WO2023155015A1 - Tubes élastomères à distension auto-régulée - Google Patents

Tubes élastomères à distension auto-régulée Download PDF

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Publication number
WO2023155015A1
WO2023155015A1 PCT/CA2023/050209 CA2023050209W WO2023155015A1 WO 2023155015 A1 WO2023155015 A1 WO 2023155015A1 CA 2023050209 W CA2023050209 W CA 2023050209W WO 2023155015 A1 WO2023155015 A1 WO 2023155015A1
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Prior art keywords
jacketed
elastomeric tube
tube
elastomeric
fabric
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English (en)
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Nathan JEN
Hyun-Joong Chung
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University of Alberta
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University of Alberta
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H1/00—Apparatus for passive exercising; Vibrating apparatus; Chiropractic devices, e.g. body impacting devices, external devices for briefly extending or aligning unbroken bones
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H1/00—Apparatus for passive exercising; Vibrating apparatus; Chiropractic devices, e.g. body impacting devices, external devices for briefly extending or aligning unbroken bones
    • A61H1/02—Stretching or bending or torsioning apparatus for exercising
    • A61H1/0274—Stretching or bending or torsioning apparatus for exercising for the upper limbs
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H1/00—Apparatus for passive exercising; Vibrating apparatus; Chiropractic devices, e.g. body impacting devices, external devices for briefly extending or aligning unbroken bones
    • A61H1/02—Stretching or bending or torsioning apparatus for exercising
    • A61H1/0274—Stretching or bending or torsioning apparatus for exercising for the upper limbs
    • A61H1/0281—Shoulder
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H9/00—Pneumatic or hydraulic massage
    • A61H9/0021—Hydraulic massage
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Program-controlled manipulators
    • B25J9/10—Program-controlled manipulators characterised by positioning means for manipulator elements
    • B25J9/14—Program-controlled manipulators characterised by positioning means for manipulator elements fluid
    • B25J9/142—Program-controlled manipulators characterised by positioning means for manipulator elements fluid comprising inflatable bodies
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B1/00—Layered products having a non-planar shape
    • B32B1/08—Tubular products
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B25/00—Layered products comprising a layer of natural or synthetic rubber
    • B32B25/10—Layered products comprising a layer of natural or synthetic rubber next to a fibrous or filamentary layer
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B25/00—Layered products comprising a layer of natural or synthetic rubber
    • B32B25/20—Layered products comprising a layer of natural or synthetic rubber comprising silicone rubber
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B5/00—Layered products characterised by the non- homogeneity or physical structure, i.e. comprising a fibrous, filamentary, particulate or foam layer; Layered products characterised by having a layer differing constitutionally or physically in different parts
    • B32B5/02—Layered products characterised by the non- homogeneity or physical structure, i.e. comprising a fibrous, filamentary, particulate or foam layer; Layered products characterised by having a layer differing constitutionally or physically in different parts characterised by structural features of a fibrous or filamentary layer
    • B32B5/026—Knitted fabric
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61H—PHYSICAL THERAPY APPARATUS, e.g. DEVICES FOR LOCATING OR STIMULATING REFLEX POINTS IN THE BODY; ARTIFICIAL RESPIRATION; MASSAGE; BATHING DEVICES FOR SPECIAL THERAPEUTIC OR HYGIENIC PURPOSES OR SPECIFIC PARTS OF THE BODY
    • A61H2201/00—Characteristics of apparatus not provided for in the preceding codes
    • A61H2201/12—Driving means
    • A61H2201/1238—Driving means with hydraulic or pneumatic drive
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B2262/00—Composition or structural features of fibres which form a fibrous or filamentary layer or are present as additives
    • B32B2262/02—Synthetic macromolecular fibres
    • B32B2262/0261—Polyamide fibres
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B2262/00—Composition or structural features of fibres which form a fibrous or filamentary layer or are present as additives
    • B32B2262/04—Cellulosic plastic fibres, e.g. rayon
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B2307/00—Properties of the layers or laminate
    • B32B2307/70—Other properties
    • B32B2307/732—Dimensional properties
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B2307/00—Properties of the layers or laminate
    • B32B2307/70—Other properties
    • B32B2307/732—Dimensional properties
    • B32B2307/737—Dimensions, e.g. volume or area
    • B32B2307/7375—Linear, e.g. length, distance or width
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B32—LAYERED PRODUCTS
    • B32B—LAYERED PRODUCTS, i.e. PRODUCTS BUILT-UP OF STRATA OF FLAT OR NON-FLAT, e.g. CELLULAR OR HONEYCOMB, FORM
    • B32B2597/00—Tubular articles, e.g. hoses, pipes

Definitions

  • the present invention relates to elastomeric tubing. More particularly, it relates to jacketed elastomeric tubing with self-regulating distension in the radial direction.
