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At least 199 records · Page 11

High Protein Intake Improves Insulin Sensitivity but Exacerbates Bone Resorption in Immobility (WISE Study)

Inactivity, like bed rest (BR), causes insulin resistance (IR) and bone loss even in healthy subjects. High protein intake seems to mitigate this IR but might exacerbate bone loss. We hypothesized that high protein intake (animal:vegetable protein ratio: 60:40), isocaloric, compared to the control group plus high potassium intake would prevent IR without affecting bone turnover. After a 20-day ambulatory adaptation to controlled confinement and diet, 16 women participated in a 60-day, 6 deg head-down-tilt BR and were assigned randomly to one of the two groups. Control subjects (CON, n=8) received 1g/kg body mass/d dietary protein. Nutrition subjects (NUT, n=8) received 1.45g/kg body mass/d dietary protein plus 7.2g branched chain amino acids per day during BR. All subjects received 1670 kcal/d. Bed rest decreased glucose disposal by 35% (p<0.05) in CON. Isocaloric high protein intake prevented insulin resistance, but exacerbated bed rest induced increase in bone resorption markers C-telopeptide (> 30%) and Ntelopeptide (>20%) (both: p<0.001). Bone formation markers were unaffected by high protein intake. We conclude from these results that high protein intake might positively affect glucose tolerance, but might also foster bone loss. Further long-duration studies are mandatory before high protein intake for diabetic patients, who have an increased fracture risk, might be recommended.

Heer, Martina↗

Overview and Evaluation of a Computational Bone Physiology Modeling Toolchain and Its Application to Testing of Exercise Countermeasures

Prolonged microgravity exposure disrupts natural bone remodeling processes and can lead to a significant loss of bone strength, increasing injury risk during missions and placing astronauts at a greater risk of bone fracture later in life. Resistance-based exercise during missions is used to combat bone loss, but current exercise countermeasures do not completely mitigate the effects of microgravity. To address this concern, we present work to develop a personalizable, site-specific computational modeling toolchain of bone remodeling dynamics to understand and estimate changes in volumetric bone mineral density (BMD) in response to microgravity-induced bone unloading and in-flight exercise. The toolchain is evaluated against data collected from subjects in a 70-day bed rest study and is found to provide insight into the amount of exercise stimulus needed to minimize bone loss, quantitatively predicting post-study volumetric BMD of control subjects who did not perform exercise, and qualitatively predicting the effects of exercise. Results suggest that, with additional data, the toolchain could be improved to aid in developing customized in-flight exercise regimens and predict exercise effectiveness.

Schepelmann, Alexander↗

Overview and Evaluation of a Computational Bone Physiology Modeling Toolchain and Its Application to Testing of Exercise Countermeasures

Prolonged microgravity exposure disrupts natural bone remodeling processes and can lead to a significant loss of bone strength, increasing injury risk during missions and placing astronauts at a greater risk of bone fracture later in life. Resistance-based exercise during missions is used to combat bone loss, but current exercise countermeasures do not completely mitigate the effects of microgravity. To address this concern, we present work to develop a personalizable, site-specific computational modeling toolchain of bone remodeling dynamics to understand and estimate changes in volumetric bone mineral density (BMD) in response to microgravity-induced bone unloading and in-flight exercise. The toolchain is evaluated against data collected from subjects in a 70-day bedrest study and is found to provide insight into the amount of exercise stimulus needed to minimize bone loss, quantitatively predicting post-study volumetric BMD of control subjects who did not perform exercise, and qualitatively predicting the effects of exercise. Results suggest that, with additional data, the toolchain could be improved to aid in developing customized in-flight exercise regimens and predict exercise effectiveness.

Schepelmann, Alexander↗

Search for Past Life on Mars: Possible Relict Biogenic Activity in Martian Meteorite ALH84001

Fresh fracture surfaces of the martian meteorite ALH84001 contain abundant polycyclic aromatic hydrocarbons (PAHs). These fresh fracture surfaces also display carbonate globules. Contamination studies suggest the PAHs are indigenous to the meteorite. High resolution scanning and transmission electron microscopy study of surface textures and internal structures of selected carbonate globules show that the globules contain fine-grained, secondary phases of single-domain magnetite and Fe-monosulfides. The carbonate globules are similar in texture and size to some terrestrial bacterially induced carbonate precipitates. Although inorganic formation is possible, formation of the globules by biogenic processes could explain many of the observed features including the PAHs. The PAHs, the carbonate globules, and their associated secondary mineral phases and textures could thus be fossil remains of a past martian biota.

