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This publication documents measurement data for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy. Materials The diaphysis of a human (92-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program. Bars (nominally 4.0 mm x 4.0 mm cross section) were extracted from the diaphysis as demonstrated in Figure-samplelocation. Two single Edge Notch Bend, SEN(B), specimens for a load span s=20 mm were machined for a three-point bend fixture for crack growth in the transverse direction. SEN(B) specimens had the following dimensions (height d, depth b, initial crack length a0): beam 1 d=4.0 mm, b=4.0 mm, a0=1.8 mm, beam 2 d=4.1 mm, b=3.9 mm, a0=1.7 mm). Osteon diameter was measured was measured on polished sections by using backscatter SEM images following Britz (2009), Figure samplelocation.jpg. Using ImageJ, a grid is imposed on the images and On.Dm is determined as the Feret Diameter for at least 40 On.Dm measures. For beam 1 mean On.Dm is 242 micrometer and for beam 2 284 micrometer. Experiments and Data Fracture experiments were conducted with a Deben 5000 load rig in a Zeiss XRADIA 3D microscope. For system details see https://www.physics.purdue.edu/xrm/about-our-instruments/index.html. Data for these experiments is given in the two csv files of this project data set. In these experiments force F (load cell) data and image frame data are obtained as machine output. Crack mouth opening displacement (CMOD) is obtained from 3D X-ray images at frame numbers synchronized to force readings. Fracture process zone (FPZ) length L. FPZ length data is obtained from 3D image data in Gallaway, G. E.; Allen, M. R.; Surowiec, R. K.; Siegmund, T. H. (2025). 3D Image Data from In-situ X-ray Imaging Transverse Crack Growth Experiments in Human Cortical Bone. Purdue University Research Repository. doi:10.4231/94PZ-AB06 Code Code (Analysis_Main.m, Analysis_Func.m) takes data from the .csv files and determines the linear elastic fracture mechanics quantities (LEFM toughness), the quasi-brittle fracture mechanics quantities (QBFM toughness), and the tissue intrinsic (size-independent) fracture properties (tissue toughness, tissue strength, tissue lengthscale). Output is depicted as force-CMOD and fracture process zone length - CMOD records, and as crack growth resistance curves (quasibrittle energy release rate vs. fracture process zone length). In addition, the microstructure constant eta is obtained as the ratio between the tissue intrinsic lengthscale and the mean osteon diameter. Code (P_star.m) is provided to determine maximum sustainable load of a femoral shaft in three-point bending. It is assumed that the beam is a pipe with a surface crack of depth equal to the mean osteon diameter. This code can be used for sensitivity studies of the dependence of whole bone maximum sustainable load on cortical thickness, tissue intrinsic strength and microstructure constant eta. Example calculations are depicted in two relevant figures. 

This publication documents 3D image stacks from HR-pQCT imaging of a femur diaphysis, as well as image stacks for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy. Imaging For HR-qQCT: HR-pQCT scans were acquired by Rachel Surowiec using an XtremeCT II scanner (SCANCO Medical AG, Bruttisellen, Switzerland) within the Musculoskeletal Function, Imaging and Tissue (MSK-FIT) Resource Core of the Indiana Center for Musculoskeletal Health’s Clinical Research Center (Indiana University, Indianapolis, IN). Scans are performed at 60.7 um resolution, a 68 kV, 1467 uA, 43 ms integration time, 1 frame averaging. Raw scans are ‘.RSQ’ file types. The ISQ file type were read into ImageJ using the Import-KHKs Scanco uCT ISQ file reader plug-in, and exported as bmp image stacks, image stacks are provided in two parts. Reconstructed images are rotated in dataviewer so that all bones are in the same orientation (prox/distal/anterior/posterior for the Femur). For in-situ fracture mechanics experiments: 3D scans were acquired by Glynn Gallaway using a 3-point bending rig for single edged notched bend specimens with a Deben CT5000N load cell (Deben, Bury St. Edmunds, UK) in a Zeiss XRADIA 510 Versa 3D X-Ray microscope (Carl Zeiss AG, Baden-Württemberg, Germany) at Purdue University. The 3-point bending frame had a span 20 mm with X-ray transparent, glassy carbon supports. To maintain hydration, the beam was wrapped in a plastic film slit at the notch. Displacements were applied at 0.1 mm/min. Load cell outputs were monitored and recorded. Displacements are held constant during image acquisitions. The first 3D image was obtained at the onset of non-linearity. Subsequently, the displacement was increased until a load increase of 10 N was observed, and another image was obtained. This sequence was repeated 6-times until peak load. 3D X-ray images were acquired with a resolution of 4.5 um, exposure time 5 sec., 801 projections, 120 kV, 10 W, 4 x objective, and a LE2 filter. X-ray projections were processed through XRADIA Scout-and-Scan Reconstructor. A recursive Gaussian smoothing filter (s=1 pixel) was applied to reduce image artifacts. Image stacks are exported as tiff files and provided individually for each load step and specimen. Two experiments are documented (beam 1 and beam 2). MaterialstThe diaphysis of a human (92-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program. 