  • EVHP ex vivo heart-perfusion device
  • a medical device which keeps a donor heart alive ex vivo by connecting it to a tubing system and pumping a blood substitute through it [6]
  • the tubing immediately connected to the donor organ in this device is on the centimetre scale and should ideally be compliant enough to act as a shock absorber for the pulsatile fluid flow (which occurs at pressures in the tens of kPa) without being so compliant as to rupture during operation [7],
  • Fiber-elastomer composites which consist of stiff fibers embedded within a compliant elastomeric matrix, have garnered much attention in the scientific community for their properties which combine the most desirable aspects of both component materials. Specifically, the elastomeric matrix provides a robust and deformable base for the material which allows it to withstand many different stresses, while the stiffer fibers act as a reinforcement to prevent excessive deformation under large stress magnitudes. Under uniaxial tension, the same ‘J-shaped’ stress-strain curve seen in aorta and many other biological tissues is also observed.
  • Fiber-elastomer composites enables their use in soft robotic actuators [11] [12] [13], biomimetic or biomedical devices [14] [15] [16], flexible yet tear- or impact- resistant garments [17], devices found in harsh tribological settings such as tire treads [18] [19], and even heat-shielding layers for space vehicles [20],
  • soft robotic actuators [11] [12] [13], biomimetic or biomedical devices [14] [15] [16], flexible yet tear- or impact- resistant garments [17], devices found in harsh tribological settings such as tire treads [18] [19], and even heat-shielding layers for space vehicles [20]
  • the soft elastomeric matrix of the composite dominates much of the material response when pressurized while an embedded fabric layer facilitates strain- stiffening if the tubing becomes overpressurized, preventing rupture.
  • the material could successfully act as a ‘neoaorta’, replicating both the structure, as shown in FIG. 1A, and the function of biological aorta (which itself is a fiber-reinforced material exhibiting J-shaped stress-strain behavior) in regulating somatic blood flow via the so-called Windkessel effect [21], Furthermore, such tubing was theorized to have great utility as a general-purpose macroscale elastomeric flow regulator, or as a static actuator with self-regulating distension in the radial direction.
  • the “embedded fibers” design later gave way to a simplified alternative in which the fabric layer was not embedded, and instead wrapped around the tubing as a ‘jacket’, as shown in FIG. 1A. This was hypothesized to retain most of the biomimetic behaviors sought after in the embedded model, while also allowing for greater movement of fibers and being easier to manufacture. While the term ‘fiber-elastomer composite’ generally refers to materials with embedded fibers, this alternative design is not without precedent. In fact, a spectrum of attachment methods for hollow or tubular complexes of fibrous and elastomeric materials has been reported in literature.
  • These methods include cast elastomer-based structures with fully embedded fibrous layers [22] [23], fiber-based structures with elastomeric layers that are laminated or otherwise adhered together [24] [25] [26], braided fiber-based structures which are impregnated with elastomeric resin [27], and lastly ‘jacketed’ elastomeric structures with one or more external layers of fibrous reinforcement that are not specifically adhered to the surface [28] [29] [30] [31] [32] [33] [34] [35] [36],
  • Hyperelasticity Elastomers are a classic example of a hyperelastic material; that is, one whose deformation behavior is nonlinear and governed by a strain energy density function rather than a constant factor [39], Many constitutive models exist to describe the behavior of different hyperelastic materials, and there is no universal agreement on which is most accurate. Furthermore, for any given hyperelastic material there may be great disagreement between sources on the material coefficients, even when the same constitutive model is used [40],
  • Hysteresis Elastomers, like all rubbers, are subject to material phenomena that increase their compliance after repeated loading-unloading cycles. The most significant of these is the Mullins effect [42], a complicated and multi-faceted phenomenon that results in gradual and irreversible increases in compliance over many strain cycles. Fabrics, including knit fabrics, have been observed to display the same hysteresis behavior as well when under cyclic stress [43] [44],
  • the present invention provides a method of passive fluid actuation that includes providing a jacketed elastomeric tube defining an internal channel, the jacketed elastomeric tube having a first end and a second end, a length extending from the first end to the second end, and a first diameter. The method then includes fixing the first end and the second end of the jacketed elastomeric tube, supplying a fluid to the internal channel of the jacketed elastomeric tube, and distending the jacketed elastomeric tube such that at least a portion of the jacketed elastomeric tube along the length expands from the first diameter to a second diameter.
  • the present invention additionally provides a jacketed elastomeric tube for use with the above described method that includes an elastomeric tube defining internal channel and having an external surface and a fabric jacket wrapped around the external surface of the elastomeric tube.
  • FIG. 1 A is a schematic cross-sectional view of a natural aorta
  • FIG. IB is a schematic cross-sectional view of a jacketed elastomeric tube according to embodiments of the present invention.
  • FIG. 1C is a schematic drawing illustrating the knit directions of the fabric jacket layer according to embodiments of the present invention.
