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Transport of volatile organic compounds (VOCs) through porous media with active surfaces takes place in many important applications, such as in cellulose-based materials for packaging. Generally, it is a complex process that combines diffusion with sorption at any time. To date, the data needed to use and validate the mathematical models proposed in literature to describe the mentioned processes are scarce and have not been systematically compiled. As an extension of the model of Ramarao et al. (Dry Technol 21(10):2007–2056, 2003) for the water vapor transport through paper, we propose to describe the transport of VOCs by a nonlinear Fisher–Kolmogorov–Petrovsky–Piskunov equation coupled to a partial differential equation (PDE) for the sorption process. The proposed PDE system contains specific material parameters such as diffusion coefficients and adsorption rates as multiplication factors. Although these parameters are essential for solving the PDEs at a given time scale, not all of the required parameters can be directly deduced from experiments, particularly diffusion coefficients and sorption constants. Therefore, we propose to use experimental concentration data, obtained for the migration of dimethyl sulfoxide (DMSO) through a stack of paper sheets, to infer the sorption constant. These concentrations are considered as the outcome of a model prediction and are inserted into an inverse boundary problem. We employ Physics-Informed Neural Networks (PINNs) to find the underlying sorption constant of DMSO on paper from this inverse problem. We illustrate how to practically combine PINN-based calculations with experimental data to obtain trustworthy transport-related material parameters. Finally we verify the obtained parameter by solving the forward migration problem via PINNs and finite element methods on the relevant time scale and show the satisfactory correspondence between the simulation and experimental results. Article Highlights: A mathematical model to describe transport of polar volatile organics through paper is proposed. Based on experimental data, the deep learning method of physics-informed neural networks (PINNs) is used to solve the inverse problem of finding the sorption time constant. Solutions for the forward problem are obtained by the standard finite element method (FEM) and PINN methods. These solutions are compared with each other as well as with the experimental data to verify the model. [ABSTRACT FROM AUTHOR]

Understanding heat transfer in corrugated fibreboard is important to the design of more effective packaging for industries which involve the freezing and chilling of food. In this work the thermal conductivity of papers which compose corrugated fibreboard were measured and used to validate finite element models of heat transfer in fibreboard. The results showed paper to be highly anisotropic, with thermal conductivity in the machine and cross machine directions being almost an order of magnitude larger than in the thickness direction. The finite element models showed good agreement with experimental results and demonstrated that the majority of heat transfer in corrugated fibreboard is though the fluted medium. Based on the finite element models, simple models for the prediction of the thermal performance of corrugated board were evaluated and shown to be very effective in reproducing the results of the more complex finite element methods. These simple methods can be used to perform corrugated fibreboard design calculations, and the models with and without radiation can be used to provide estimates of the lower and upper bounds of the thermal resistance for a given board design. [ABSTRACT FROM AUTHOR]

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]