Understanding bone strength is important when assessing bone diseases and their treatment. Bending experiments are often used to determine strength. Then, flexural stresses are calculated from elastic bending theory. With a brittle failure criterion, the maximum flexural tensile stress is equated to (nominal) strength. However, bone is not a perfectly brittle material. A quasi-brittle failure criterion is more appropriate. Such an approach allows for material failure to occur before full fracture. The extent of the subcritical damage domain then introduces a length scale. The intrinsic strength of the bone is calculated from the critical load at fracture and the failure process zone dimensions relative to the specimen size. We apply this approach to human cortical bone specimens extracted from a femur. We determine strength measures in the untreated reference state and after treatment with the selective estrogen receptor modulator raloxifene. We find that the common nominal strength measure does not distinguish between treatments. However, the dimensions of the failure process zone differ between treatments. Intrinsic strength measures then are demonstrated as descriptors of bone strength sensitive to treatment. An extrapolation of laboratory data to whole bone is demonstrated. 

A series of files for the execution of finite element simulations of topologically interlocked assemblies are provided and can be executed with the finite element code ABAQUS (or similar). In all files the following structure is present: -- For each part of the assembly (frame, indenter, building block), a definition of nodes (*node) and sets of nodes (*nset), elements (*element) and set of elements (*elset) is provided. -- Instances of parts are defined an placed in the assembly at position according to the assembly plan. -- Parts frame and indenter are defined as rigid bodies (*rigid body) . Building blocks as linear elastic (*elastic). -- Boundary conditions and constraints are defined (*boundary) -- Surfaces (*surface), surface behavior (*surface behavior) and contact interactions (*contact) are given. -- A mass scaled explicit solution is used (*dynamic, explicit) -- Computed values are recorded (*node output, *energy output, *element output) ABAQUS inp file for a 6 by 6 assembly of hexagonal scutoids, coefficient of friction 0.4: HexScutoid6x6mu4.inp ABAQUS inp file for a 6 by 6 assembly of hexagonal scutoids, all building blocks fused to a monolithic system: HexScutoid6x6mu4_fused.inp ABAQUS inp file for a 7 by 7 assembly of hexagonal scutoids, coefficient of friction 0.4: HexScutoid6x6mu4.inp ABAQUS inp file for a 6 by 6 assembly of pentagonal scutoids, coefficient of friction 0.4: PentagonScutoid6x6mu4.inp ABAQUS inp file for a 7 by 7 assembly of pentagonal scutoids, coefficient of friction 0.4: PentagonScutoid6x6mu4.inp ABAQUS inp file for a 6 by 6 assembly of tetrahedra, coefficient of friction 0.4: Tetrahedra6x6mu4.inp ABAQUS inp file for a 7 by 7 assembly of tetrahedra, coefficient of friction 0.4: Tetrahedra7x7mu4.inp This work was supported by NSF Award 16622177. 

