Optimal Rotation Age in Fast Growing Plantations: A Dynamical Optimization Problem.

Forest plantations are economically and environmentally relevant, as they play a key role in timber production and carbon capture. It is expected that the future climate change scenario affects forest growth and modify the rotation age for timber production. However, mathematical models on the effect of climate change on the rotation age for timber production remain still limited. We aim to determine the optimal rotation age that maximizes the net economic benefit of timber volume in a negative scenario from the climatic point of view. For this purpose, a bioeconomic optimal control problem was formulated from a system of Ordinary Differential Equations (ODEs) governed by the state variables live biomass volume, intrinsic growth rate, and area affected by fire. Then, four control variables were associated to the system, representing forest management activities, which are felling, thinning, reforestation, and fire prevention. The existence of optimal control solutions was demonstrated, and the solutions of the optimal control problem were also characterized using Pontryagin's Maximum Principle. The solutions of the model were approximated numerically by the Forward-Backward Sweep method. To validate the model, two scenarios were considered: a realistic scenario that represents current forestry activities for the exotic species Pinus radiata D. Don, and a pessimistic scenario, which considers environmental conditions conducive to a higher occurrence of forest fires. The optimal solution that maximizes the net benefit of timber volume consists of a strategy that considers all four control variables simultaneously. For felling and thinning, regardless of the scenario considered, the optimal strategy is to spend on both activities depending on the amount of biomass in the field. Similarly, for reforestation, the optimal strategy is to spend as the forest is harvested. In the case of fire prevention, in the realistic scenario, the optimal strategy consists of reducing the expenses in fire prevention because the incidence of fires is lower, whereas in the pessimistic scenario, the opposite is true. It is concluded that the optimal rotation age that maximizes the net economic benefit of timber volume in P. radiata plantations is 24 and 19 years for the realistic and pessimistic scenarios, respectively. This corroborates that the presence of fires influences the determination of the optimal rotation age, and as a consequence, the net economic benefit.

Experimental Characterization and Analysis of the In-Plane Elastic Properties and Interlaminar Fracture Toughness of a 3D-Printed Continuous Carbon Fiber-Reinforced Composite.

The use of continuous fiber as reinforcement in polymer additive manufacturing technologies enhances the mechanical performance of the manufactured parts. This is the case of the Carbon-Fiber reinforced PolyAmide (CF/PA) used by the MarkForged MarkTwo® 3D printer. However, the information available on the mechanical properties of this material is limited and with large variability. In this work, the in-plane mechanical properties and the interlaminar fracture toughness in modes I and II of Markforged's CF/PA are experimentally investigated. Two different standard specimens and end-tabs are considered for the in-plane properties. Monolithic CF/PA specimens without any additional reinforcement are used for the interlaminar fracture toughness characterization. Two different mode I specimen configurations are compared, and two different test types are considered for mode II. The results show that prismatic specimens with paper end-tabs are more appropriate for the characterization of the in-plane material properties. The use of thick specimens for mode I fracture toughness tests complicates the characterization and can lead to erroneous results. Contrary to what has been reported in the literature for the same material, fracture toughness in mode I is lower than for mode II, which agrees with the normal tendency of traditional composite materials.