For the Lamé system with two hard inclusions a distance ε apart, all m-th derivatives blow up at the optimal rate (ε+...)^(-m/2), with log factors in 3D and matching lower bounds in symmetric cases.
Stress concentration for two nearly touching circular holes
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abstract
We consider the plane elasticity problem for two circular holes. When two holes are close to touching, the stress concentration happens in the narrow gap region. In this paper, we characterize the stress singularity between the two holes by an explicit function. A new method of a singular asymptotic expansion for the Fourier series with slowing decaying coefficients is developed to investigate the asymptotic behavior of the stress.
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Optimal higher derivative estimates for solutions of the Lam\'e system with closely spaced hard inclusions
For the Lamé system with two hard inclusions a distance ε apart, all m-th derivatives blow up at the optimal rate (ε+...)^(-m/2), with log factors in 3D and matching lower bounds in symmetric cases.