High Strain Energy Density Research Articles

The Electrochemical Actuation Performances of Nanoporous Ternary AlCoCu Alloy with a Unique Nanosheet Structure.

Compared to traditional actuators (such as piezoelectric ceramics), metal actuators possess the advantages of a low energy consumption, large strain amplitude, and high strain energy density. However, most of the existing metal actuators with an excellent comprehensive performance are composed of precious metals, which are limited by high costs and have almost no possibility for large-scale production in the future. This study focuses on non-precious metal materials and exploits a one-step chemical dealloying method to prepare bulk nanoporous (NP) CoCuAl actuators (NP-CCA) from Al70Co20Cu10 alloy. The microstructure and actuation properties of the NP-CCA were analyzed in detail. The dense continuous nanoscale pores provide an excellent network connectivity for a large strain response, enabling the NP-CCA to achieve a strain amplitude of up to 1.19% (more than eight and two times that of NP-Pt and NP-Ag, respectively), comparable to precious metal actuators. In addition, the NP-CCA possesses a high strain energy density, which is prominent in many precious metal actuation materials (such as NP-Au, NP-Ag, and NP-Pt).

Ultra-tough artificial woods of polyphenol-derived biodegradable Co-polymer with Poly(butylene succinate)

Large productions of plastics worldwide are greater concern to the environment because of their non degradability and thus, damaging the ecosystem. Recent advancements in biobased plastics are growing exponentially because of their promise of a sustainable environment. Biobased polycoumarates plastics have a wood-like appearance with liquid crystalline grains, light brown color, and cinnamon-like aroma, but have very low toughness. The polycoumarates were hybridized via main-chain transesterification with poly (butylene succinate) (PBS). PBS itself being a biobased material has added more value to the final product due to biodegradability. The mechanical flexibility and toughness of the bio-based copolymers were controlled by varying the PBS content. As a result, well-processable and in-soil degradable artificial woods with a high strain energy density of approximately 76 MJ/m3 were developed while maintaining the wood-like appearance.

Controlled Allocation of Aromatic/Aliphatic Substituents to Polysaccharides and Lignin in Sugarcane Bagasse via Successive Homogeneous Transesterification Using Ionic Liquid.

Lignocellulosic agricultural waste is an abundant renewable feedstock that can be utilized as a sustainable source of biomass-based plastics. Ideally, it is used without discarding any components, including cellulose, hemicellulose, and lignin. However, their utilization as lignocellulose-based plastics has been limited because of the low compatibility between the polysaccharides and lignin derivatives and the resulting poor mechanical properties of the final products. Here, we demonstrate a facile but highly controllable conversion of sugarcane bagasse into valuable thermoplastics by utilizing the excellent solubility and unique organocatalytic abilities of an ionic liquid, 1-ethyl-3-methylimidazolium acetate. In a homogeneous and one-pot chemical modification reaction system, the substitution ratio of an aromatic benzoyl group to an aliphatic hexanoyl group in the bagasse derivative was adjusted by the ratio of acyl reagents used. Moreover, the allocation of these two acyl groups to polysaccharide and lignin components in bagasse was successfully controlled only by exchanging the order of the acyl reagents introduced into the reaction system. The controlled introduction of the acyl groups into bagasse achieved a homogeneous polymer phase in the resultant multicomponent hot-pressed film, resulting in enhanced mechanical properties such as sufficient tensile strength (∼20 MPa) and excellent ductility with a high strain energy density (∼5 MJ m-3).

Potentiostatic Dealloying Fabrication and Electrochemical Actuation Performance of Bulk Nanoporous Palladium

Metallic actuators increasingly exhibit superiority over conventional actuators (such as piezoelectric ceramics) via low energy consumption and large strain amplitude. Large strain amplitude and high strain energy density (or work density) are required for an actuator with excellent comprehensive performance. Herein, we fabricated bulk nanoporous Pd (np-Pd) with a dense nanoporous structure by two-step potentiostatic dealloying of as-annealed Ni–Pd alloy with chemical corrosion resistance, and investigated the dealloying behaviors as well as electrochemical actuation performance. A visible current density oscillation occurred during dealloying, which is related to formation/dissolution of the passivating film. Additionally, since the dense and continuous ligaments establish a good network connectivity for large strain response, the np-Pd achieves a strain amplitude of up to 3.74% and high strain energy density, which stands out among many actuator materials (e.g., np-AuPt, np-Ni, and np-AlNiCu). Our study provides a useful guidance for fabricating metallic actuators with excellent comprehensive performance.