  • FIG. ID is a graph showing trends in radial distension vs. pressure for jacketed tubes according to embodiments of the present invention and unjacketed tubes under hydrostatic pressure;
  • FIG. 2A schematic drawing of an inventive flow loop system according to embodiments of the present invention
  • FIG. 2B is a photograph of the compliant chamber of the flow loop of FIG. 2 A with elastomeric tube inserted
  • FIG. 2C is an image of a distended elastomeric tube, with initial and final diameter measurements shown;
  • FIG. 2D is a plot of radial tube distension (mm) vs. pressure (kPa);
  • FIG. 2E is a plot of rate of distension (mm/kPa) vs. pressure (kPa);
  • FIG. 2F are a series of experimental images for bare EcoFlex tubes at pressures of i)
  • FIG. 3 A is a labeled diagram of “dogbone” sample used for tensile testing elastomers’
  • FIG. 3B is a labeled diagram of a strip sample used for testing fabric
  • FIG. 3C is a quasihysteresis plot of EcoFlex, with selected curve highlighted;
  • FIG. 3D is a zoomed-in version of FIG. 3C
  • FIG. 3E is a stress-strain plot of selected curve from quasi-hysteresis test overlaid with theoretical curve produced by fitted coefficients;
  • FIG. 3F is a stress-strain curves of EcoFlex, fabric, and EcoFlex-fabric bilayer using fitted coefficients
  • FIG. 4A is an ABAQUS-modeled ‘slice’ of cylindrical tube wall, with coordinate system labeled;
  • FIG. 4B is an assembly of the tube slice and analytical rigid roller
  • FIG. 4C shows a distended tube slice
  • FIG. 4D shows a full tubular representation of the distended slice in FIG. 4C;
  • FIG. 4E shows a plot of simulated radial tube distension (mm) vs. pressure (kPa), overlaid with experimental data;
  • FIG. 4F shows a plot of simulated rate of distension (mm/kPa) vs. pressure (kPa), overlaid with experimental data;
  • FIG. 4G show a series of finite element models of bare EcoFlex tubes at pressures of i) 6.52 kPa, ii) 10.25 kPa, and iii) 13.99 kPa, and jacketed EcoFlex tubes at pressures of iv) 8.84 kPa, v) 18.99 kPa, and vi) 36.95 kPa;
  • FIG. 5A is a photograph of a bare EcoFlex tube at high pressure displaying marked asymmetric distension
  • FIG. 5B is a photograph of a jacketed EcoFlex tube at high pressure
  • FIG. 6A shows an ABAQUS models of a fabric-jacketed tube (left) and a jacketed tube with kirigami patterns cut into the fabric (right) with the portions of the tube below the cuts defined as bare EcoFlex while the rest is defined to be the EcoFlex-fabric composite;
  • FIG. 6B shows the models of FIG. 6A with distended profiles of the tubes when clamped and subject to a 25 kPa hydrostatic pressure
  • FIG. 7 is a graph showing experimental distension vs. pressure
  • FIG. 8 is a graph showing experimental rate of distension vs. pressure
  • FIG. 9 is a graph showing experimental volume vs. pressure
  • FIG. 10 is a graph showing experimental rate of expansion vs. pressure
  • FIG. 11 is a quasi-hysteresis plot for EcoFlex
  • FIG. 12 is a closeup quasi-hysteresis plot of FIG. 11;
  • FIG. 13 is a quasi-hysteresis plot for Dragon Skin
  • FIG. 14 is a closeup quasi-hysteresis plot of FIG. 13;
  • FIG. 15 is a quasi-hysteresis plot for rayon-spandex fabric;
  • FIG. 16 is a theoretical stress-strain data using fitted EcoFlex coefficients
  • FIG. 17 is a theoretical stress-strain data using fitted DragonSkin coefficients
  • FIG. 18 is a theoretical stress-strain data using fitted rayon-spandex fabric coefficients
  • FIG. 19 is a theoretical stress-strain curve for EcoFlex and fabric
  • FIG. 20 is a theoretical stress-strain curve for EcoFlex and fabric (closeup);
  • FIG. 21 is a theoretical stress-strain curve for Dragon Skin and fabric
  • FIG. 22 is a theoretical stress-strain curve for DragonSkin and fabric (closeup);
  • FIG. 23 is a simulated distension vs. pressure plot
  • FIG. 24 is a simulated volume vs. pressure plot
  • FIG. 25 is a simulated rate of distension vs. pressure plot
  • FIG. 26 is a simulated rate of expansion vs. pressure plot
  • FIG. 27 is a comparison of experimental and simulated distension values
  • FIG. 28 is a comparison of experimental and simulated rate of distension values
  • FIG. 29 is a comparison of experimental and simulated volume values
  • FIG. 30 is a comparison of experimental and simulated rate of expansion values
  • FIG. 31 is a EcoFlex tube distension parity plot
  • FIG. 32 is a DragonSkin tube distension parity plot
  • FIG. 33 is a EcoFlex tube volume parity plot
  • FIG. 34 is a DragonSkin tube volume parity plot
  • FIG. 35 is a EcoFlex + fabric tube distension parity plot
  • FIG. 36 is a DragonSkin + fabric tube distension parity plot
  • FIG. 37 is a EcoFlex + fabric tube volume parity plot
  • FIG. 38 is a DragonSkin + fabric tube volume parity plot
  • FIG. 39 is a graph showing a waveform of a rigid plastic tube under cyclic hydrodynamic pressure, which has a ‘jagged’ quality, with a large negative pressure at the cycle midpoint;
  • FIG. 41 is a single hysteresis loop for a single tube length of a given material
  • EFO Ecoflex 00-50 + pre-stressed 93-7% rayon-spandex fabric
  • ESFW Ecoflex 00- 50 + 95-5% viscose-spandex fabric
  • ESTW Ecoflex 00-50 + 65-30-5% rayon-nylon-spandex fabric
  • the present invention has utility as a highly tunable centimeter- scale jacketed elastomeric tubing and a method of predicting the distension behavior of such jacketed elastomeric tubing, the method taking in to account the combination of several key material properties including hyperelasticity, strain- stiffening, anisotropy, and hysteresis.