McKay, David S.↗

Improved Damage Resistant Composite Materials Incorporating Shape Memory Alloys

Metallic shape memory alloys (SMA) such as nitinol have unique shape recovery behavior and mechanical properties associated with a material phase change that have been used in a variety of sensing and actuation applications. Recent studies have shown that integrating nitinol-SMA actuators into composite materials increases the composite material's functionality. Hybrid composites of conventional graphite/epoxy or glass/epoxy and nitinol-SMA elements can perform functions in applications where monolithic composites perform inadequately. One such application is the use of hybrid composites to function both in load bearing and armor capacities. While monolithic composites with high strength-to-weight ratios function efficiently as loadbearing structures, because of their brittle nature, impact loading can cause significant catastrophic damage. Initial composite failure modes such as delamination and matrix cracking dissipate some impact energy, but when stress exceeds the composite's ultimate strength, fiber fracture and material perforation become dominant. One of the few methods that has been developed to reduce material perforation is hybridizing polymer matrix composites with tough kevlar or high modulus polyethynylene plies. The tough fibers increase the impact resistance and the stiffer and stronger graphite fibers carry the majority of the load. Similarly, by adding nitinol-SMA elements that absorb impact energy through the stress-induced martensitic phase transformation, the composites' impact perforation resistance can be greatly enhanced. The results of drop-weight and high velocity gas-gun impact testing of various composite materials will be presented. The results demonstrate that hybridizing composites with nitinol-SMA elements significantly increases perforation resistance compared to other traditional toughening elements. Inspection of the composite specimens at various stages of perforation by optical microscope illustrates the mechanisms by which perforation is initiated. Results suggest that the out-of-plane transverse shear properties of the composite and nitinol elements have a significant effect on the perforation resistance. Applications that can utilize the hybrid composites effectively will also be presented with the experimental studies.

Paine, Jeffrey S. N.↗

Design, Fabrication and Test of Composite Curved Frames for Helicopter Fuselage Structure

Aspects of curved beam effects and their importance in designing composite frame structures are discussed. The curved beam effect induces radial flange loadings which in turn causes flange curling. This curling increases the axial flange stresses and induces transverse bending. These effects are more important in composite structures due to their general inability to redistribute stresses by general yielding, such as in metal structures. A detailed finite element analysis was conducted and used in the design of composite curved frame specimens. Five specimens were statically tested and compared with predicted and test strains. The curved frame effects must be accurately accounted for to avoid premature fracture; finite element methods can accurately predict most of the stresses and no elastic relief from curved beam effects occurred in the composite frames tested. Finite element studies are presented for comparative curved beam effects on composite and metal frames.

Lowry, D. W.↗

Search for past life on Mars: possible relic biogenic activity in martian meteorite ALH84001

Fresh fracture surfaces of the martian meteorite ALH84001 contain abundant polycyclic aromatic hydrocarbons (PAHs). These fresh fracture surfaces also display carbonate globules. Contamination studies suggest that the PAHs are indigenous to the meteorite. High-resolution scanning and transmission electron microscopy study of surface textures and internal structures of selected carbonate globules show that the globules contain fine-grained, secondary phases of single-domain magnetite and Fe-sulfides. The carbonate globules are similar in texture and size to some terrestrial bacterially induced carbonate precipitates. Although inorganic formation is possible, formation of the globules by biogenic processes could explain many of the observed features, including the PAHs. The PAHs, the carbonate globules, and their associated secondary mineral phases and textures could thus be fossil remains of a past martian biota.

NASA Discipline Number 52-10↗

Methods for assessing the structural reliability of brittle materials

Failure from contact-induced surface flaws is considered along with controlled indentation flaws for construction of toughness and fatigue master maps, fatigue properties of ceramics with natural and controlled flaws, and a statistical analysis of size and stress state effects on the strength of an alumina ceramic. Attention is also given to dynamic and static fatigue of a machinable glass ceramic, the effect of multiregion crack growth on proof testing, and a fracture mechanics analysis of defect sizes. Other topics explored are related to the effect of temperature and humidity on delayed failure of optical glass fibers, subthreshold indentation flaws in the study of fatigue properties of ultrahigh-strength glass, the lifetime prediction for hot-pressed silicon nitride at high temperatures, static fatigue in high-performance ceramics, and requirements for flexure testing of brittle materials.