Enhancing long-term tensile performance of Engineered Cementitious Composites (ECC) using sustainable artificial geopolymer aggregates

Artificial geopolymer aggregate is an emerging technology in the field of solid waste recycling, aiming to ease the exploitation of natural aggregates as well as reduce the environmental burden of industrial/urban/agricultural waste and by-product accumulations. In this study, geopolymer aggregates (GPA) were strategically utilized to enhance long-term tensile performance and sustainability of high-strength Engineered Cementitious Composites (ECC). Accelerated aging test was conducted to evaluate the long-term performance of GPA-ECC, with the conventional fine silica sand ECC (FSS-ECC) as the control group. It was found that after accelerated aging (i.e., to simulate long-term curing condition), the compressive and tensile strengths of both GPA-ECC and FSS-ECC increased. In addition, owing to the flaw effect of GPA, the long-term tensile ductility of GPA-ECC was maintained, while that of FSS-ECC decreased significantly. Compared with FSS-ECC, GPA-ECC showed better multiple cracking behavior, higher strain energy density, and finer crack width under both short- and long-term conditions. Finally, a cost analysis of ECC matrix was conducted to exhibit the cost-efficiency and sustainability of GPA-ECC. This study provides a sustainable approach for enhancing the long-term tensile performance of high-strength ECC based on artificial aggregates.

Numerical study on impact resistance of novel multilevel bionic thin-walled structures

Inspired by impact-resistant hedgehog spine and beetle's forewing, the thin-walled structures of simple hedgehog spine and multilevel hedgehog spine were designed. Numerical simulations of rigid flat plate impacting on thin-walled structures showed that the deformation coordination ability and stress distribution of the structure are improved effectively by the hedgehog spine section design. This makes the specific energy absorption of the simple hedgehog spine thin-walled structure just before failure increase to 9.6 times and 5.7 times those of the single-walled cylinder and simple spider web thin-walled structures, respectively. Furthermore, the sub-circle multilevel design was introduced to further increase the range of high strain energy density, and the specific energy absorption of the multilevel hedgehog spine thin-walled structure was 2.1 times that of the simple hedgehog spine thin-walled structure.

Self-Standing Nanomembranes of Super-Tough Plastics.

Nanomembranes are effective coating materials for protecting substrates from external stimuli; however, they are generally not self-standing owing to their low mechanical toughness. Self-standing nanomembranes would be an innovative development in the field of nanotechnology including miniaturized devices. In this study, self-standing nanomembranes were developed by spin-casting supertough polyamides over dimethylformamide solution. The polyamides were synthesized by the polycondensation of two derivatives of 4,4'-diamino-α-truxillic acid (4ATA) with slightly bent diphenylcyclobutane in the core. Mechanical evaluation of the 4ATA polyamides having an appropriate composition of aliphatic diacids revealed a high strain-energy density of 231 MJ m-3 at its maximum, which is significantly tougher than spider silk. The nanocoats with a thickness of several hundred nanometers showing interference fringes were able to be peeled off the glass substrate without breaking, owing to its ultrahigh toughness. The self-standing nanomembrane would be applied to flexible devices in the future.

Stability of Cu-islands formed on Si substrate via ‘dewetting’ under subsequent thermal cycling

Very thin metallic films deposited on a substrate often dewet upon thermal exposure, forming discrete islands of micrometer and nanometer-sized metal particles. Herein, Cu islands on Si substrate, which were formed due to agglomeration (or ‘dewetting’) of Cu thin film at 600 °C, were exposed to thermal cycling, and the ensuing evolution in their morphology was monitored. Thermal cycling was performed between either −25 °C and 150 °C or 25 °C and 400 °C, using different heating and cooling rates. With faster heating-cooling rates, a change in the shape and size of the Cu islands was observed, whereas a slow heating-cooling rate did not induce noticeable effect on their morphology. Furthermore, the formation of new nano- and micro-sized particles, probably through the dewetting of the ultra-thin layer of Cu that was left intact during the initial agglomeration treatment, was observed during the thermal cycling performed at fast rates up to 400 °C. Finite element analysis, incorporating Anand’s viscoplasticity model, revealed the existence of high strain energy density in the vicinity of the particle-Si interface when the thermal cycling is carried at a faster ramp rate, suggesting the pivotal role of thermal stresses, in addition to the maximum temperature, in controlling the morphology of the Cu particles and the dewetting of the residual ultra-thin layer of Cu on Si.

