Plans d'expérience: constructions et analyses statistiques

Tinsson, Walter

doi:10.1007/978-3-642-11472-4

Cited by 7 publications

(3 citation statements)

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“…A metric-specific hypersurface over the hyperplane spanned by the normalized parameters

was fitted by means of second-order polynomial with first-order interactions, reading mathematically as ( Tinsson, 2011 ):

where x i , with i = 1, 2, 3, refers to the normalized parameters according to Eq. 47 , Y is one of the five previously cited output metrics of the model, β 0 covers the portion of the metric Y which is not depending on x 1 , x 2 , and/or x 3 ; and where β i , β ij , and β ii , with i , j = 1, 2, 3, reflect the sensitivity of the model with respect to the parameters x 1 , x 2 , and x 3 .…”

Section: Micromechanical Modeling Resultsmentioning

confidence: 99%

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Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

Morin

Hellmich

Nejim

et al. 2021

Front. Bioeng. Biotechnol.

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It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented through a number of hypoelastic straight fiber phases with different orientations, being embedded into a hypoelastic matrix phase. The corresponding representative volume element (RVE) hosting these phases is subjected to “macroscopic” strain rates, which are downscaled to fiber and matrix strain rates on the one hand, and to fiber spins on the other hand. This gives quantitative access to the fiber decrimping (or straightening) phenomenon under non-affine conditions, i.e. in the case where the fiber orientations cannot be simply linked to the macroscopic strain state. In the case of tendinous tissue, such an RVE relates to the fascicle material with 50 μm characteristic length, made up of crimped collagen bundles and a gel-type matrix in-between. The fascicles themselves act as parallel fibers in a similar matrix at the scale of a tissue-related RVE with 500 μm characteristic length. As evidenced by a sensitivity analysis and confirmed by various mechanical tests, it is the initial crimping angle which drives both the degree of straightening and the shape of the macroscopic stress-strain curve, while the final linear portion of this curve depends almost exclusively on the collagen bundle elasticity. Our model also reveals the mechanical cooperation of the tissue’s key microstructural components: while the fibers carry tensile forces, the matrices undergo hydrostatic pressure.

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“…A metric-specific hypersurface over the hyperplane spanned by the normalized parameters

was fitted by means of second-order polynomial with first-order interactions, reading mathematically as ( Tinsson, 2011 ):

Section: Micromechanical Modeling Resultsmentioning

confidence: 99%

“…was fitted by means of second-order polynomial with first-order interactions, reading mathematically as (Tinsson, 2011):…”

Section: Sensitivity Analysis: Uniaxial Stress-stretch Behavior Governed By Collagen Bundle Propertiesmentioning

confidence: 99%

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

Morin

Hellmich

Nejim

et al. 2021

Front. Bioeng. Biotechnol.

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“…The preparation of PIR foams was the same as RPUF with a 5-s mixing time because of isocyanate reactivity. In this analysis, a composite experimental plan determined the optimal formulations in density and mechanical resistance using the NEMROD statistical analysis [15]. The iso-response surfaces of density and mechanical properties gave a simple visualization of the optimum fiber size and proportion (Figure S1).…”

Section: Polyisocyanurate Foamsmentioning

confidence: 99%

Synthesis and Characterization of Wood Rigid Polyurethane Composites

et al. 2022

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Incorporating biodegradable reinforcement, such as wood particles, into rigid polyurethane foams (RPUFs) is among the alternatives to reduce their environmental impact. This study aims to assess the effect of different wood particles as reinforcement in RPUFs. Reinforced rigid polyurethane foams are synthesized with milled wood particles of various forms and sizes and commercial polyol and isocyanate. The effect of fiber treatments and mechanical stirring on foams’ properties is also studied. Additional tests on polyisocyanurate foams (PIR) were undertaken to assess the effect of reinforcement on their properties. Mechanical properties are measured to investigate the impact of wood particle reinforcement on the foam. Confocal microscopy and Fourier-transform infrared spectroscopy (FTIR) showed the interaction between the wood fibers and the matrix. Despite the adhesion observed for some fibers, most of the cell walls of RPUFs were punctured by the rigid wood fibers, which explained the decrease in the compressive strength of the composites for manually mixed foams. Mechanical stirring proved to be an efficient method to enhance the reinforcement power of untreated fibers. RPUF foams’ properties showed similar changes when untreated wood flour was introduced to the formula, increasing compressive strength significantly.

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Plans d'expérience: constructions et analyses statistiques

Cited by 7 publications

References 0 publications

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

Synthesis and Characterization of Wood Rigid Polyurethane Composites

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