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This study aims to present an experimental approach to develop a high-strength 3D-printed recycled polymer composite reinforced with continuous metal fiber.

The continuous metal fiber composite was 3D printed using recycled and virgin acrylonitrile butadiene styrene-blended filament (RABS-B) in the ratio of 60:40 and postused continuous brass wire (CBW). The 3D printing was done using an in-nozzle impregnation technique using an FFF printer installed with a self-modified nozzle. The tensile and single-edge notch bend (SENB) test samples are fabricated to evaluate the tensile and fracture toughness properties compared with VABS and RABS-B samples.

The tensile and SENB tests revealed that RABS-B/CBW composite 3D printed with 0.7 mm layer spacing exhibited a notable improvement in Young’s modulus, ultimate tensile strength, elongation at maximum load and fracture toughness by 51.47%, 18.67% and 107.3% and 22.75% compared to VABS, respectively.

This novel approach of integrating CBW with recycled thermoplastic represents a significant leap forward in material science, delivering superior strength and unlocking the potential for advanced, sustainable composites in demanding engineering fields.

Limited research has been conducted on the in-nozzle impregnation technique for 3D printing metal fiber-reinforced recycled thermoplastic composites. Adopting this method holds the potential to create durable and high-strength sustainable composites suitable for engineering applications, thereby diminishing dependence on virgin materials.

Additive manufacturing is a recent technology used in the production of composite materials. The use of continuous fibres as reinforcement is necessary to achieve high mechanical performance. However, making these materials more environmentally friendly is still challenging. The purpose of this study was to investigate the feasibility of 3D printing a composite made of continuous regenerated cellulose fibres using a standard 3D printer generally used for printing polymers.

The production process was based on a pre-impregnated filament made from a tape containing continuous cellulose fibres and Pebax^® matrix. 3D printed composite samples were fabricated using fused deposition modelling. The tape, filament and 3D printed composites were first analysed by means of modulated differential scanning calorimetry and micrography. Tensile tests were then performed, and the mechanical characteristics were determined at each step of the production process. Fracture surfaces were investigated by field-emission gun–scanning electron microscopy.

Results showed that the mechanical behaviour of the material was maintained throughout the production process, and the 3D printed biocomposites had a stiffness equivalent to that of traditionally manufactured continuous cellulose fibre composites. The obtained 3D printed composites showed an increase in strength value by a factor of 4 and in tensile modulus by a factor of 20 compared to those of unreinforced Pebax^® polymer.

This paper demonstrates the feasibility of 3D printing composites based on continuous cellulose fibres, paving the way for new biocomposites made by additive manufacturing.

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.