A variational formulation is provided for the modified couple stress theory of Yang et al. by using the principle of minimum total potential energy. This leads to the simultaneous determination of the equilibrium equations and the boundary conditions, thereby complementing the original work of Yang et al. where the boundary conditions were not derived. Also, the displacement form of the modified couple stress theory, which is desired for solving many problems, is obtained to supplement the existing stress-based formulation. All equations/expressions are presented in tensorial forms that are coordinate-invariant. As a direct application of the newly obtained displacement form of the theory, a simple shear problem is analytically solved. The solution contains a material length scale parameter and can capture the boundary layer effect, which differs from that based on classical elasticity. The numerical results reveal that the length scale parameter (related to material microstructures) can have a significant effect on material responses. (2000). 74A10, 74A20, 74A60, 74B05. Mathematics Subject Classification

Biopolymers from soy protein isolate (SPI) crosslinked with glutaraldehyde (GA) were prepared. Surface hydrophobicities of SPI-GA biopolymers and SPI were 4.4 and 11.5, respectively. The solubility profile of SPI was slightly higher than that of SPI-GA biopolymers. Foaming capacities of SPI-GA biopolymers (23 mL) were higher than that of SPI (19 mL), but similar to egg white (22 mL). Foaming stabilities of SPI-GA biopolymers (120 min) were significantly higher than those of SPI (40 min) and egg white (98 min). The emulsifying properties of SPI-GA biopolymers were lower than those of SPI and bovine serum albumin (P > 0.05). Tensile strength (TS) and elongation at break (ETB) of SPI-GA biopolymer films were significantly higher than those of glycerol-plasticized soy protein films. TS and ETB of SPI-GA biopolymer films increased with increasing GA concentrations. GA treatment intensified yellowness of SPI-GA biopolymer films. SPI-GA biopolymers may have potential use for biodegradable packaging materials.

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