  • the present invention having utility in a wide range of applications including in biomedical “exomuscles”, massage therapy implements, or soft robotic actuators for various industrial purposes.
  • the present invention provides a highly tunable design for centimeter-scale elastomeric tubing 100 wrapped with a knit fabric jacket 102.
  • the elastomeric tubing 100 is formed of RTV silicone rubber and the knit fabric jacket 102 is formed of knitted rayon spandex fabric. It is appreciated that the tube scale can extend between 0.1 and 1000 centimeters.
  • a hydraulic or pneumatic flow loop for testing jacketed elastomeric tubing is provided which clamps the ends of such tubes and pumps fluids into the tubes to subject them to known hydrostatic pressures to measure trends in radial distension.
  • the jacketed tubing is initially very compliant and deforms rapidly when first pressurized but displays marked self-regulation behavior at high pressures where their continued distension is tempered by the stiffening of fibers in the fabric jacket, a behavior that is not present in bare elastomeric tubes such as those shown in the graph of FIG. 1C.
  • Further some inventive embodiments provide methods of 3D finite element simulations using material coefficients obtained from uniaxial, quasi-hysteresis tensile tests of the materials of interest to closely replicate experimental distension trends while also predicting a continuation of the observed trends at pressures beyond the experimental range. Such method of predicting the behavior of such jacketed elastomeric tubes provides a method of predicting deformation behavior of even more complex tube designs.
  • elastomeric tubes are provided. According to other inventive embodiments, such elastomeric tubes are cast in 3D printed molds using EcoFlex 00-50 (EF) and/or Dragon Skin 10 SLOW (DS), or another commercially available silicone rubber. According to other inventive embodiments, a fabric jacket is provided on an outer surface of the elastomeric tube. According to still other inventive embodiments, the fabric jackets are cut from a knit fabric blend, such as a 93-7% rayon-spandex. A fabric jacket is wrapped around an elastomeric tube. According to still other inventive embodiments, the fabric jackets wraps the tube such that the wale direction runs parallel to the longitudinal axis of the tube, as shown in FIG. IB.
  • bare (unjacketed) and jacketed EF and DS tubes are subjected to hydrostatic pressure testing in an inventive custom-built hydraulic or pneumatic ‘flow loop’, as shown schematically in FIG. 2A.
  • a single tube is clamped in place in the compliant chamber, as shown in FIG. 2B, and is increasingly pressurized by running the centrifugal pump at incrementally faster speeds.
  • a camera facing the compliant chamber captures images of the tubes at each pressure level, as shown in FIG. 2C, which are later analyzed to measure the extent of distension. Tests continue until significantly asymmetric distension of the tube is observed, such as in FIG. 2F:iii.
  • Distension in this context, is defined as the difference between the initial and final diameters, as shown in FIG. 2C, where final diameter is taken as an average value over the middle 3 cm of the image of the tube.
  • a plot of distension vs. pressure values for all tested tubes is shown in FIG. 2D and some corresponding real-life images are shown in FIG. 2F:i-vi.
  • the most notable trend is the difference in the shape of the curves for unjacketed and jacketed tubes. Unjacketed tubes display an exponential growth curve, rapidly approaching failure with increasing pressure. Conversely, jacketed tubes display a sigmoid (‘ S-shaped’) curve in which the exponential growth begins but is eventually halted, entering a region of self-regulation in which the increasing tube distension slows and even appears to plateau.
  • S-shaped sigmoid
  • FIG. 2E illustrates the self-regulating effect experienced by the jacketed tube at the highest pressures.
  • the x-axis is pressure at each data point as shown in FIG. 2D, whereas y-axis is the unit ‘rate of distension’; that is, the mean increase in distension per kPa between each point and the one directly previous. While the rate of distension only increases across the pressure range for EF and DS tubes, it peaks and eventually decreases for the jacketed tubes.
