We explore the use of various element-based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis. The rules studied encompass tensor-product Gauss and Gauss-Lobatto rules, and certain so-called monomial rules that do no possess a tensor-product structure. The objective of the study is to determine quadrature strategies, which enjoy the same accuracy and stability behavior as full Gauss quadrature, but with significantly fewer quadrature points. Several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard C 0 -continuous finite elements of the same order.

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The contribution of carbon black (CB) on changes in cross-link density and physical entanglement has been quantified by swelling and uniaxial stress–strain measurements considering Mooney–Rivlin parameters. Solution SBR (SSBR) vulcanizates with varying content of high abrasion furnace (HAF) CB were studied. Rubber–filler networks increase the cross-link density values, which were determined by using Flory–Rehner and modified Guth–Gold equations by equilibrium swelling study. The Mooney–Rivlin parameter C1 was quantified using cross-link density, whereas parameter C2, representing physical entanglement, was determined for filled rubber by correlating with tensile results. The parameter C2 is monitored to be decreased with increasing CB (HAF) loading. A simple parabolic trend for physical entanglement parameter with increasing CB loading is proposed, and it shows a correlation coefficient of 0.99595. Atomic force microscopy study confirms the generation of filler networking in the rubber matrix. The current findings elucidate a way for quantifying physical network changes due to fillers in an unfilled rubber system.

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