Changing the Diameter of the Bone Tunnel Is More Effective Than Changing the Tunnel Shape for Restoring Joint Functionality After ACL Reconstruction

The clinical implications of changing the shape of the bone tunnel for Anterior cruciate ligament reconstruction (ACLR) is controversial and few studies have reported on the long-term prevalence for osteoarthritis. As such, this study aims to evaluate the effect of tunnel shape on joint biomechanics. Finite element models of an ACLR were constructed with different shapes (circular, oval, rounded rectangular, rectangular, and gourd-shaped) and diameters (7.5, 8.5, and 9.5 mm) for the bone tunnel. A combined loading of 103 N anterior tibial load, 7.5 Nm internal tibial moment and 6.9 Nm valgus tibial moment was applied at a joint flexion angle of 20°. Joint kinematics and the strain energy density (SED) on the articular cartilage were compared among the different groups. The results showed that conventional ACLR (circular tunnel) lead to an increase in joint kinematics over the intact joint, a lower ligament force and a higher SED on the lateral tibial cartilage. ACLR using the other tunnel shapes resulted in even greater joint kinematics, lower graft force and greater SED on the lateral tibial cartilage. Increasing the tunnel diameter better restored joint kinematics, graft force and articular SED, bringing these values closer to those from the intact knee. In conclusion, increasing the tunnel diameter may be more effective than changing the tunnel shape for restoring joint functionality after ACLR.

High strain and high energy density of lead-free (Bi0.50Na0.40K0.10)0.94Ba0.06Ti(1−x)(Al0.50Ta0.50)xO3 perovskite ceramics

Lead-free perovskite materials for capacitors have been recognized worldwide attention in recent times with high storage energy density and efficiency. A series of (Bi0.50Na0.40K0.10)0.94Ba0.06Ti(1−x)(Al0.50Ta0.50)xO3 ceramics are synthesized using traditional mixed oxide route. All ceramics are in single-phase perovskite-like structure. At room temperature, high storage energy density, Wr ~ 1.67 J/cm3, and conversion efficiency, η ~ 81.46%, are perceived for x = 0.06 composition at 115 kV/cm. Temperature-dependent study obtains Wr ~ 1.21 J/cm3 and η ~ 84.96% at 80 °C with 80 kV/cm field. In addition, composition x = 0.06 is fatigue-free from 1 to 105 cycles measured at 80 kV/cm field. Furthermore, ceramic x = 0.04 is obtained a high bipolar strain ~ 0.31% at 80 kV/cm compared to other compositions. Hence, the compositions x = 0.06 for high energy density and x = 0.04 for strain might be useable in many electronic components.

Predicting the propagation and interaction of frontal accretionary thrust faults with work optimization

This study uses work optimization to predict the spatial and temporal development of faults. We focus on the growth of small fractures that develop into thrust faults at the toe of accretionary prisms because observations from physical laboratory accretion experiments provide rich data with which to validate the models, and the processes of accretionary thrust fault initiation remain unclear. In order to model these systems, we apply new implementations to the fault growth code GROW that improve its prediction of fault interaction using work optimization, including: 1) CPU parallelization, 2) a new growth algorithm that propagates only the most efficient fault in each growth increment, the single run mode, and 3) a new growth algorithm that only considers fault propagation from fault tips that host high sums of modes I and II stress intensity factors, KG, the limiting mode. The new single and limiting mode produce the geometries that best match the observed geometries, rather than the algorithm that allows all the faults to propagate simultaneously, regardless of KG, the multiple and non-limiting mode. The single limiting models predict that frontal accretionary thrusts initiate at the midpack or shallower depths, consistent with findings of previous studies. The thrusts propagate upward, link with the surface, and then propagate downward and link with the detachment. The backthrust tends to propagate before the forethrust, and then influences the forethrust propagation. This temporal and spatial sequence of faulting arises from the lower compression, higher shear strain, higher Coulomb stress and higher strain energy density that develop near the wedge surface and the inflection of the wedge slope. The models reveal that the final slip distributions do not reliably indicate the initiation location of the faults, in contrast to widespread assumptions.