  • 3 -dimensional finite element simulations are provided using ABAQUS using material coefficients obtained from uniaxial tensile tests of the tubing materials; these simulations are successful in predicting distension trends of all tested tubes across the entire tested pressure range and beyond.
  • ABAQUS requires that the coefficients of an appropriate constitutive model, selected from a list, are associated with the materials being simulated. Therefore, 1) the constitutive material model and material coefficients selected represents the behavior of both the elastomers and fabric used.
  • the Mooney-Rivlin model [45] is used for the elastomers based on its previously established accuracy in describing elastomeric deformation behavior [7], For a uniaxial tensile test the Mooney-Rivlin equation takes the form of Equation 1.
  • Equation 1 where t 1 , elastomer is the true stress in the direction of uniaxial elongation (Pa), ⁇ 1 is the stretch ratio in the direction of elongation (mm/mm) and Cio and Coi (both Pa) are the coefficients of interest that must be fit to the uniaxial tensile test data.
  • the Holzapfel-Gasser-Ogden (HGO) model is used as it is supported by ABAQUS and was originally conceived to describe the hyperelastic anisotropic behavior of aortic tissue [41], Ordinarily, the HGO model takes the form shown in Equation 2.
  • Equation 2 where the first term represents the elastomer behavior and the second term represents the fiber behavior.
  • the Coi term from the Mooney-Rivlin equation is dropped as it mainly affects the behavior of the elastomer at low strains, while the focus of the HGO equation is modeling the strain- stiffening behavior at higher strains.
  • the equation is meant to describe aorta, which may be thought of as an embedded fiber-elastomer composite, the present invention establishes that the equation still holds for jacketed elastomer tubes where the fabric is not specifically adhered to the elastomer in any way.
  • Equation 2 is adapted for this scenario such that for the fabric alone, the uniaxial stress equation is based on Equation 3.
  • Equation 3 where t 1 , f abric is the fabric’s true stress in the direction of elongation (Pa), and k 1 (Pa) and (dimensionless) are the coefficients of interest.
  • Table 1 Fitted coefficients for all tested materials.
  • a fabric jacketed tube is therefore be assumed to have a uniaxial tensile stress equation equivalent to Equation 2, using a combination of the coefficients in Table 1.
  • the associated stress- strain curve is shown in FIG. 3F.
  • the elastomer material response is dominant at the lower strains while the fabric quickly becomes responsible for most of the stiffness at higher strains.
  • 3-dimensional finite element models are designed in ABAQUS to replicate the hydrostatic testing for all tested tubes. Since the base design of the tubes is axisymmetric, only a thin ‘slice’ of each tube, as shown in FIG. 4A, is modeled to save computational power. Different models are created to represent EF, DS, EFF, and DSF tubes, each using the relevant coefficients from Table 1 to define the material. Hydrostatic loads are applied to the inner surface of these modeled tube slices with analytical rigid rollers used to represent the clamps in the physical experiment, as in FIG. 4B.
  • the load is gradually increased to reflect each pressure level to which the physical tubes are subject during the experiment, plus one or more extra levels beyond the experimental maximum to monitor the continued evolution of the distension trends.
  • the tube slice takes on a distended shape, as shown in FIG. 4C. Performing a 360-degree sweep of this shape allows for a better visualization of the distended profile of the entire tube, as shown in FIG. 3D.
  • Analysis of the deformed models allows for calculation of maximum distension at each simulated pressure level and rate of distension per unit pressure increase using the same equations provided above, where maximum distension is defined as the average difference between final and initial diameter over the middle 3 cm of the tube.
  • FIGS. 4E-4F show that there is good agreement between physical experiment and numerical simulation for the distension trends of all tested tubes.
  • the distension-pressure curves for the unjacketed elastomer tubes experience are exponential (continually increasing distension rates) whereas for the jacketed tubes they are sigmoidal (distension rates that peak and then fall).
  • the numerical values of both distension and volume over the entire tested pressure range This is quantifiable by using a least-squares reduction to determine R 2 values, as listed in Table 2.
  • Table 2 R 2 values of experimental tube distensions and volumes against simulated tube distensions and volumes.
  • the asymmetric distension observed in the elastomeric tubes at high pressures did not occur in the simulations.
  • This discrepancy is reconciled by considering the real- life limitations of the tubular cast geometry and the flow loop setup. For example, due to printing errors or gradual warping of the 3D printed mold, there may be localized ‘thin’ regions on the tube where the wall thickness is slightly decreased. Alternatively, due to slight misalignment of the tube or clamps in the compliant chamber, there may be regions of the tube which are subject to more fluid pressure than others. In either case, there will be small areas of elevated stress on the tube wall which would result in localized regions of greater distension.
  • FIG. 5B shows a clear difference in distension profiles between an unjacketed and jacketed elastomeric tube near the upper limits of their tested pressures.