This publication provides files for the finite element simulation of the mechanical behavior of a set of topologically interlocked material (TIM) systems. Files are to be executed with the FE code ABAQUS (TM), Simulia Inc., or need a file translator to be used by other codes if needed. Files are provided for even (i=10) and odd (i=11) numbered square assemblies of (i x i) blocks confined by a rigid frame and subjected to a transverse displacement load at the assembly center. The following files are provided: The simulations are executed as explicit dynamic simulations with a mass-scale approach to extract the quasi-static response. Building blocks are linear elastic and interact with neighbors by contact and friction. The following files are provided BR_tet_i6.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 6 x 6 blocks. This is the reference model 1. BR_tet_i8.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 8 x 8 blocks. This is the reference model 1. BR_tet_i10.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 10 x 10 blocks. This is the reference model 1. BR_tet_i12.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 12 x 12 blocks. This is the reference model 1. BR_tet_i5.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 5 x 5 blocks. This is the reference model 2. BR_tet_i7.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 7 x 7 blocks. This is the reference model 2. BR_tet_i9.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 9 x 9 blocks. This is the reference model 2. BR_tet_i11.inp: File for a TIM system constructed from regular, truncated tetrahedra shaped building blocks. An assembly of 11 x 11 blocks. This is the reference model 2. BT1_tet_i6.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 6 x 6 blocks. BT1_tet_i8.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 8 x 8 blocks. BT1_tet_i10.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 10 x 10 blocks. BT1_tet_i12.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 12 x 12 blocks. BT1_tet_i5.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 5 x 5 blocks. BT1_tet_i7.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 7 x 7 blocks. BT1_tet_i9.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 9 x 9 blocks. BT1_tet_i11.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks. BT2_tet_i6.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 6 x 6 blocks. BT2_tet_i8.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 8 x 8 blocks. BT2_tet_i10.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 10 x 10 blocks. BT2_tet_i12.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 12 x 12 blocks. BT2_tet_i5.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 5 x 5 blocks. BT2_tet_i7.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 7 x 7 blocks. BT2_tet_i9.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 9 x 9 blocks. BT2_tet_i11.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks. BT1_tet_i6_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 6 x 6 blocks. BT1_tet_i8_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 8 x 8 blocks. BT1_tet_i10_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 10 x 10 blocks. BT1_tet_i12_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 12 x 12 blocks. BT1_tet_i5_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 5 x 5 blocks. BT1_tet_i7_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 7 x 7 blocks. BT1_tet_i9_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 9 x 9 blocks. BT1_tet_i11_0_34.inp: File for a TIM system constructed from single-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 11 x 11 blocks. BT2_tet_i6_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 6 x 6 blocks. BT2_tet_i8_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 8 x 8 blocks. BT2_tet_i10_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 10 x 10 blocks. BT2_tet_i12_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 17 degree. An assembly of 12 x 12 blocks. BT2_tet_i5_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 5 x 5 blocks. BT2_tet_i7_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 7 x 7 blocks. BT2_tet_i9_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 9 x 9 blocks. BT2_tet_i11_0_34.inp: File for a TIM system constructed from double-skewed, truncated tetrahedra shaped building blocks. Skew angle is 12 degree. An assembly of 11 x 11 blocks. 

This publication contains ABAQUS inp files supporting the publication Numerical study on wave propagation in a row of topologically interlocked tetrahedra in Granular Matter (2023), 25 (1) This study is concerned with the mechanics of wave propagation in a type of architectured, granular, material system. Specifically, we investigate wave propagation in a topologically interlocked material (TIM) system. TIM systems are assemblies of polyhedrons in which individual polyhedrons cannot be removed from the assembly without complete disassembly due to the geometric interlocking of the polyhedrons. The study employs an explicit finite element code to compute phase velocities, amplitude distributions, and wave patterns in a linear assembly of topologically interlocking tetrahedra. Tetrahedra are considered fully 3D linear elastic bodies interacting with neighboring tetrahedra by contact and friction. This publication contains the following inp files for use with the FE code ABAQUS: FullChainMu0V01Linear.inp -- A row of tetrahedra, constant contact stiffness, no friction, impact velocity 1.0 m/s. FullChainMu5V01Linear.inp -- A row of tetrahedra, constant contact stiffness, Coulomb friction with coefficient of friction 0.5, impact velocity 1.0 m/s. ExpAV01.inp -- A row of tetrahedra, variable contact stiffness, no friction, impact velocity 1.0 m/s. ExpBV01.inp -- A row of tetrahedra, variable contact stiffness, no friction, impact velocity 1.0 m/s. PartiallyFused.inp -- A row of tetrahedra with several tetrahedra fused together, constant contact stiffness, no friction, impact velocity 1.0 m/s. PartiallyFusedFric.inp -- A row of tetrahedra with several tetrahedra fused together, constant contact stiffness, Coulomb friction with coefficient of friction 0.5, impact velocity 1.0 m/s. 

Topologically Interlocked Material systems are a class of architectured materials. TIM systems are assembled from individual building blocks and are confined by an external frame. In particular, 2D, plate-type assemblies are considered. This publication contains files for the numerical analysis of the mechanical behavior of TIM systems through the use of finite element analysis. ABAQUS model files (inp format) for the study of the chiral/achiral response are provided. Files chirality_s1_in.inp are for type I square assemblies. n=3,5,7,9 Files chirality_s2_in.inp are for type II square assemblies. n=4,6,8,10 Files chirality_h1_in.inp are for type I hexagon assemblies. n=2,3,4,5 Files chirality_h2_in.inp are for type II hexagon assemblies. n=2,3,4,5 File chirality_s1i5_center_dissection.inp is for an assembly with a dissection of the central tile of type I square assembly with n=5. File chirality_s2i6_center_dissection.inp is for an assembly with a dissection of the central tile of type II square assembly with n=6. File chirality_s1i5_center_surrounding_dissection.inp is for an assembly with dissections of the tiles surrounding the center tile of type I square assembly with n=5. File chirality_h1i3_center_dissection.inp is for an assembly with a dissection of the central tile of type I hexagon assembly with n=3. File chirality_h2i3_center_dissection.inp is for an assembly with a dissection of the central tile of type II hexagon assembly with n=3. File chirality_h1i3_center_surrounding_dissection.inp is for an assembly with dissections of the tiles surrounding the center tile of type I hexagon assembly with n=3. 

