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We develop a theory for continuous-time non-Markovian stochastic control problems which are inherently time-inconsistent. Their distinguishing feature is that the classical Bellman optimality principle no longer holds. Our formulation is cast within the framework of a controlled non-Markovian forward stochastic differential equation, and a general objective functional setting. We adopt a game-theoretic approach to study such problems, meaning that we seek for sub-game perfect Nash equilibrium points. As a first novelty of this work, we introduce and motivate a new definition of equilibrium that allows us to establish rigorously an extended dynamic programming principle, in the same spirit as in the classical theory. This in turn allows us to introduce a system of backward stochastic differential equations analogous to the classical HJB equation. We prove that this system is fundamental, in the sense that its well-posedness is both necessary and sufficient to characterise the value function and equilibria. As a final step we provide an existence and uniqueness result. Some examples and extensions of our results are also presented.

Nowadays the use of natural fiber composites has gained significant interest due to their low density, high availability, and low cost. The present study explores the development of sustainable 3D printing filaments based on rice husk (RH), an agricultural residue, and recycled polypropylene (rPP) and the influence of fiber weight ratio on physical, thermal, mechanical, and morphological properties of 3D printing parts. Thermogravimetric analysis revealed that the composite’s degradation process started earlier than for the neat rPP due to the lignocellulosic fiber components. Mechanical tests showed that tensile strength increased when using a raster angle of 0° than specimens printed at 90°, due to the weaker inter-layer bonding compared to in-layer. Furthermore, inter layer bonding tensile strength was similar for all tested materials. Scanning electron microscope (SEM) images revealed the limited interaction between the untreated fiber and matrix, which led to reduced tensile properties. However, during the printing process, composites presented lower warping than printed neat rPP. Thus, 3D printable ecofriendly natural fiber composite filaments with low density and low cost can be developed and used for 3D printing applications, contributing to reduce the impact of plastic and agricultural waste.

Natural filler-based composites are an environmentally friendly and potentially sustainable alternative to synthetic or plastic counterparts. Recycling polymers and using agro-industrial wastes are measures that help to achieve a circular economy. Thus, this work presents the development and characterization of a 3D printing filament based on recycled polypropylene and cocoa bean shells, which has not been explored yet. The obtained composites were thermally and physically characterized. In addition, the warping effect, mechanical, and morphological analyses were performed on 3D printed specimens. Thermal analysis exhibited decreased thermal stability when cacao bean shell (CBS) particles were added due to their lignocellulosic content. A reduction in both melting enthalpy and crystallinity percentage was identified. This is caused by the increase in the amorphous structures present in the hemicellulose and lignin of the CBS. Mechanical tests showed high dependence of the mechanical properties on the 3D printing raster angle. Tensile strength increased when a raster angle of 0° was used, compared to specimens printed at 90°, due to the load direction. Tensile strength and fracture strain were improved with CBS addition in specimens printed at 90°, and better bonding between adjacent layers was achieved. Electron microscope images identified particle fracture, filler-matrix debonding, and matrix breakage as the central failure mechanisms. These failure mechanisms are attributed to the poor interfacial bonding between the CBS particles and the matrix, which reduced the tensile properties of specimens printed at 0°. On the other hand, the printing process showed that cocoa bean shell particles reduced by 67% the characteristic warping effect of recycled polypropylene during 3D printing, which is advantageous for 3D printing applications of the rPP. Thereby, potential sustainable natural filler composite filaments for 3D printing applications with low density and low cost can be developed, adding value to agro-industrial and plastic wastes.

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