In this paper, we applied the nonlocal continuum mechanics to deriving a complete and asymptotic representation of the infinite higher-order governing differential equations for nano-beam and nano-plate models. Results show that the vanishing issue of small scale effects under some boundary conditions such as a clamped nano-beam subjected to distributed uniformly load is solved by using the present nonlocal continuum model. Several typical examples for nano-beam and nano-plate are studied and the scale effect on bending deflection is discussed at length. The analytical prediction for nonlocal bending deflection gives a good prediction of molecular dynamics simulation results which confirms the accuracy of the present model. It is found that when the external characteristic length tends to internal characteristic length, a property of a rigid body for the nano-beam and nano-plate is presented.

This paper develops a mathematical model to depict the energy absorption properties of multi-layered corrugated paperboard (MLCP) in various ambient humidities. It is a piecewise function to model the energy absorptions corresponding to three deformation stages of MLCP (elastic stage, plateau stage and densification stage) separately. Simple formulas are derived for each stage which relating the energy absorption capacity of MLCP to the thickness-to-flute pitch ratio (tc/λtc/λ) of corrugated-core cell, the mechanical properties of corrugated medium tested under a controlled atmosphere [23 °C and 50% relative humidity (RH)], and the RH. The theoretical energy absorption curves are then compared with experimental ones and good agreements are achieved for MLCP with wide range ratios of tc/λtc/λ in various ambient humidities. Results of this research can be applied in the optimum design and material selection of cushioning packaging with multi-layered corrugated paperboard.Graphical abstractThis paper develops a mathematical model to depict the energy absorption properties of multi-layered corrugated paperboard (MLCP) in various ambient humidities. The theoretical energy absorption curves are compared with experimental ones and good agreements are achieved. The results can be applied in the optimum design and material selection of cushioning packaging with multi-layered corrugated paperboard.Research highlights► A model is developed to predict the energy absorption of MLCP. ► Theoretical energy absorption curves are compared with experiments. ► Energy absorption increases with thickness-to-flute pitch ratio.

A mathematical model was developed to describe the relationship between the energy absorption properties of paper honeycombs and ambient humidity, as well as the structural parameters thereof. The model is a piecewise function modelling the energy absorption of four deformation stages of paper honeycomb (linear-elastic stage, yield stage, plateau stage and densification stage) separately. Function of each stage is a simple formula relating the energy absorption capacity to the thickness-to-length ratio of honeycomb cell, the mechanical property of a cell-wall material tested under a controlled atmosphere [23 °C and 50% relative humidity (RH)] and the RH. Energy absorption curves were thereby obtained for paper honeycombs with a wide range of thickness-to-length ratios in arbitrary humidity environments. The created model was then verified by comparing the predicted energy absorption curves with the experimental ones. A good accordance between the predictions and the observations was achieved, indicating that the energy absorption models developed here could be used to practical application for the designing optimisation and material selection of paper honeycombs.

Respiration modelling is the fundamental of the packaging and storage of fresh fruit and vegetables. Previous model of respiration rate accounted for external forcing from temperature and modified atmosphere but did not attempt to predict internally generated natural variability such as maturity. We present two types of respiration models here that predict the respiration rate of fresh papaya in response to changes of temperature, CO2/O2 concentrations and maturity as well. These two models were separately developed using a quadratic polynomial with four parameters and fifteen coefficients and using an artificial neural network (ANN) model with 4-15-2 architecture trained by Levenberg–Marquardt algorithm, in which the maturity of papaya covers skin yellowing from 10 to 90% and the temperatures vary over 10–30 °C. Comparison between the two types of respiration models shows a predictive superiority of the ANN-based model over the regressive one, demonstrating that the use of ANN technique can provide a reliable and effective approach to describe papaya’s respiration rate as a function of multivariate influencing factors.

The respiration rate prediction of fresh produce is crucial for designing and operating postharvest storage systems. This paper constructs and evaluates respiration models of guava fruit by using not only the enzyme, chemical kinetics but also artificial neural network (ANN) with the experimental data obtained from 5, 10, 15, 20, 25 and 30 °C (for constructing) as well as 12 and 22 °C (for evaluating) by closed system method. All of the developed models showed good agreement with actual observations. As regards fidelity the ANN model with topologic structure of 3 × 9×1 trained by the Levenberg–Marquardt algorithm, evaluation results were such that the mean absolute percentage error (MAPE) and the two-tailed Pearson correlation coefficient (r) were 5.31 and 0.997 for 12 °C, 4.85 and 0.995 for 22 °C, had superiority over the two other models. The results indicate that the ANN approach is a more precise method, and can be used for predicting the respiration rate of guava fruit.