Freiman, S. W.↗

Monitoring of Volcanogenic CO2-Induced Tree Kills with AVIRIS Image Data at Mammoth Mountain, California

Elevated cold CO2 emissions from the flank of Mammoth Mountain volcano on the southwest rim of the Long Valley Caldera, eastern California, have been the cause of over 100 acres of dead trees in that area since 1990. The source of the CO2 gas is thought to be from one or more magmatic intrusion(s) beneath Mammoth Mountain and is probably related to a period of seismic unrest that began in 1989. The gas rises to the surface probably from depths of a few kilometers, along faults and fracture zones. The gas is at ambient temperature and diffuses from the soil rather than discharging from distinct vents. Typically, soil gas concentrations in tree-kill areas range from 10% to over 90% CO2 by volume, as compared to normal background of < 1% in healthy forest. The gas composition is predominantly CO2 mixed with air (sulfur gases are not elevated), and C and He isotopic ratios are consistent with a magmatic origin for the gas. The total CO2 emission has been estimated at 1200 tons/day, comparable to the emissions at Kilauea. Some of the dead trees are as old as 250 years, suggesting that similar anomalous gas discharge has not occurred over the previous few hundred years. The delta C-13/12 ratio in the Mammoth Mountain CO2 emission averages about -4.5 (PDB standard). This is consistent with a mantle source for the carbon. However, the large volume of the emission suggests that not all of the CO2 is necessarily being generated from the 1989 intrusion. The voluminous gas could be leaking from a vapor-rich zone, capped by an impermeable layer, that was supplied CO2 from degassing of many small magma bodies that intruded beneath the mountain over a period of decades or centuries. Earthquakes in 1989 could have fractured the capping layer and provided pathways for the escape Of CO2 to the surface. Alternatively, some of the CO2 could be derived from contact metamorphism of carbonate rocks intruded by magma. Carbonate-bearing Paleozoic roof pendents crop out in close proximity to Mammoth Mountain. It is possible that similar rocks could occur at depth beneath Mammoth Mountain, and could have contributed CO2 from thermal decomposition caused from recent intrusions. We hope to determine the C-13/12 ratio of a suite of samples to demonstrate if the carbonate rocks could be the source of at least part of the 1990-97 CO2 emission. To better understand the behavior of the CO2 gas, we have used hyperspectral imagery data of Mammoth Mountain acquired from the Airborne Visual/Infrared Imaging Spectrometer (AVIRIS) to map out areas of dead trees. The areas of tree kill have increased in size from about 50 acres in 1994 to about 100 acres in 1997. Tree kill is the major surface manifestation of the carbon dioxide flux at Mammoth Mountain, is widely dispersed, and has been cursorily mapped by regular field mapping techniques in the area. Initial investigations using airborne digital imagery from the Thematic Mapper Simulator (NS001) and AVIRIS instruments have shown extremely encouraging results for complete delineation of the vegetation anomalies. The most successful maps (when compared with ground truth) were developed using AVIRIS data with spectral angle mapper and matched filter algorithms with a data set that was reduced to maximum variance via the minimum noise fraction transformation. The result of this work is a series of maps that show the tree kill areas occurring in an halo-pattern surrounding the base of Mammoth Mountain. We are applying these same techniques to earlier AVIRIS images of Mammoth Mountain to examine the progression of the tree kill areas over time. Temporal maps of the tree kill areas may assist in constructing a picture of the structure beneath Mammoth Mountain.

