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A structured approach to derive the water activity function of cellulose-based materials which describe the sorption behavior from dry fiber up to the fiber saturation point is proposed. The coupling between the sorption isotherm and the net isosteric heat of sorption is incorporated in a consistent way, which allows for coupled heat-diffusion problems to be solved. Three different models are derived, generalizations of the classic Oswin and Henderson isotherm models and a new model denoted LW. Experimental data from the literature is used to evaluate and compare model performance to the GAB model, and it is shown that generalizations of the classic Oswin, Henderson isotherms and the new LW model perform well. [ABSTRACT FROM AUTHOR]

The inverse motion concept is used to optimize thermo-hyperelastic structures using an exact description of the deformed geometry. This method prescribes the shape of the structure in the deformed state, and the optimization yields the shape of the undeformed configuration, i.e. the manufactured state. The kinematics of the thermoelastic model is defined through the multiplicative decomposition of the deformation gradient in combination with neo-Hookean hyperelasticity. To regularize the optimization problem and obtain distinct boundaries, the mathematical design field is thresholded using a smoothed Heaviside function and smeared using a partial differential equation. The sensitivity analyses of the objective function and constraints are both based on the adjoint method. The capabilities of the proposed approach are shown by numerical examples wherein the weight is minimized and the performance of multi-material compliant mechanisms is optimized. [ABSTRACT FROM AUTHOR]