  • the observed self-regulation behavior in jacketed elastomeric tubes may play a pivotal role in several of its applications.
  • the present invention provides a proof of concept for a material phenomenon using a limited set of experiments.
  • tubing design is carefully altered to induce onset of self-regulation at a particular pressure or distension.
  • inventive tunable tubing has utility for a myriad of purposes.
  • the tubing is tunes by changing the circumference of the sewn fabric jacket. Increasing the circumference (introducing slack into the jacket) delays the onset of the self-regulation response, whereas decreasing the circumference introduces pre-stretch in the fabric (essentially changing its material coefficients) and hastens the onset of self-regulation. Similarly, by printing a new mold design, the base elastomeric tubing is customized by changing its radius, length, or wall thickness.
  • Kirigami the Japanese art of cutting and folding paper to produce repeated patterns
  • folds are induced in the fabric jacket to control the distension profile of the jacketed tube. Strategically cut regions in the fabric jacket create localized regions of increased compliance in the tube, which are then controlled carefully in accordance with the working conditions to produce highly specific material responses.
  • a simple simulation is designed to illustrate this concept. The left half of FIG. 6A depicts a jacketed EcoFlex tube, while the right half has a simple circumferential kirigami pattern cut into the fabric.
  • the present invention provides a design for jacketed elastomeric tubes that display self-regulation behavior at elevated hydrostatic pressures.
  • the jacketed tube are manufactured using 93-7% rayon-spandex blend knit fabric and cast elastomeric tubes made of both EcoFlex 00-50 and Dragon Skin 10 SLOW.
  • the jackets are created by sewing rectangular pieces of fabric along their long edges to form closed loops, then sliding them over the elastomeric tubes.
  • the jacketed tubes of the present invention have sigmoidal distension pressure curves and largely symmetric distension profiles. Further, the expansion of the knit fibers led to strain- stiffening, which is the basis of the self-regulation response.
  • the present invention provides a series of hydrostatic pressure tests and finite element models that validate, and expand on, the trends seen in the physical experiments.
  • Material behavior in the simulation is defined using hyperelastic constitutive models, which required numerical coefficients; these coefficients were obtained by fitting them to uniaxial tensile test data of the materials of interest.
  • a single uniaxial tensile test to failure could not be used.
  • a quasi-hysteresis test is conducted (loading cycles measured only), and the coefficients are fit to a single curve on the overall plot that is deemed to best represent the extent of hysteresis experienced by the material. Simulations are successful in replicating the experimental results, both in terms of overall trends and numerical values.
  • the present invention additionally provides a highly tunable and customizable tube, making it potentially suitable for a wide variety of applications.
  • Prospective applications for the presented design span the biomedical, soft robotic, and industrial sectors. Small changes to the design such as altering tube wall thickness, fabric jacket circumference, or knit fabric orientation may be made to yield simple, uniform changes to the material behavior. More complex alterations, such as cutting kirigami designs in the jacket, are also contemplated to induce more complex material responses.
  • EcoFlex 00-50 and Dragon Skin 10 SLOW are platinum-catalyzed RTV silicone elastomers obtained from Smooth-On Inc. (US).
  • EF and DS have 2 components that are mixed in a 1 : 1 ratio and degassed before being poured into molds to cure in their desired shape.
  • Knitted fabric (93% rayon and 7% spandex) sourced from Telio (Canada) is obtained from Marshall Fabrics.
  • Elastomeric tubes are manufactured by pouring mixed and degassed liquid resin into a 3D printed cylindrical mold and allowed to cure for a minimum of 3 hours.
  • the mold produces tubes with an outer diamter of 27.05 mm and had a center insert to produce an inner diameter of 19.05 mm.
  • the fabric is cut into rectangular pieces and sewn to form ‘jackets’ 12 cm in length and 8 cm in circumference, with the wale direction parallel to the longitudinal direction of the tube.
  • the fabric jackets are then pulled over the elastomeric tubes.
  • An image of the compliant tube is shown in FIG. 1.
  • a custom-built closed flow loop system is used to test the tubes under hydrostatic pressure.
  • a schematic of the flow loop is shown in FIG. 2A.
  • the system is reconfigured for hydrostatic tests; namely, one of the two pumps is unused, and fluid does not flow continuously through the entire loop.
  • the compliance chamber houses a length of elastomeric tubing with the ends clamped in place as shown in FIG. 2B, and fluid flows into it via the centrifugal pump at the top of the flow loop.
  • the check valve beneath the tube is closed to prevent fluid flow past the compliant chamber, achieving hydrostatic conditions.
  • a degree of pre-stretch is applied by running the centrifugal pump at increasingly higher speeds until severe, asymmetric distension of the tube occurs (jacketed tubes are pre-stretched without the jacket on). Centrifugal pump speed is increased in 200 rpm increments and the corresponding pressure is measured by a tap just below the compliant chamber. As fluid flows into the tube, it distends and a camera facing the compliance chamber takes pictures of the distended tube’s profile.
