The phrase "assumed to be a linear function" is correct and usable in written English.
It can be used in mathematical or scientific contexts when discussing functions or models that are expected to behave in a linear manner.
Example: "In this study, we will analyze the data under the assumption that the relationship between the variables is assumed to be a linear function."
Alternatives: "presumed to be a linear function" or "expected to be a linear function".
The specific form of the distribution of eigenstrains is assumed to be a linear function in Cartesian coordinates of the points of the inhomogeneity.
On considering the relatively narrow ranges of operating conditions in a specified application, the equilibrium humidity ratio of desiccant solution was assumed to be a linear function of its temperature and concentration.
The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range.
The FGM is divided into several sub-layers and in each sub-layer the shear modulus is assumed to be a linear function while the Poisson's ratio is assumed to be a constant.
In the piezoelectric FGM plates, the properties of core material are assumed to be graded through the thickness by the power law distribution while the electric potential is assumed to be a linear function through the thickness of each piezoelectric sub-layer.
It is shown that the biaxial drawing of poly ethylene terephthalate) at temperatures above the glass transition temperature Tg can be satisfactorily described by the Ball model of rubber elasticity (Polymer, 1981, 22, 1010), providing that the chain entanglement density is assumed to be a linear function of the logarithmic shear strain rate.
The capillary radius variation was assumed to be a simple linear function and applied in the capillary model.
The scale parameter of the Weibull failure time distribution at constant stress levels is assumed to be a log-linear function of the stress level.
The nonlinearity is assumed to be an unknown function of the linear block output.
The in-plane displacement fields in each sublaminate are assumed to be piecewise linear functions and vary in a zig-zag fashion through-the-thickness of the sublaminate.
The noise amplitudes are assumed to be linear functions of α for simplicity.