Comprehensive Review on Effective Strategies and Key Factors for High Performance Piezoelectric Energy Harvester at Low Frequency

In the past decade, there has been rapid development in piezoelectric energy harvester due to its limited application and low output power. This paper critically reviews the strategies implemented to improve the power density for low-frequency applications. These strategies include piezoelectric material selection as well as optimisations of shape, size and structure. The review also focuses on the recent advances in multi-modal, nonlinear and multi-directional energy harvesting. Based on the comprehensive summary of the normalised power density at 1g acceleration, it was found that most works fell in the second quadrant of low frequency and high power density. The maximum value was around 1mW/mm3 /g. Adding an extension of beam or spring to the conventional piezoelectric beam could enhance the normalised power density dramatically. Additionally, the multi-modal energy harvester exhibits broader bandwidth when its multiple resonance peaks get closer. The findings indicate that the anticipated performance of a piezoelectric harvester can be attained by achieving the trade-off between output power and bandwidth. To achieve high performance at low frequency, the following factors are essential: excellent material characteristics optimised geometry for high strain energy density, excellent flexibility, high excitation amplitude and broad bandwidth.

Intracortical Bone Mechanics Are Related to Pore Morphology and Remodeling in Human Bone.

During aging and in osteoporosis, cortical bone becomes more porous, making it more fragile and susceptible to fractures. The aim of this study was to investigate the intracortical compression- induced strain energy distribution, and determine whether intracortical pores associated with high strain energy density (SED) in the surrounding bone matrix have a different morphology and distribution, as well as different remodeling characteristics than matrix with normal SED. Fibular diaphyseal specimens from 20 patients undergoing a jaw reconstruction (age range 41 to 75 years; 14 men and 6 women) were studied. Bone specimens were µCT-scanned, plastic embedded, and sectioned for histology. Three-dimensional microfinite element models of each specimen were tested in compression, and the SED of the bone immediately surrounding the intracortical pores was calculated within a plane of interest corresponding to the histological sections. The SED of a pore, relative to the distribution of the SED of all pores in each specimen, was used to classify pores as either a high or normal SED pore. Pores with high SED were larger, less circular, and were located closer to the endosteal surface of the cortex than normal SED pores (p < 0.001). Histological analysis of the remodeling events generating the pores revealed that the high SED pores compared with normal SED pores had 13.3-fold higher odds of being an erosive (70%) or formative (7%) pore versus a quiescent pore (p < 0.001), 5.9-fold higher odds of resulting from remodeling upon existing pores (type 2 pore) versus remodeling generating new pores (type 1 pore) (p < 0.001), and 3.2-fold higher odds of being a coalescing type 2 pore versus a noncoalescing type 2 pore (p < 0.001). Overall, the study demonstrates a strong relationship between cortical bone mechanics and pore morphology, distribution, and remodeling characteristics in human fibular bone. © 2018 American Society for Bone and Mineral Research.

Strain energy density distribution of a tight gas sandstone reservoir in a low-amplitude tectonic zone and its effect on gas well productivity: A 3D FEM study

The tight gas sandstone reservoirs in the Paleozoic of the Sulige gas field in China are highly heterogeneous, and fractures are key factors for stable reservoir production. Low-amplitude folds or nose-like structures are widely developed in the Upper Paleozoic strata in this area. To effectively predict gas well productivity, in this paper, a 3D FEM numerical simulation based on the deformation and energy variation of the rock mass was used to predict the "sweet spots" of gas well productivity in a tight gas sandstone reservoir using the He8 segment of the Middle Permian Xiashihezi Formation in the Central Sulige block as an example. The paleotectonic stress field of the study area during the maximum episode of compression in the Yanshanian movement was restored, and the two rupture parameters of the integrated rupture rate (IF) and strain energy density (U) were constructed. The strain energy density distribution has a high correlation with gas well productivity, indicating that it can better predict the rock rupture degree in low-amplitude tectonic zones. A complex relationship exists between the strain energy density distribution and low-amplitude folds. The high strain energy density zones are mainly distributed among the high positions and wing areas of the low-amplitude fold zone, but the top area of the low-amplitude fold does not necessarily have a high strain energy density. Portions of the high strain energy density zones are located in the gentle tectonic zone, located near but outside the low-amplitude fold zone. The strain energy in these gentle tectonic zones with a high strain energy density value is relatively high, and the rock mass is prone to rupture. This study is of great value in enriching the prediction of "sweet spots" in tight gas sandstone reservoirs in low-amplitude tectonic zones worldwide.

