Dynamic Molding Deposition: The additive manufacturing in partially ordered system

: Additive manufacturing (AM) is now identified as a powerful bundle of fabrication techniques. Limitations were identified to be mostly related to the availability of reformulated materials 10 compatible with existing AM technologies. What if we were able to dynamically generate sacrificial molds with unlimited architectures and material composition? We have discovered such a process, called Dynamic Molding Deposition (DMD) in partially ordered powder system and demonstrated its capacity to produce highly complex objects with 100 µm resolution, without any building plate or support structures. The DMD compatible materials were shown to be almost 15 infinite, from low to high viscosity, from thermoplastic to elastomers. Our process enables us to build unexpected composite objects made up of injection material and powder grains from the dynamic mold. This feature opens the path to a complete new field of research and applications. technicality


Main Text:
Additive manufacturing is now identified by academics and industries as a powerful bundle of fabrication techniques enabling the rapid, free-form, sometime low-cost and surely straightforward production of prototypes and functional parts (1). Applications are widespread from aerospace to biology, from energy to food but the processes hidden behind the machines are always focused on 5 physico-chemical reactions enabling liquid-solid transition of the printed material (polymerization, recrystallization, gelation…) (2,3). This phase transition on the one hand permits the creation of self-standing complex architectures but on the other hand usually demands specific re-formulation of the initial manufacturing material (4,5). The consequence being here that materials not compatible with re-formulation are automatically excluded of the additive manufacturing world 10 and remain then in the molding/injection/thermoforming domain.
What if we were able to dynamically generate sacrificial molds with unlimited architectures? This might be the innovation the community was waiting, the missing link between molding and extrusion-based additive manufacturing. Such a manufacturing process, able to print in three dimensions all materials regardless of their chemistry, would provide a breakthrough in the field 15 and complement all existing additive manufacturing methods.
Attempts to such progress have been made in the last 5 years with the tremendous successes of the Freeform Reversible Embedding of Suspended Hydrogels (FRESH) (6), the Embedded 3D Printing (EMB3D) (7), the PICSIMA technique using a 2-part A/B silicone where the part Asilicone catalyst-cross-linker is extruded into a bath of part B-silicone (8), the Sacrificial Writing 20 Into Functional Tissue (SWIFT) (9) and the more recent in-bath print and cure (IBPC) (10), allowing the printing of low static yield stress materials (11) within a suspending gel environment.
It was then possible to print some classical viscoelastic materials (silicones and hydrogels) without re-formulation. Nevertheless the application range of these gel-based embedded techniques remained restricted by the necessary chemical and rheological compatibility of the printed material with the suspending environment (12).
In a bid to solve these incompatibilities and propose a universal additive manufacturing process, we discovered the Dynamic Molding Deposition (DMD), allowing us to produce free-form 5 geometries through extrusion-based additive manufacturing of a wide range of injectable materials in a partially ordered system of solid granular material (13). The DMD approach is characterized by several advantages such as the absence of support or building table, the possibility to process materials regardless their viscosity and chemistry, the potentiality to create new hybrids materials through the process (porosity, composites, gradient properties and surface modification). Figure   10 1-A presents the DMD conceptual approach. The DMD process assumes that all manufacturing materials can be 3D printed when the printing environment fulfil at least 3 functions: 1) SUPPORTING the deposited material (just like when using suspended hydrogels), 2) COMPRESSION of the deposited material in a filament-like structure and 3) SELF-REPAIRING itself after disruption by the printing head movement. Thus, using these three properties, low and 15 high viscosity materials shall be 3D shaped without collapsing, the system being able to counterbalance gravity deleterious effects. In a similar way, slow and rapid phase changing constituents might be used since the produced dynamic mold shall be stable long enough to enable cross-linking, polymerization or recrystallization of the material.
In the DMD approach, the printing environment is composed of a dynamic mold (a partially 20 ordered powder system) (13). Its flowability properties (14), density and grain shape bringing altogether the necessary properties to the environment. Figure 1-B presents the positioning of the different DMD environments within an ability diagram (Compressibility vs Mean diameter (D50)).
As can be seen, a large range of powder compositions, from organic to mineral (see Table S1 and S3), from water soluble to insoluble, can be used, bringing infinite material-powder association possibilities. The obtained new composites at reach being also infinite. Some molds were also unreachable (cement for example), mainly because of the powder grain to grain electrostatic interaction (at low diameter) and cohesion (at high compressibility) (15). 5 The behavior of the deposited material within the dynamic mold during 3D deposition was partially simulated using Computational Fluid Dynamics (CFD) modelling (16). The supporting and containment properties of the powder were thus investigated at the powder grain level. A Volume Of Fluid (VOF (17)) method for two-phases flow combined with dynamic mesh capabilities based on overset mesh technics were used to simulate a viscoelastic material 10 deposition within a dynamic mold. The VOF model captures the free surface of the viscoelastic fluid and takes into account interfacial tension effects. Overset mesh technics (18) were used to move the extrusion nozzle over the dynamic mold. Figure 1-C depicts the simulated deposition.
