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non-local continuum

wave propogation in with non local deformation

I have a one dimensional bar with a triangular pulse given at one end for 2 microseconds. The boundary conditions are free-free.I am having two cases. One in which the deformation is local (Hooke's law) and other in which the deformation is dependent on a kernel of radius r (say 5* element length).I find that the wave speed is higher when the deformation is non-local as compared to local deformation case. Is this correct? Is there a way to verify the solution?

WaiChing Sun's picture

representative elementary volume of non-local continuum

Dear mechanicans,

        For non-local continuum, is there a proper approach to determine the size of the REV in experiment? For the classical linear elastic continuum, one can measure the homogeneized stress and strain (or local averaged stress/strain)  and compute a homogeneized elastic constitutive tensor. However, I am not sure how to do it for non-local continuum, since the constitutive response is now sensititve to the gradient term. Any comment/suggestion is appreciated. 


 WaiChing Sun


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