Spatial relationship between bone formation and mechanical stimulus within cortical bone: Combining 3D fluorochrome mapping and poroelastic finite element modelling

Bone is a dynamic tissue and adapts its architecture in response to biological and mechanical factors. Here we investigate how cortical bone formation is spatially controlled by the local mechanical environment in the murine tibia axial loading model (C57BL/6). We obtained 3D locations of new bone formation by performing ‘slice and view’ 3D fluorochrome mapping of the entire bone and compared these sites with the regions of high fluid velocity or strain energy density estimated using a finite element model, validated with ex-vivo bone surface strain map acquired ex-vivo using digital image correlation. For the comparison, 2D maps of the average bone formation and peak mechanical stimulus on the tibial endosteal and periosteal surface across the entire cortical surface were created. Results showed that bone formed on the periosteal and endosteal surface in regions of high fluid flow. Peak strain energy density predicted only the formation of bone periosteally. Understanding how the mechanical stimuli spatially relates with regions of cortical bone formation in response to loading will eventually guide loading regime therapies to maintain or restore bone mass in specific sites in skeletal pathologies.

Modeling mechanical inhomogeneities in small populations of proliferating monolayers and spheroids.

Understanding the mechanical behavior of multicellular monolayers and spheroids is fundamental to tissue culture, organism development, and the early stages of tumor growth. Proliferating cells in monolayers and spheroids experience mechanical forces as they grow and divide and local inhomogeneities in the mechanical microenvironment can cause individual cells within the multicellular system to grow and divide at different rates. This differential growth, combined with cell division and reorganization, leads to residual stress. Multiple different modeling approaches have been taken to understand and predict the residual stresses that arise in growing multicellular systems, particularly tumor spheroids. Here, we show that by using a mechanically robust agent-based model constructed with the peridynamic framework, we gain a better understanding of residual stresses in multicellular systems as they grow from a single cell. In particular, we focus on small populations of cells (1-100 s) where population behavior is highly stochastic and prior investigation has been limited. We compare the average strain energy density of cells in monolayers and spheroids using different growth and division rules and find that, on average, cells in spheroids have a higher strain energy density than cells in monolayers. We also find that cells in the interior of a growing spheroid are, on average, in compression. Finally, we demonstrate the importance of accounting for stochastic fluctuations in the mechanical environment, particularly when the cellular response to mechanical cues is nonlinear. The results presented here serve as a starting point for both further investigation with agent-based models, and for the incorporation of major findings from agent-based models into continuum scale models when explicit representation of individual cells is not computationally feasible.

Work Optimization Predicts Accretionary Faulting: An Integration of Physical and Numerical Experiments

AbstractWe employ work optimization to predict the geometry of frontal thrusts at two stages of an evolving physical accretion experiment. Faults that produce the largest gains in efficiency, or change in external work per new fault area, ΔWext/ΔA, are considered most likely to develop. The predicted thrust geometry matches within 1 mm of the observed position and within a few degrees of the observed fault dip, for both the first forethrust and backthrust when the observed forethrust is active. The positions of the second backthrust and forethrust that produce &gt;90% of the maximum ΔWext/ΔA also overlap the observed thrusts. The work optimal fault dips are within a few degrees of the fault dips that maximize the average Coulomb stress. Slip gradients along the detachment produce local elevated shear stresses and high strain energy density regions that promote thrust initiation near the detachment. The mechanical efficiency (Wext) of the system decreases at each of the two simulated stages of faulting and resembles the evolution of experimental force. The higher ΔWext/ΔA due to the development of the first pair relative to the second pair indicates that the development of new thrusts may lead to diminishing efficiency gains as the wedge evolves. The numerical estimates of work consumed by fault propagation overlap the range calculated from experimental force data and crustal faults. The integration of numerical and physical experiments provides a powerful approach that demonstrates the utility of work optimization to predict the development of faults.