As can be seen, the developed simulation is able to describe material flow through the grains but also the potential material transfer to other layers. It highlights also the interaction between injected 15 material and previously printed filaments ( Figure S2, Movie S1 and Movie S2). Clear proofs of the ability of the dynamic mold to maintain the printed material in a controlled geometry were here numerically obtained. The DMD resolution, based on these simulations, shall be in the order of magnitude of the powder grain size. The best results being obtained using ~100 µm diameter grains, an average resolution of 100 µm is expected and was validated experimentally (Figure S4). 20 The simulation was also of great help understanding the DMD behaviors of materials with different viscosities, which leads to different powder integration within the final composite (Table S2).
We modified two 3D printing systems to produce two experimental set-ups used in this work (Figure 1-D). A 3-axis (Cartesian) and a 6-axis 3D printers were thus hybridized with a thermoregulated dynamic mold and a deposition head composed of a microdosing system (vipro-HEAD 5, ViscoTec, Germany) or a pressure-controlled system, respectively. Since the material used for the additive manufacturing using DMD can be theoretically of very low viscosity, the strategy was 5 here to implement a system handling from 10 -3 to 10 6 Pa.s viscosity. An interesting example of the DMD versatility is the printing of the polycaprolactone (PCL) (Figure 2-B) which was simply dynamically molded in a 100°C heated glass beads dynamic mold. At this temperature, PCL viscosity is closed to 10 -1 Pa.s and the polymer is easily extruded but also kept liquid within its dynamic mold. Once the manufacturing completed, the DMD environment is then slowly cooled 10 down until solidification at room temperature. The obtained objects were of acceptable fidelity and made up of a new organic-inorganic composite material. Achieving these composites is a particular case of the DMD process where powder grains are trapped between the injected material layers ( Figure S5).   (Figure 2-B insert). Briefly, the green plane of the FingerMap defines the limit of printability and all blue scattered dots above this plane are non-printable voxels. This information is translated in the 3D visualization were green parts are printable and red parts of the STL are not printable.
Obviously, 3D printing of these objects, in non-suspended conditions and using the selected silicone material, is impossible. Nevertheless, when looking at the DMD-based prints of these 20 STLs (Figure 2-C), overhanging and disconnected parts were easily produced. This is the strength of the DMD process and the uniqueness of the approach which was pushed forward with a wide range of highly complex structures (Figure 3 and FingerMap printability evaluation in Table S4). This exceptional property also brings new engineering capabilities where objects can be formed through multiple directions within the dynamic mold. A first example of this capacity has been the simultaneous production of multiple H2 tensile bars with variable angle with respect to normal (from 0 to 90°) or at different deepness within the dynamic mold (from 40 to 80 mm). The 5 mechanical properties (Figure 4-A) of these tensile bars were strongly conserved (Young's modulus and fracture strains) with a minimized effect of the printing angle upon the expected interlayer failure (lowering of the fracture strain) (22).
A second example is the capacity of producing multi-material complex objects, represented in As a final example of the extreme freeform capability of DMD, we rendered a highly complex physiological shape composed of a mitral valve, eight chordae tendineae and two medial papillary muscles (Figure 3-D). Here, the printing sequence was composed of three different steps, i) a planar layer by layer deposition of the mitral valve, ii) a 6-axis path-based multidirectional 15 deposition of the eight chordae tendineae and iii) a final planar layer by layer deposition of the two medial papillary muscles. These three sequences were supposed to bring even more complexity to the printing process since multiple objects shall be connected within the dynamic mold with enough cohesion. Here, it is worth to point out that the 8 chordae tendineae were printed as single 1 mm filaments, positioned between the two other sequences but still cohesive with the other 20 objects. Figure 3-D presents the silicone final object obtained using a glass beads dynamic mold.
As can be seen, all the parts were cohesive with a surface quality and a fidelity toward the initial STL file. To document this fidelity, dimensional measurements of the printed object were performed and compared to the initial STL (printing fidelity: 97.49%, Table S5). Another example of the power of the DMD to enable the production of complex structures is depicted in Figure 4-E where a lattice structure, characterized by a hyper-viscoelastic behavior was obtained using pathbased 6-axis deposition. In this configuration, the object was fully designed as 6-axis paths and the final rendering of the lattice with its deformability are presented in Movie S3 and Movie S4. 5 From uniaxial compression tests, an expected clear non-linear stress-strain relationship was identified (load cure). Thus, hysteresis between load and unload steps represents the configurational free energy of the viscoelastic solid and characterizes the non-equilibrium state.
The object mechanical properties can then be described by a hyper-viscoelastic behavior using the following constitutive equation (23): (1) DMD has been developed to fulfil the gap between molding and 3D printing, but an additional extraordinary feature of the technique is its ability to produce, directly during fabrication, composites of various composition.