  • FIG. 2C is an example of an image taken by the camera facing the compliant chamber.
  • the images of the distended tubes are assessed to measure the amount of radial deformation experienced by the tube and the volume increase at each pressure level.
  • a MATLAB program is written that binarizes the grayscale images and calculates the ‘width’ of the tube along its entire length, one row at a time from top to bottom.
  • the maximum distension is defined as the difference between the tube’s maximum pressurized diameter and undeformed diameter.
  • the ‘maximum distension’ is defined as the average distension measurement of the middle 3 cm of the image taken.
  • a row-by-row integration approximation method is used to measure the distended volume of the tube.
  • the loading is performed at an extension rate of 0.1 ⁇ .
  • S - 1 based on previous literature that conducted similar tests [47], The stress-strain plots for the load ‘cycles’ is then superimposed to see the increase in compliance as the quasi-hysteresis test progresses, as shown in FIGS. 3C- 3D. Further information on this process is provided below regarding Hydrostatic Pressure Testing.
  • each tube is modeled as a longitudinal ‘slice’ encompassing a portion of the circumference equivalent to the thickness of a single element (approximately 0.5 mm).
  • the tube slices are defined in a cylindrical coordinate system as shown FIG. 4A.
  • the tube slice’s material behavior is defined to be hyperelastic and governed by the coefficients obtained from the uniaxial tests performed.
  • the material is assumed to be a homogeneous fiber-elastomer composite with fiber families running in the circumferential and longitudinal directions. Since most of the distension in the fabric jacket is circumferential, it is assumed that most of the material response is governed by the stiffness of the fabric in the course direction; therefore, the uniaxial coefficients of the fabric’s course direction are assumed to be representative of the fabric’s behavior in the simulation.
  • the ‘cut faces’ of the tube slices are restricted from moving in the circumferential direction; this essentially functions as a cyclic symmetry condition.
  • the top and bottom faces of the tube slice are restricted from moving in the z-direction.
  • the outer face of the tube is constrained by analytical rigid parts at the top and bottom of the tube, which are loosely representative of the real-life clamps used to hold the tube in place in FIG. 2B.
  • Contact between the tube and the clamps is defined to be frictionless and the clamp’s cross- sectional geometry is designed to maximize the stability of the simulation without greatly affecting the results.
  • the finite element assembly is shown in FIG. 4B.
  • the pressure load is defined as hydrostatic, applied across the entire inner face of the tube, and its magnitude is increased with each sequential step of the analysis to reflect each of the experimental pressures.
  • the distended finite element tube slice is pictured in FIG. 4C, the face of which could be swept to form a distended tube, as in FIG. 4D.
  • measurements of maximum tube distension and distended tube volume are calculated for each tested pressure.
  • max tube distension is defined as the mean displacement of all nodes along the middle 3 cm of the tube’s outer edge.
  • Tube volume is calculated using a trapezoidal approximation method similar to the pixel-by-pixel approximation used for the experimental images.
  • a MATLAB program calculates the maximum distension of the tubes by averaging the distended tube’s outer diameter D f over the middle 3 cm of the image and subtracting the undistended outer diameter D i . More specifically, the program splits the image into ‘rows’ of pixels and measures the width of the distended tube, in pixels, for each row. The measurements are later converted to SI units using a known calibration.
  • the volume of the distended tubes is calculated by taking row-by-row measurements of the tube’s width for the entire image except for the middle 3 cm. However, the images only measure the middle 8 cm of the 12 cm tubes. Since 1 cm on either end of the tube is clamped (and is ignored in the volume calculation), there is still an additional 1 cm of the distended tube wall which is not shown in the image. To account for this, an extrapolation method is used in which the tube diameter is assumed to return to the undistended diameter Di linearly over the missing 1 cm (the pictures in FIG. 5 support this approximation). The formula to calculate the volume is then given in Equation 5.
  • D f,k is the distended outer diameter of the tube for row k in the image (mm)
  • V exp is the volume (mL)
  • k max is the height of the image plus the extrapolated regions in pixels (px)
  • h pixel is the calibration length represented by one pixel in the image (mm/px).
  • V walls is the volume of the tube walls (mL), which are assumed to be incompressible and can have their volume calculated using Equation 6.
  • FIGS. 7-10 Plots of the experimental data for tube distension, rate of distension, tube volume, and rate of volumetric expansion are shown in FIGS. 7-10.
  • the volume plots follow the same trends seen in the distension plots; unjacketed tubes undergo exponential volume increase and steadily increasing rate of volumetric expansion with increasing pressure, whereas jacketed tubes experience a plateau in volume increase due to the self-regulation behavior.
  • elastomers are hyperelastic materials; this means their deformation behavior is governed by a strain energy density function instead of a single constant.
  • Zhalmuratova et al. [7] performed a review of different constitutive hyperelastic material models to model the stress-strain behavior of fiber-elastomer composites.
