Numerical simulation of deformation behavior of additively manufactured polymer lattice structures with a porosity gradient

Tashkinov M.A.

• Approach for localization of mechanical behavior in random media is presented. • Multipoint correlation functions are used for characterization of morphology. • The developed formulations are independent of meshing of geometrical models. • Application is demonstrated on case studies of bicontinuous heterogeneous RVEs. • The method is suitable for analysis of materials with complex microstructure. The paper is devoted to the method of evaluation of local mechanical state in microscale components of random heterogeneous media taking into account their morphological features. According to the proposed approach, a representative volume element (RVE) of heterogeneous medium can be considered as a system of random interacting components with distinguishable properties. In this case, internal mechanical response to the load applied to an RVE can be expressed via continuous distributions of microscale stress and strain fields. The novelty of this work is connected with the methodology of restoration of parameters of these distributions using the solutions of the stochastic boundary value problems (SBVPs) that consider multipoint statistical correlations between different points within RVE, in contrast to the traditionally widely used two-point correlations. This allow to obtain more accurate results for the problems of localization of mechanical behavior for materials with complex random microstructure. The computational techniques, which are essential for numerical implementation of the developed approach, are described. The case studies connected with analysis of local stress and strain fields distributions in random bicontinuous media with interpenetrating phases are investigated using the developed approach and verified with the finite element analysis.

Su Y., He J., Jiang N., Zhang H., Wang L., Liu X., Li D., Yin Z.

Additively-manufactured PEEK orthopedic implants have recently gained extensive attention due to their prominent characteristics such as good biocompatibility, low radiographic artifacts and similar elastic modulus to native bones. However, the inherent drawback associated with PEEK implants was their biologically inert surface which caused unsatisfactory cellular response and poor adhesion between the implants and surrounding soft tissues. Here we developed a sulfonation-treatment strategy to create microporous architectures onto the filaments of the additively-manufactured PEEK lattice scaffolds. The sulfonation time in the range of 30–45 s was found to facilitate the formation of uniform microscale pores throughout the printed PEEK lattice scaffolds and simultaneously have slight effect on their composition and mechanical properties. Biological results showed that the presence of microscale pores on the additively-manufactured PEEK lattice scaffolds significantly improved the spreading, proliferation and calcium deposition of bone-specific cells in comparison with the untreated PEEK lattice scaffolds. In vivo experiments demonstrated that the sulfonation-treated micropores facilitated the adhesion of newly-regenerated soft tissues to form tight implant-tissue bonding interfaces. The presented method provides a promising approach to improve the surface bioactivity of additively-manufactured PEEK lattice scaffolds for enhanced cellular response and soft tissue adhesion.

Smith J.A., Mele E., Rimington R.P., Capel A.J., Lewis M.P., Silberschmidt V.V., Li S.

Functionally graded materials (FGMs), with varying spatial, chemical and mechanical gradients (continuous or stepwise), have the potential to mimic heterogenous properties found across biological tissues. They can prevent stress concentrations and retain healthy cellular functions. Here, we show for the first time the fabrication of polydimethylsiloxane and poly(ether) ether ketone (PDMS-PEEK) composites. These were successfully manufactured as a bulk material and functionally graded (stepwise) without the use of hazardous solvents or the need of additives. Chemical, irreversible adhesion between layers (for the FGMs) was achieved without the formation of hard, boundary interfaces. The mechanical properties of PDMS-PEEK FGMs are proven to be further tailorable across the entirety of the build volume, mimicking the transition from soft to harder tissues. The introduction of 20 wt% PEEK particles into the PDMS matrix resulted in significant rises in the elastic modulus under tensile and compressive loading. Biological and thermal screenings suggested that these composites cause no adverse effects to human fibroblast cell lines and can retain physical state and mass at body temperature, which could make the composites suitable for a range of biomedical applications such as maxillofacial prosthetics, artificial blood vessels and articular cartilage replacement.

Liu F., Mao Z., Zhang P., Zhang D.Z., Jiang J., Ma Z.

Functionally Graded Porous Scaffold (FGPS) becomes an attractive candidate for bone graft due to its combination of better mechanical and biological requirements with the scaffold gradient to better mimic host tissue. This paper focuses on the graded change requirements of bio-porous scaffolds in terms of physical and mechanical properties. Gradients in three patterns (density, heterostructure and cell-size gradients) with Gyroid and Diamond unit cells were proposed based on Triply Periodic Minimal Surfaces (TPMS), and fabricated by Selective Laser Melting (SLM) using Ti-6Al-4V. Among them, cell-size gradient was described for the first time, realizing a variation of graded pore size on a specific way. Morphological properties of porous samples were characterized by micro-CT and SEM, followed by compressive tests for determining their mechanical behaviors. It was found that the TPMS method is an effective way to achieve gradients in multiple patterns which are comparable to natural tissue with respect to both continuous topology and interconnectivity. The porous surface area and pore size, could be controlled by the cell-size gradient without relatively density alteration, stabilizing the modulus and strength within 11% and 20%, respectively. Both Gyroid and Diamond structures possess a superior strength (152.6 MPa, 145.7 MPa) and comparable elastic modulus (3.8GPa) with natural cortical bone.

Bargmann S., Klusemann B., Markmann J., Schnabel J.E., Schneider K., Soyarslan C., Wilmers J.

This work reviews state of the art representative volume element (RVE) generation techniques for heterogeneous materials. To this end, we present a systematic classification considering a wide range of heterogeneous materials of engineering interest. Here, we divide heterogeneous solids into porous and non-porous media, with 0

Chen F., Ou H., Lu B., Long H.

A modified Johnson-Cook (JC) model was proposed to describe the flow behaviour of polyether-ether-ketone (PEEK) with the consideration of coupled effects of strain, strain rate and temperature. As compared to traditional JC model, the modified one has better ability to predict the flow behaviour at elevated temperature conditions. In particular, the yield stress was found to be inversely proportional to temperature from the predictions of the proposed model.

Rahman K.M., Letcher T., Reese R.

Polyether ether ketone (PEEK) is introduced as a material for the additive manufacturing process called fused filament fabrication (FFF), as opposed to selective laser sintering (SLS) manufacturing. FFF manufacturing has several advantages over SLS manufacturing, including lower initial machine purchases costs, ease of use (spool of filament material vs powder material), reduced risk of material contamination and/or degradation, and safety for the users of the equipment. PEEK is an excellent candidate for FFF due to its low moisture absorption as opposed to other common FFF materials, such as Acrylonitrile Butadiene Styrene (ABS). PEEK has been processed into a filament and samples have been manufactured using several build orientations and extrusion paths. The samples were used to conduct tensile, compression, flexural, and impact testing to determine mechanical strength characteristics such as yield strength, modulus of elasticity, ultimate tensile strength and maximum elongation, etc. All tests were conducted at room temperature. A microscope analysis was also conducted to show features on the failures surfaces. The mechanical property results from this study are compared to other published results using traditional thermo-plastic manufacturing techniques, such injection molding. Tensile testing was conducted at three raster orientations, 0°, 90° and alternating between 0° and 90°. Average ultimate tensile stresses were determined to be 73 MPa for 0° orientation, and 54 MPa for 90° orientation, with alternating 0°/90° orientations of 66.5 MPa. Compression testing was conducted at two raster orientations, 0° and alternating between 0° and 90°. Average ultimate strength for the single orientation direction was 80.9 MPa with the alternating orientations at 72.8 MPa. Flexural testing was conducted at three raster orientations, 0°, 90° and alternating between 0° and 90°. Ultimate flexural stress was determined to be 111.7 MPa for 0°, 79.7 MPa for 90°, and 95.3 MPa for orientations alternating between 0° and 90°. Finally, impact testing was conducted at three raster orientations, 0°, 90° and alternating between 0° and 90°. Average impact energy absorbed was determined to be 17.5 Nm in the 0° orientation, 1.4 Nm in the 90° orientation, and 0.7 Nm for the alternating 0° and 90° orientations.

Elenskaya N., Koryagina P., Tashkinov M., Silberschmidt V.V.

Porous polymeric scaffolds are used in tissue engineering to maintain or replace damaged biological tissues. Once embedded in body, they are involved into different physical and biological processes, among which their degradation and dissolution of their material can be singled out as one of the most important ones. Degradation parameters depend mostly on the properties of both the material and surrounding native tissues, which can substantially alter the original mechanical parameters of the scaffolds. The aim of this study is to examine the change in the effective mechanical properties of functionally graded additively manufactured polylactide scaffolds with a linear porosity gradient and morphology based on triply periodic minimal surfaces during simultaneous degradation and compressive loading. Two main types of scaffold-degradation processes, bulk and surface erosions are simulated with two suggested modelling methods. The fundamental differences in the proposed approaches are identified and the influence of different types of scaffold morphology on the change in effective elastic properties is evaluated. The results of this study can be useful for design of optimal scaffolds taking into account the effect of the degradation process on their structural integrity.

Krasnyakov I., Bratsun D.

In this work, we present a mathematical model of cell growth in the pores of a perfusion bioreactor through which a nutrient solution is pumped. We have developed a 2-D vertex model that allows us to reproduce the microscopic dynamics of the microenvironment of cells and describe the occupation of the pore space with cells. In this model, each cell is represented by a polygon; the number of vertices and shapes may change over time. The model includes mitotic cell division and intercalation. We study the impact of two factors on cell growth. On the one hand, we consider a channel of variable cross-section, which models a scaffold with a porosity gradient. On the other hand, a cluster of cells grows under the influence of a nutrient solution flow, which establishes a non-uniform distribution of shear stresses in the pore space. We present the results of numerical simulation of the tissue growth in a wavy channel. The model allows us to obtain complete microscopic information that includes the dynamics of intracellular pressure, the local elastic energy, and the characteristics of cell populations. As we showed, in a functional-graded scaffold, the distribution of the shear stresses in the pore space has a complicated structure, which implies the possibility of controlling the growth zones by varying the pore geometry.

Elenskaya N., Tashkinov M., Vindokurov I., Pirogova Y., Silberschmidt V.V.

Applications of additive manufacturing (AM) in tissue engineering develop rapidly. AM offers layer-by-layer creation of complex objects, developed to restore functionality of, or replace, damaged tissues. Porous 3D-printed functional gradient structures are of particular interest: their special architecture makes it possible to simulate the heterogeneity of the replaced tissue and, by continuously changing the mechanical properties, to avoid the concentration of stresses that can be caused by abrupt geometric changes. Such structures also allow combinations of different types of unit cells and a smooth transition between them, making design of personalised scaffolds with optimal parameters for the replacement of damaged host tissue at the interface between tissues possible. This paper presents the results of development of scaffold structures with gradients of porosity and multi-morphology using unit cells based on triply periodic minimal surfaces (TPMS). The mechanical behaviour of additively manufactured scaffold prototypes made of polylactide acid (PLA) was studied under compressive loading. Strain fields on their surface were captured using the Vic-3d Micro-DIC digital image correlation system and compared with those obtained with detailed numerical simulations, employing elastic-plastic properties of PLA, obtained in experiments. The effect of gradient parameters and unit-cell morphology on the stress distribution in scaffolds was analysed. A smooth gradient transition between cells with different morphologies was found to reduce the probability of structural failure under intense compressive loading. A good agreement between numerical results and experimental data was achieved, which justifies application of the developed approach to design of personalised bone scaffolds.

Elenskaya N., Koryagina P., Tashkinov M., Silberschmidt V.V.

Artificial porous scaffolds are used in biomedical applications to sustain or replace damaged biological tissues. Embedded into a body, such scaffolds become involved in many physical and biological processes, with degradation and dissolution of the scaffold material being among the most important. Parameters of degradation depends, first of all, on material properties as well as on the properties of the surrounding tissues. It can drastically change the initial mechanical properties of scaffolds. The aim of this work is to investigate the change in effective mechanical properties of polylactide (PLA) porous scaffolds, with morphology based on triply periodic minimum surfaces (TPMS) during degradation and simultaneous compressive loading. Two strategies for modelling of scaffold degradation processes - volumetric and surface degradation - are proposed. Fundamental differences in the proposed approaches are identified and the effects of different types of scaffold morphology on changes in effective elastic properties evaluated. The present study may be useful for design of optimal TPMS scaffold structures taking into account the effect of degradation process on their structural integrity.