Arnav Sanyal The Quartic Piecewise-Linear Criterion for the Multiaxial Yield Behavior of Human Trabecular Bone

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (lCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5 mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09-0.36), mechanical anisotropy (range of E 3 /E 1 ¼ 3.0-12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension, compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space. The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal-normal loading and either a rhomboidal boxlike shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalizedstrain space combined with a piecewise linear yield criterion in two planes for normalshear loading (mean error 6 SD: 4.6 6 0.8% for the finite element data versus the criterion). This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture

Comparison of Four Stimulus-Response Modalities in Paired-Associate Learning With Down's Syndrome Children

67 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1967.The purpose of this study was to investigate the relative effectiveness of four stimulus-response modalities (visual-motor, visual-vocal, auditory-motor, and auditory-vocal) in the learning of paired-associates by children diagnosed as having Down's Syndrome. These mentally retarded children have been found to perform better in visual-motor, rather than auditory-vocal, tasks of cognitive ability.Four lists of eight pairs each were developed, using 32 common objects as first members and eight parts of the body as second members of the pairs. Twenty-four children with Down's Syndrome from day school classes for the trainable mentally retarded were given the task in the four stimulus-response (S-R) modalities thus having each S serve as his own control. Pre-training insured Ss ability to perform the responses. The order of lists and of stimulus-response modalities were counter-balanced. The learning criterion was two consecutive correct anticipations of the pairs, or ten trials, whichever came first, with the Gillette drop-out procedure used on learned pairs.Mean error scores for the four S-R modalities were visual-motor, 21; visual-vocal, 24; auditory-motor, 20; and auditory-vocal, 42. A 4 x 24 factorial analysis of variance of the error scores demonstrated a significant main effect of S-R modality (F = 20.82, p < .001). By the Scheffe method of multiple comparisons, the auditory-vocal modality was found to have been the most difficult; the other S-R modalities were not significantly different from each other. Neither stimulus modality nor response modality alone had a significant effect on learning.This sample of Down's Syndrome children experienced great difficulty in associating pairs of spoken words in the auditory-vocal modality. This result was explained in terms of an analysis of the paired-associate task into two phases, the acquisition phase and the recall phase. In the acquisition phase, there are two stimuli and one response: in S and R modality terms, S-S-R. In the recall phase, there is one stimulus and one response: S-R. When both stimuli were words, these Ss experienced great difficulty in associating pairs. Three aspects of words as stimuli may be related to the difficulty in association: words are auditory, symbolic, and similar to each other.The results suggest four questions for research: (1) To what extent is this finding generalizable to a wider population of children? (2) Is the difficulty in associating pairs of words due to the degree of symbolism, to the auditory nature, or to the similarity? (3) Is the difficulty due to the combination of two words and a vocal response? (4) Is the difficulty traceable to experience, or is it a basic characteristic of Down's Syndrome children?**Originally published in DAI Vol. 28, No. 12. Reprinted here with corrected title.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

The Quartic Piecewise-Linear Criterion for the Multiaxial Yield Behavior of Human Trabecular Bone

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (μCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5 mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36), mechanical anisotropy (range of E(3)/E(1) = 3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension, compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space. The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal boxlike shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized-strain space combined with a piecewise linear yield criterion in two planes for normal-shear loading (mean error ± SD: 4.6 ± 0.8% for the finite element data versus the criterion). This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture

The Quartic Piecewise-Linear Criterion for the Multiaxial Yield Behavior of Human Trabecular Bone

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (lCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36),mechanical anisotropy (range of E3/E1¼3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension,compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space.The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal box like shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized strain space combined with a piecewise linear yield criterion in two planes for normalshear loading (mean error SD: 4.660.8% for the finite element data versus the criterion).This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture