This work derives internal pressure induced stresses in material imbedded with square-shaped microchannels. The first part provides background on microchanneled materials at micro and nanoscale to motivate investigating the stress and deformation states. The second part develops a simplified model to characterize the plastic flow and/or motion of dislocations within crystalline, microchanneled materials. The model helps identify slip bands around the channels under plane strain deformation

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... tions. The third part derives solutions to the stress states around the microchannels, obtaining closed form solutions which hold for regions containing and away from the channel boundary. Figures depict the stress solutions in both physical and stress space. The results predict nonuniform deformation states around the channels and also reveal the yield conditions associated with the plastic flow along different slip bands. The work concludes with case studies on the stress states of microneedles containing square microchannels for applications such as fluid injection, nanofiber growth, and cell registration.