Hausback, Brian P.↗

Modeling Space Radiation Induced Bone Changes in Rat Femurs through Finite Element Analysis

As the duration of manned missions outside of the Earth’s protective shielding increase, astronauts are at risk for exposure to space radiation. Various organ systems may be damaged due to exposure. This study investigates the bonestrength changes using finite element modeling of Long Evans rats (n=85) subjected to graded, head-only proton (0, 10, 25, and 100 cGy, 150 MeV/n) and 28silicon (0, 10, 25, and 50 cGy, 300 MeV/n) radiation. The strength of the femoral neck will be examined due its clinical relevance to hip fractures. It has been shown in previous studies that bone mineral density was not reduced at the site of fracture. These findings question whether measurements of bone mineral density may be used to assess risk of hip fracture. The mechanisms leading to the irregular relationship between bone density and strength are still uncertain within literature and investigated to greater extent in clinical applications. Finite element analysis within this study simulated physiological loading of the femoral neck. No significant changes in femoral neck strength were found across doses of proton or 28silicon head-only radiation. Future work includes performing mechanical testing of the bone samples. Moving from mouse to larger animal models may also provide the increased lifespan for assessing the long-term outcomes of radiation exposure.

Dale Johnson↗

Effect of Ex Vivo Ionizing Radiation on Static and Fatigue Properties of Mouse Vertebral Bodies

For a variety of medical and scientific reasons, human bones can be exposed to a wide range of ionizing radiation levels. In vivo radiation therapy (0.05 kGy) is used in cancer treatment, and ex vivo irradiation (25-35 kGy) is used to sterilize bone allografts. Ionizing radiation in these applications has been shown to increase risk of fracture, decrease bone quality and degrade collagen integrity. Past studies have investigated the deleterious effects of radiation on cortical or trabecular bone specimens individually, but to date no studies have examined whole bones containing both cortical and trabecular tissue. Furthermore, a clear relationship between the dose and the mechanical and biochemical response of bone's extracellular matrix has yet to be established for doses ranging from cancer therapy to allograft sterilization (0.05-35 kGy). To gain insight into these issues, we conducted an ex vivo radiation study to investigate non-cellular (i.e. matrix) effects of ionizing radiation dose on vertebral whole bone mechanical properties, over a range of radiation doses (0.05-35 kGy), with a focus on any radiation-induced changes in collagen. With underlying mechanisms of action in mind, we hypothesized that any induced reductions in mechanical properties would be associated with changes in collagen integrity. METHODS: 20-week old female mice were euthanized and the lumbar spine was dissected using IACUC approved protocols. The lumbar vertebrae (L1- S1) were extracted from the spine via cuts through adjacent intervertebral discs, and the endplates, posterior processes, surrounding musculature, and soft tissues were removed (approx. 1.5mm diameter, approx. 2mm height). Specimens were randomly assigned to one of five groups for ex vivo radiation exposure: x-ray irradiation at 0.05, 1, 17, or 35 kGy, or a 0 kGy control. Following irradiation, the vertebrae were imaged using microcomputed tomography (micro-CT) and then subjected to either monotonic compressive loading to failure or uniform cyclic compressive loading. During cyclic testing, samples were loaded in force control to a force level that corresponded to a strain of 0.46%, as determined in advance by a linearly elastic micro-CT-based finite element analysis for each specimen. Tests were stopped at imminent fracture, defined as a rapid increase in strain. The main outcome for the monotonic test was the strength (maximum force); for cyclic testing it was the fatigue life (log of the number of cycles of loading at imminent failure). A fluorometric assay was used on the S1 vertebrae to measure the number of non-enzymatic collagen crosslinks[4]. A one-way ANOVA was performed on mechanical properties and collagen crosslinks; means were compared with controls using Dunnett's method, with a Tukey-Kramer post-hoc analysis when significance was found (p < or = 0.05). RESULTS: Compared to the unirradiated control group, the concentration of non-enzymatic collagen crosslinks was significantly increased for all irradiated groups (p < 0.0001), and being higher by at least 50% (Figure 1a). By contrast, the radiation effects on the collagen were only evident at the higher doses. For irradiation exposures of 17 kGy or more, strength decreased substantially as the radiation level was increased, but no effect was evident below 17 kGy (Figure 1b). There was no significant change in the stiffness or maximum displacement for any radiation dose (p>0.05). The finite element analysis prescribed force level for cyclic loading exceeded the measured (monotonic) strength of the 17 and 35 kGy irradiated groups (mean +/- SD, 20.6 +/- 5.6 N; 13.2 +/- 3.7 N, respectively) and therefore these groups were eliminated from the fatigue study. The fatigue life for the 0.05 and 1 kGy groups were similar to each other and were not statistically significantly different from the control group (Figure 1c).