Experimental characterization of a dielectric elastomer fluid pump and optimizing performance via composite materials

Dielectric elastomer is a class of soft actuators with exceptionally high strain capabilities and energy density. It is being studied for wide range of various applications and has been hypothesized to be a good material for biomedical blood pumps. We performed experimental characterization of a simple dielectric elastomer fluid pump to test this feasibility. We achieved substantial flow rates (10 mL/s) and actuation pressure (45 mm Hg) and found that dielectric elastomer fluid pump performance can exhibit significant resonance effects, with drastic reduction in performance at non-resonance frequencies. The elastomer, VHB™, a soft acrylic polymer, is frequently used to fabricate dielectric elastomer due to high deformation abilities and dielectric constant but has a well-known shortcoming of high viscoelasticity, which severely limited the dielectric elastomer pumps’ performance except at very low frequencies. In this study, we demonstrated that the introduction of a thin elastic and non-viscous layer to the VHB, such as latex, to form a composite dielectric elastomer could address this limitation. The composite dielectric elastomer pump has an increased resonance frequency, significantly improved performances at frequencies of 0.75–2 Hz, and higher maximum achievable actuation volume, flow rate, actuation pressures, and power output. Remaining challenges of realizing a dielectric elastomer blood pump are discussed.

Retraction Statement: "High-Volumetric Performance Aligned Nano-Porous Microwave Exfoliated Graphite Oxide-based Electrochemical Capacitors" and "Aligned Nano-Porous Microwave Exfoliated Graphite Oxide Ionic Actuators with High Strain and Elastic Energy Density".

These articles first published on 15 August 2013 and 21 August 2013 on the Wiley Online Library have been retracted at the request of the Research Integrity Officer (RIO) of The Pennsylvania State University, in agreement with the corresponding authors, the journal's Editor-in-Chief, and Wiley-VCH Verlag GmbH & Co. KGaA, because portions of the reported results cannot be considered reliable or reproducible. Following an investigation by the RIO of The Pennsylvania State University, it was found that the data in Figure 2a,b and Figure S1a,b (Supporting Information) of the article with DOI: 10.1002/adma.201301243, and Figure S3 (Supporting Information) of the article with DOI: 10.1002/adma.201301370 were falsified. Data regarding the carbon electrode material, A-aMEGO, reported to have a density of 1.15 g cm-3 , in the article with DOI: 10.1002/adma.201301243, were falsified. The RIO of The Pennsylvania State University confirms that the investigation found that the mentioned data were falsified by the first author. No findings of research misconduct were made against the co-authors of these publications. [1] M. Ghaffari, Y. Zhou, H. Xu, M. Lin, T. Y. Kim, R. S. Ruoff, Q. M. Zhang, Adv. Mater. 25: 2013, 4879. doi:10.1002/adma.201301243 [2] M. Ghaffari, W. Kinsman, Y. Zhou, S. Murali, Q. Burlingame, M. Lin, R. S. Ruoff, Q. M. Zhang, Adv. Mater. 25: 2013, 6277. doi:10.1002/adma.201301370.

Spatial relationships between bone formation and mechanical stress within cancellous bone

Bone adapts to mechanical stimuli. While in vivo mechanical loading has been shown to increase the density of cancellous bone, theory suggests that the relationship between tissue stress/strain and subsequent bone formation occurs at the scale of individual trabeculae. Here we examine bone formation one week following mechanical stimulus. Three bouts of cyclic loading (300 cycles/day on 3 consecutive days) were applied to caudal vertebrae of female rats (n=7). Bone formation was determined using three-dimensional images of fluorescent markers of bone formation (0.7×0.7×5.0μm3) and local tissue stress/strain was determined using high-resolution finite element models. Three days of mechanical stimuli resulted in an increase in mineralizing surface (loaded: 17.68±2.17%; control: 9.05±3.20%; mean±SD) and an increase in the volume of bone formed (loaded: 7.09±1.97%; control: 1.44±0.50%). The number of bone formation sites was greater in loaded animals (650.71±118.54) than pinned not loaded controls (310.71±91.55), a difference that was explained by the number of formation sites at regions with large local tissue strain energy density (SED). In addition, the probability of observing bone formation was greater at locations of the microstructure experiencing greater SED, but did not exceed 32%, consistent with prior work. Our findings demonstrate that bone formation in the week following a short term mechanical stimulus occurs near regions of bone tissue experiencing high tissue SED, although the ability of finite element models to predict the locations of bone formation remains modest and further improvements may require accounting for additional factors such as osteocyte distribution or fluid flow.