A pressurized liquid-filled parallel-channel network embedded in an elastic beam, asymmetrically to the neutral plane, will create a deformation-field within the beam. Deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotic applications. Expanding on this concept, configurations can be designed so that the pressure in the channel-network is created directly from external forces acting on the beam, and thus these configurations can be viewed as passive solid-liquid composite structures. We approximate the deformation of such structures and relate the liquid pressure and geometry of the network to a continuous deformation-field function. For cases in which the characteristic time-scale of the flow is much small than the characteristic time-scale of the external forces, the pressure distribution within the network is spatially uniform. For this case we can design networks creating steady arbitrary deformation-fields as well as to eliminate deformation created by external time-varying forces, thus increasing the effective rigidity of the beam. In addition, by including the effects of the deformation created by the channel network on the beam inertia, we can modify the response of the beam to external oscillating forces. This enables to design channel networks which create pre-defined oscillating deformation patterns in response to external oscillating forces.