Other Supplementary Materials for this manuscript include the following:
Movies S1 to S7 20

S1. Characterizing powder according to Dynamic Molding
Mean diameter (D50) 15 The particle size distribution was obtained with the use of Mastersizer 2000 coupling with the dry dispersion accessory Scirocco 2000 (Malvern Instruments, UK). Light from a laser is shone on a cloud of particles, which are suspended in a dispersant (in this study: air). The particles scatter the light, the larger the particles the smaller the scattering angles. The scattered light is measured by a series of photodetectors placed at different angles. This is known as the diffraction pattern for the sample. The diffraction pattern can be used to measure the size of the particles using Mie or Fraunhofer theory. Obtained results allow to draw a curve, called particle size distribution (volumic distribution), and to calculate parameters such as mean diameter D50. 5

Compressibility
The compressibility is defined as the reduction of volume according to an applied pressure. Here, the compressibility was evaluated with a rheometer DHR2 (TA instruments, USA) in compression mode and the use of Peltier Concentric Cylinder Temperature System and its standard cup, then a top geometry of 25 mm as diameter. A 20 ml powder sample was included in a Falcon 50 ml tube The compressibility in mm/N was defined as the slope of distance/force graph (step 2) through linear regression on TRIOS software (TA Instruments, USA).

S2. Simulation of the Dynamic Molding process
In order to study the behavior of the deposited material in details, the decision has been made to 20 simulate the product injection at the grain level. This is achieved using Computational Fluid Dynamics (CFD) simulations with advanced models. First, a free surface method is used to simulate the moving interface between the deposited material and air. There are two main methods to compute the free surface: the interface tracking method and the front capturing method. The former treats the free surface as a sharp interface whose motion is followed by moving the grid 25 defining the free surface. The latter, commonly used, is performed on a fixed grid and the shape of the interface is determined by the volume fraction of each fluid in the cells. In our case, the front capturing method has been used based on a volume of fluid method ("VOF"). The "VOF" method is a two-phase surface compression method that solves the Navier-Stokes equations and a transport equation for the volume fraction: deposited materials is taken in account. Here, two different materials respectively described by a Power-law (PL) and Herschel-Bulkley model (HBM) have been tested. In both case surface tension effects are computed with the "CSF" model (for Continuum Surface Force). Moreover, in order to simulate deposition process, a dynamic mesh is used to move the needle over the grains based on sliding mesh [2] with an interface between fixed and moving mesh zones. The interface 40 is non-conformal and ensure flow from the moving to the static part.

S3. Dynamic molding printer modifications
Two DMD printers were used in the present study, each derived from existing systems. The first one, a 3-axis system, was designed on a T333 TOBECA (France) 3D printer. The modifications of the initial printer were: 5 -Addition of a 20 L heating powder bath instead of the building plate. Heating was obtained through the use of 2x1000 W heating coiled directly connected and controlled by the 3D printer interface. -Interfacing of a liquid dispensing system (mono or bi component) from ViscoTec (Germany). Special holder were designed and produced through 3D printing (ObjetPro, 10 Stratasys, USA). Stepper motor driver were used to interface the microdosing system with the G-code. -Interfacing of an air pressure controller (Ultimus TM V, Nordson EFD, USA) through a dedicated electronic board so that the extrusion coded ion the G-code can be translated in pressure delivery information. 15 The second one, was modified from a 6-axis robotic system (BioAssemblyBot®, Advanced Lifescience Solutions, USA). The modifications of the initial printer were: -Addition of a 20L heating powder bath instead of the building plate. Heating was obtained through the use of 2x1000W heating coiled directly connected and controlled by 20 the 3D printer interface. -A special 30CC syringe holder was designed in order to cope with the poor resistance of the initial holder dedicated to 3D printing in non-granular environment. The additional part to the initial holder (STL downloadable at https://github.com/FabricAdvancedBiology/Bioprinter_parts) was 3D printed using an 25 Original Prusa (Prusa3D, Poland). -For DMD experiments, the BioAssemblyBot® was customized to accommodate printing in the dynamic mold, outside the initial enclosure. To do so, a special safety enclosure was designed which enable the secure operation of the robotic arm while reaching the much larger arena created at the back side of the machine.