radiation↗

Working toward a three-dimensional fatigue closure model for surface cracks

The first reliable elastic fracture mechanics solutions for a surface crack in a plate were obtained by Newman and Raju. The authors, both from the Mechanics of Materials Branch at NASA-Langley, used a highly detailed finite element solution requiring substantial computational resources. Computers have since become more powerful and available; however, many important related problems remain computationally expensive. The problem of three-dimensional fatigue crack growth taking into account plasticity-induced crack closure is one such problem. It is the goal of this research to provide an efficient method to account for three-dimensional crack closure in fatigue. Newman developed a two-dimensional plasticity-induced crack closure model for center cracked specimens. This model requires iterations to determine both the contact solution at each growth step and the extent of the plastic zone at the crack tip. A three-dimensional version of this model would require obtaining these nonlinear variables all along the crack front. This model must be efficient so that repeated calculations can be performed during crack growth simulations. The highly versatile line spring model (LSM) with contact, fatigue, and plasticity will form the basis of the closure model. There are several required additions to past work to address the three-dimensional crack closure problem. Initially, these additions will include (1) an improved LSM to more accurately obtain the crack opening displacement, stress intensity factors, and elastic T-stress near the ends of the surface crack; (2) a method to determine the extent of the plastic zone all along the crack front; (3) a method to determine the contact zone given a perfectly plastic layer of material on the crack surfaces; (4) a method to determine the magnitude of the compressive contact stress; and (5) a way to implement the degree of constraint along the curved crack front. During the summer ASEE program an enhanced LSM was developed. A method similar to that of 'strip synthesis' first introduced by Fujimoto was used. Briefly, the crack opening displacements of 'slices' of the surface crack in a direction parallel to the plate surface are considered in addition to the standard LSM approach that makes use of springs obtained from slices perpendicular to the plate surface. This enhancement is necessary so that an accurate three-dimensional representation of quantities such as contact zone size, plastic zone size, stress intensity factors, T-stress, and crack opening displacement can be determined. By combining results of previous investigations with the LSM, the problem of three-dimensional crack closure will be addressed. In addition to a closure model, the enhanced LSM can be used for many other problems including interacting surface cracks and fatigue crack growth of a through crack with a curved crack front.

Joseph, Paul F.↗

Development of GENOA Progressive Failure Parallel Processing Software Systems

A capability consisting of software development and experimental techniques has been developed and is described. The capability is integrated into GENOA-PFA to model polymer matrix composite (PMC) structures. The capability considers the physics and mechanics of composite materials and structure by integration of a hierarchical multilevel macro-scale (lamina, laminate, and structure) and micro scale (fiber, matrix, and interface) simulation analyses. The modeling involves (1) ply layering methodology utilizing FEM elements with through-the-thickness representation, (2) simulation of effects of material defects and conditions (e.g., voids, fiber waviness, and residual stress) on global static and cyclic fatigue strengths, (3) including material nonlinearities (by updating properties periodically) and geometrical nonlinearities (by Lagrangian updating), (4) simulating crack initiation. and growth to failure under static, cyclic, creep, and impact loads. (5) progressive fracture analysis to determine durability and damage tolerance. (6) identifying the percent contribution of various possible composite failure modes involved in critical damage events. and (7) determining sensitivities of failure modes to design parameters (e.g., fiber volume fraction, ply thickness, fiber orientation. and adhesive-bond thickness). GENOA-PFA progressive failure analysis is now ready for use to investigate the effects on structural responses to PMC material degradation from damage induced by static, cyclic (fatigue). creep, and impact loading in 2D/3D PMC structures subjected to hygrothermal environments. Its use will significantly facilitate targeting design parameter changes that will be most effective in reducing the probability of a given failure mode occurring.

Abdi, Frank↗

Sustained load crack growth design data for Ti-6Al-4V titanium alloy tanks containing hydrazine

Results are presented for an experimental study intended to provide sustained load crack growth (SLCG) data for Ti-6Al-4V titanium alloy tanks containing MIL-P-26536 hydrazine and refined hydrazine. Fracture mechanics data on crack growth threshold for heat-treated forgings, aged and unaged welds, and aged and unaged heat-affected zones (HAZ) are presented. All tests were made on uniaxially loaded fracture mechanics specimens involving part-through cracks, and an electrical discharge machined notch was used to start the crack. Fracture mechanics design curves of crack growth threshold stress intensity versus temperature are obtained for the temperature range 40-71 C. Major conclusions are that extreme susceptibility to SLCG in hydrazine is a universal property of unaged weld metal in Ti-6Al-4V titanium alloy of normal interstitial content, and that aging both weld metal and HAZ at 510 C for 4 hr after welding completely removes all susceptibility to SLCG induced by hydrazine, with less susceptibility to SLCG in refined hydrazine.

