An apparatus and method for control of stiffness and damping in a flexible composite structure by the application of an electric field to an electrophoretic fluid forming part of the structure. The structure includes spaced, parallel, flexible layers of material which include confronting electrodes. The electrophoretic fluid is capable of separating into particle-rich and particle-deficient phases by electrophoresis and operates in surface contact with the layers. An electrically nonconductive material having raised surface areas and spaces between the surface areas is associated with one or more of the layers. When a voltage is applied between the layers in a first direction, the particle-rich phase of the fluid collects on one of the layers and also makes contact with the spaces and the raised surface areas of the material associated with the other layer thereby engaging or locking the layers together to increase the shear strength of the layers and thus the complex stiffness of the structure. When the voltage potential is applied in the opposite direction, the particle-rich phase migrates to the other layer and collects in the spaces between the raised surfaces of the material, thereby disengaging the layers to decrease their shear strength and thus the stiffness of the structure. The structure may be configured as a panel, plate, or beam, in association with a variety of mechanical systems.