrease of critical strain (strain at peak stress) in compression at high stain
rates has been observed, but no visible change of critical stain in tension with the strain rate can be
found. Some researchers indicated that the Poisson's ratio of concrete increases with the strain rate
when subjected to tension and decreases with the strain rate when subjected to compression. In our
experiments test results dispersed to some extent, it is difficult to correlate the dynamic Poisson's
ratio with the stain rate.
RATE-DEPENDENT CONSTITUTIVE MODEL OF CONCRETE
Wang (1997) proposed a viscoplastic consistency model for analyzing metal, which can be seen as
an extension of the classical elasto-plastic approach to account for rate dependency. The model can
relatively, easily be implemented in place of classical rate-independent plasticity models (Winnicki
et al 2001). In this model during viscoplastic flow, the actual stress state must remain on the yield
surface. That is, for visvcoplastic loading, the yielding surface is expressed as
/(cr y ,/r,K-) = 0 for A>0 (3)
Where o;, is the component of stress tensor; K is the internal variable and A is the viscoplastic
multiplier. The viscoplastic strain rate is defined as €"f - /bi y , and for the associated flow rule
m tj = d//3cr y . Thus, the yield surface is rate dependent and can change its size and shape
according to the value of the viscoplastic strain rate.
The consistency condition is formulated as
Assume that the rate of internal variable K is a linear function of viscoplastic multiplier of the form