Julie Vaughan Sallquist, Nancy Eisenberg, Tracy L Spinrad, Mark Reiser, Claire Hofer, Qing Zhou, Jeffrey Liew, Natalie Eggum
Positive and negative emotionality: trajectories across six years and relations with social competence
Emotion (Washington, D.C.)
cube cube approach used paul ishaicohen model derive formulas filler content dependent youngs moduli particle filled composites assuming perfect filler matrix adhesion formulas chosen simplicity recalculated using elementary volume approach transforms spherical inclusions cubic inclusions ev approach led expression composites moduli allows introducing adhesion factor kadh ranging 0 1 take account reduced filler matrix adhesion adhesion factor scales edge length cubic inclusions thus reducing stress transfer area matrix filler fitting experimental data modified paul model provides reasonable kadh pa66 pbt pp peld br line surface energies analysis showed stiffening occurs kadh exceeds formula see text depends ratio matrix modulus filler modulus modified model allows quick calculation particle filled composites known matrix modulus em filler modulus ef filler volume content vf adhesion factor kadh thus finite element analysis fea simulations particle filled polymer parts well materials selection significantly eased fea cubic hexagonal ev arrangements show stress distributions within ev exhibit shear stresses one deviates cubic arrangement high filler contents assumption property ev representative whole composite holds filler volume contents 15 20 corresponding 30 40 weight thus vast majority commercially available particulate composites modified model applied furthermore indicates cube cube approach reaches two limits occurrence increasing shear stresses filler contents 20 due deviations ev arrangements spatial filler distribution cubic arrangements singular ii increasing interaction particles formation particle network within matrix violating ev assumption homogeneous dispersion