  • the Mooney-Rivlin model was used for elastomer strain energy density
  • the Holzapfel-Gasser-Ogden (HGO) model was used for composite strain energy density.
  • Equation 11 Equation 12: where a is defined as the angle between the fiber direction and stretching direction and 3 is defined as the angle between the two fiber families (0 and 90 degrees respectively). This leads to Equations 13 and 14.
  • strain energy density functions may be most easily converted to Cauchy stress equations under controlled conditions where the strain invariants are more easily determinable.
  • Equation 15 [00150]
  • the Holzapfel model is a decoupled strain energy density model for fiber-elastomer composites [41], where terms for strain energy density of the bulk elastomer and fabric layer can be considered separately, shown in Equation 16.
  • Equation 17 which, combined with Equations 13 and 14, leads to Equation 18 for the uniaxial tensile stress of fabric.
  • FIGS. 11-15 Complete quasi-hysteresis plots for all materials are shown in FIGS. 11-15.
  • the legend associates the color of each plot curve with the maximum level of strain for that test. With the exception of some of the last entries in the legend, there will be two curves for each color: one with higher stress values and one with lower. These correspond to the first and third tensile tests to that level of strain, respectively.
  • tube volume is calculated using a trapezoidal approximation method.
  • the volume approximation was made by summing many thin volumes of revolution as shown in Equation 19.
  • V sim is the volume (mL)
  • D k is the diameter of node k (in mm, noting there are k mx:.: + 1 nodes in the region of interest)
  • h k is the thickness of the trapezoid, or the distance in the z-direction between nodes n + 1 and n (mm).
  • V walls retains the same definition as in Equation 6.
  • FIGS. 27- 30 Comparison plots of tube distension, rate of tube distension per unit pressure increase, tube volume, and rate of volumetric expansion per unit pressure increase are shown in FIGS. 27- 30. Superimposition of the experimental and simulated data allows for visual confirmation of the agreement between the two sets.
  • the benefit of the jackets during this round of testing is its ability to act as a ‘fail-safe’ and broaden the working conditions of the tube.
  • the jacketed tubes have a much larger range of backpressures under which an acceptable distension waveform could be obtained, and they are generally able to operate under higher pressures and at higher levels of distension.
  • the mean distension is lower than that of the unjacketed tubes. This indicates that the desired distension behavior can be achieved with a lower ‘baseline’ level of distension, i.e. the material experiences less constant strain when in use.
  • FIG. 41 is a single hysteresis loop for a single tube length of a given material.
  • FIG. 41 is a single hysteresis loop for a single tube length of a given material.
  • FIG. 41 is a single hysteresis loop for a single tube length of a given material.
  • Patent documents and publications mentioned in the specification are indicative of the levels of those skilled in the art to which the invention pertains. These documents and publications are incorporated herein by reference to the same extent as if each individual document or publication was specifically and individually incorporated herein by reference.

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Abstract

Un procédé d'actionnement de fluide passif comprend la fourniture d'un tube élastomère gainé définissant un canal interne, le tube élastomère gainé ayant une première extrémité et une seconde extrémité, une longueur s'étendant de la première extrémité à la seconde extrémité, et un premier diamètre. Le procédé consiste ensuite à fixer la première extrémité et la seconde extrémité du tube élastomère gainé, à fournir un fluide au canal interne du tube élastomère gainé et à distendre le tube élastomère gainé de telle sorte qu'au moins une partie du tube élastomère gainé le long de la longueur s'étend du premier diamètre à un second diamètre. Un tube élastomère gainé destiné à être utilisé avec le procédé décrit ci-dessus comprend un tube élastomère définissant un canal interne et ayant une surface externe et une gaine de tissu enroulée autour de la surface externe du tube élastomère.
PCT/CA2023/050209 2022-02-18 2023-02-17 Tubes élastomères à distension auto-régulée Ceased WO2023155015A1 (fr)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP3251716B1 (fr) * 2009-08-11 2019-02-20 ResMed Motor Technologies Inc Ventilateur avec un appareil de soufflage à symétrie axiale et à un seul étage
US11090458B2 (en) * 2012-04-13 2021-08-17 Fresca Medical, Inc. Auto-feedback valve for a sleep apnea device
US20210338922A1 (en) * 2013-03-15 2021-11-04 Bayer Healthcare Llc Fluid delivery system including a high crack pressure valve and methods for its use

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP3251716B1 (fr) * 2009-08-11 2019-02-20 ResMed Motor Technologies Inc Ventilateur avec un appareil de soufflage à symétrie axiale et à un seul étage
US11090458B2 (en) * 2012-04-13 2021-08-17 Fresca Medical, Inc. Auto-feedback valve for a sleep apnea device
US20210338922A1 (en) * 2013-03-15 2021-11-04 Bayer Healthcare Llc Fluid delivery system including a high crack pressure valve and methods for its use

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