The present study focuses on the mechanical chirality in plate-type topologically interlocked material systems. Topologically interlocked material (TIM) systems are a class of dense architectured materials for which the mechanical response emerges from the elastic behavior of the building blocks and the contact-frictions interactions between the blocks. The resulting mechanical behavior is strongly non-linear due to the stability-instability characteristics of the internal load transfer pattern. Two tessellations are considered (square and hexagonal) and patches from each are used as templates. While individual building blocks are achiral, chirality emerges from the assembly pattern. The measure of \textit{microstructure circulation} is introduced to identify the geometric chirality of TIM systems. TIM systems identified as geometrically chiral are demonstrated to possess mechanical chiral response with a force-torque coupling under transverse mechanical loading of the TIM plate. The chiral length is found to be constant during the elastic response, yet size-dependent. During nonlinear deformation, the chiral length scale increases significantly and again exhibits a strong size dependence. The principle of dissection is introduced to transform non-chiral TIM systems into chiral ones. In the linear deformation regime, the framework of chiral elasticity is shown to be applicable. In the non-linear deformation regime, chirality is found to strongly affect the mechanical behavior more significantly than in the linear regime. Experiments on selected TIM systems validate key findings of the main computational study with the finite element method. 

This publication documents 3D image stacks for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy, 2D image stacks of the crack mouth opening displacement during said loading, and analysis codes which supported the publication. Materials: The diaphysis of a human (75-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program. Nominal 4 mm x 4 mm x 24 mm beams were sectioned from the femur diaphysis. Experiments were conducted on 12 beams. Beams were assigned to 2 groups: treated with Raloxifene (RAL), treated with a vehicle (VEH) control. Image data are provided for one beam from the RAL group and one beam from the VEH group. Additional images can be made available upon request to the corresponding author. Imaging: ;For in-situ fracture mechanics experiments: 2D and 3D scans were acquired by Glynn Gallaway using a 4-point bending rig for single edged notched bend specimens in a water bath with a Deben CT5000N load cell (Deben, Bury St. Edmunds, UK) in a Zeiss XRADIA 510 Versa 3D X-Ray microscope (Carl Zeiss AG, Baden-Wuerttemberg, Germany) at Purdue University. The 4-point bending frame had a span 16 mm with X-ray transparent, glassy carbon supports. To maintain hydration, bending frame was situated in a waterbath filled with DI water. Displacements were applied at 0.1 mm/min. Load cell outputs were monitored and recorded. During loading 2D images were obtained every 1 second. 3D X-ray images were acquired with a resolution of 4.5 um, exposure time 6 sec., 2401 projections, 120 kV, 10 W, 4 x objective, and a LE2 filter. X-ray projections were processed through XRADIA Scout-and-Scan Reconstructor. A recursive Gaussian smoothing filter (1 pixel) was applied to reduce image artifacts. Image stacks are exported as tiff files and provided for each specimen. Images are provided for one RAL treated sample and one VEH treated sample. 

A 2D plane strain extended finite element method (XFEM) model was developed to simulate three-point bending fracture toughness tests for human bone conducted in hydrated and dehydrated conditions. Bone microstructures and crack paths observed by micro-CT imaging were simulated using an XFEM damage model. Critical damage strains for the osteons, matrix, and cement lines were deduced for both hydrated and dehydrated conditions and it was found that dehydration decreases the critical damage strains by about 50%. Subsequent parametric studies using the various microstructural models were performed to understand the impact of individual critical damage strain variations on the fracture behavior. The study revealed the significant impact of the cement line critical damage strains on the crack paths and fracture toughness during the early stages of crack growth. Furthermore, a significant sensitivity of crack growth resistance and crack paths on critical strain values of the cement lines was found to exist for the hydrated environments where a small change in critical strain values of the cement lines can alter the crack path to give a significant reduction in fracture resistance. In contrast, in the dehydrated state where toughness is low, the sensitivity to changes in critical strain values of the cement lines is low. Overall, our XFEM model was able to provide new insights into how dehydration affects the micromechanisms of fracture in bone and this approach could be further extended to study the effects of aging, disease, and medical therapies on bone fracture.