Lewis, J. C.↗

The formation of antipodal-impact terrains on Mars

The regions antipodal to Mars' three largest impact basins, Hellas, Isidis, and Argyre, were assessed for evidence of impact induced seismically disrupted terrains. Photogeology and preliminary computer modeling using the Simplified Arbitrary Lagrangian-Eulerian computer program suggest such terrain could have been formed by the Hellas and Isidis impacts. Previously, the only assessment of potential surface disruptions on Mars antipodal to large impacts was by Peterson (1978). Herein, the results give credence to Peterson's assertions. For Hellas, the computer model clearly suggests that antipodal pressures were probably strong enough to have fractured the crust and disrupted the surface, and may account for aspects of volcanism at Alba Patera. It is suggested that the Hellas impact produced sufficient focused energy at its antipode to produce deep fracture in the Martian crust centered below the current caldera for Alba Petera. With the generation and evolution of magma in the Tharsis area, the fracture system provided a ready conduit for early stage eruptions of Martians lavas derived from deep in the crust and/or upper mantle, perhaps of komatiitic composition.

Williams, D. A.↗

Microcracking, microcrack-induced delamination, and longitudinal splitting of advanced composite structures

A combined analytical and experimental study was conducted to analyze microcracking, microcrack-induced delamination, and longitudinal splitting in polymer matrix composites. Strain energy release rates, calculated by a variational analysis, were used in a failure criterion to predict microcracking. Predictions and test results were compared for static, fatigue, and cyclic thermal loading. The longitudinal splitting analysis accounted for the effects of fiber bridging. Test data are analyzed and compared for longitudinal splitting and delamination under mixed-mode loading. This study emphasizes the importance of using fracture mechanics analyses to understand the complex failure processes that govern composite strength and life.

Nairn, John A.↗

Crack Development in Cross-Ply Laminates Under Uniaxial Tension

This study addresses matrix-dominated failures in carbon fiber/polymer matrix composite laminates in a cross-ply lay-up. The events of interest are interlaminar fracture in the form of transverse cracks in the 90' plies and longitudinal splitting in the 0 deg plies and interlaminar fracture in the form of 0/90 delamination. These events were observed using various nondestructive evaluation (NDE) techniques during static tensile tests. Acoustic emission (AE) x radiography, and edge view microscopy were the principal ones utilized in a real-time environment. A comparison of the NDE results with an analytical model based on the classical linear fracture mechanics concept of strain energy release rate as a criterion for crack growth was performed. The virtual crack closure theory was incorporated with a finite element model to generate strain energy release rate curves for the analytical case. Celion carbon fiber/polyimide matrix (G30-500/PMR-15) was the material tested with cross-ply lay-ups of (0(2)/90(6))s and (0(4)/90(4))s. The test specimens contained thermally induced cracks caused by the high-temperature processing. The analytical model was updated to compensate for the initial damage and to study further accumulation by taking into account the crack interactions. By correlating the experimental and analytical data, the critical energy release rates were found for the observable events of interest.

Gyekenyesi, Andrew L.↗

Relation between surface slip topography and stress corrosion cracking in Ti-8 wt % Al

The deformation behavior of Ti-8 wt % Al has been investigated in an inert environment (air), and an aggressive environment (salt water). Details of surface slip geometry were examined by high resolution surface replicas at various stages of deformation in both environments. Specimens aged to contain a fine dispersion of Ti3Al precipitates failed by subcritical crack growth in salt water, whereas specimens in the single phase condition showed no effects of environment on the yield or fracture characteristics. The Ti3Al precipitates produce little change in strength level or slip character compared to the single phase alloy, and there is no evidence of any effects of environment on the character of surface slip. Rather, the presence of trenches along slip bands on the surface of aged specimens suggest that the specific effect of the Ti3Al precipitates is to render the surface slip steps chemically active relative to the surrounding matrix by slip induced dissolution of the particles.

Boyd, J. D.↗