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-The material dynamic molding was then started at a speed rate of 10 mm/s. -Once the printing completed, a 12 hours material cool down was performed before taking the printed parts out of the mold.

S5. Post-processing
When printing using dynamic molds, powder residues are present at the surface or within the material composing of the obtained objects. A post-treatment can then be applied to remove these residues. 5 For non-sacrificial powder (silica, glass or cenosphere for example), a high pressure water cleaner was used once the printed material fully reticulated. For PMMA sacrificial material, once the printed material fully reticulated, the parts were immersed in acetone for 2 hours, then rinsed with ethanol for an additional 2 hours and air dried. Young's modulus of each samples was obtained from the following equation using the true stress ( ) and the true strain ( ) between 0 to 10%. The fracture strain was defined as the true strain when the printed H2 form was broken.
Where 0 is the initial length, the displacement, the force, the thickness and the width.

S9.
Deposition elastomer material properties and dynamic molding

S11. Simulation
The resulting simulations for the two different fluids are presented in Figure S2 and Movie S1 and Movie S2. One can see the influence of material property on deposition process. These information are valuable to understand and improve deposition process. 5 Here, according to the material viscosity (see Table S2), inter-particles flow of the material was demonstrated, leading to the production of highly charged composites. Movie S1: simulations of SYLGARD™ 567 deposition in glass beads dynamic mold Movie S2: simulations of AMSil™ 20101 deposition in glass beads dynamic mold  (3) A custom MATLAB (MathWorks® R2018B, USA) code was used. The code uses an STL file as an input and indicates troublesome areas to print on the basis of the measured and the known formulation density. To briefly resume, the code first voxelizes the STL file (each point of the object volume being represented by a voxel), then treats each voxel 5 to determine its carried mass, detects its overhanging status and determines its overhanging angle value. From this voxelization, the Fingermap of the 3D object can be built. The prediction level is given when the FingerMap is compared to the printability volume as a function of material rheological properties. The voxel displays as red if the is not high enough to withstand the shape complexity. Otherwise, the voxel displays as green. 10 Table S4. Printability of the different objects simulated using the FingerMap program. The voxel displays as red if the is not high enough to withstand the shape complexity. Otherwise, the voxel displays as green. 5

STL file FingerMap
S13. Lattice structure printing in 6-axis In Movie S3 and Movie S4, an AMSil™ 20101 silicone complex lattice molded in glass bead using a 6-axis system is shown.

S14. Softness of the obtained material
In Movie S5, the extension capability of an AMSil™ 20101 silicone complex textile molded in 5 glass bead is shown. In Movie S6, the compressibility capability of a SYLGARD™ 567 silicone ball molded in PMMA is shown. S15. Multiple material object 10 In Movie S7, the multimaterial AMSil™ 20101 silicone voroid sphere molded in glass bead is shown.
S16. Dimensional analysis of the highly complex physiological shape composed of a mitral valve, eight chordae tendineae and two medial papillary muscles Overall print fidelity (%) 97.49 S16. DMD resolution estimation DMD resolution was estimated through the dynamic molding of 400 µm thick and 2 cm high thin silicone membrane in glass beads #4. Then, thin cuts of the object were performed, parallel or 5 perpendicular to the filament deposition, and the thickness of the membrane estimated from microscopy images ( Figure S3). As can be seen, the final thickness of the object was 595 µm or 552 µm, depending of the cut direction. These values correspond to the size of the injected silicone, i.e. 400 µm, plus 2-times the mean roughness given by the glass beads (60 µm). 10 Interestingly, low variation coefficients were found for the object thickness (7-8%), corresponding to a standard deviation of 41-46 µm. Finally, out of these measurements, a mean resolution (the largest obtained roughness) of 100 µm can be estimated.
15 Figure S3. Microscopy images of cuts of a 400µm thick silicone membrane produced in a glass beads mold. Figure S4. Conceptual approach of the DMD showing the alternative process in which composite is produced and shall lead to three different type of objects. 5