Theory of deformation in small volumes of material

It has long been controversial as to whether small volumes of material are, or should be, more resistant to plastic deformation than is implied by the yield strength of bulk material. We generalize the established theory of critical thickness for strained layers to show that there is an increase in the initial yield stress for geometrical reasons wherever there is a strain gradient. The theory is in quantitative agreement, without free fitting parameters, with the classic experimental data on the torsion of thin wires and on the bending of thin beams.