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    Numerical simulation of the edge stress singularity and the adhesion strength for compliant mushroom fibrils adhered to rigid substrates
    (Amsterdam : Elsevier, 2016) Balijepalli, R.G.; Begley, M.R.; Fleck, N.A.; McMeeking, R.M.; Arzt, E.
    Bio-inspired adhesion of micropatterned surfaces due to intermolecular interactions has attracted much research interest over the last decade. Experiments show that the best adhesion is achieved with compliant “mushroom”-shaped fibrils. This paper analyses numerically the effects of different mushroom shapes on adhesion to a rigid substrate. When a remote stress is applied on the free end of a fibril perfectly bonded to a rigid substrate, the resultant stress distribution along the fibril is found to change dramatically between the straight punch and mushroom fibrils. A singular stress field is present at the edge of the fibril where it contacts the substrate and, in this work, the amplitude of the singularity is evaluated for fibrils perfectly bonded to a flat substrate so that sliding cannot occur there. This exercise is carried out for fibril geometries involving combinations of different diameters and thicknesses of the mushroom cap. By assuming a pre-existing detachment length at the corner where the stress singularity lies, we predict the adhesive strength for various mushroom cap shapes. Our study shows that a smaller stalk diameter and a thinner mushroom cap lead to higher adhesive strengths. A limited number of results are also given for other shapes, including those having a fillet radius connecting the stalk to the cap. The results support the rational optimization of synthetic micropatterned adhesives.
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    Adhesion of a cylindrical punch with elastic properties that vary radially
    (Amsterdam [u.a.] : Elsevier, 2023) Kossa, Attila; Hensel, René; McMeeking, Robert M.
    The adhesion of a rigid substrate and an adhered straight cylindrical punch with a non-homogeneous elastic modulus is analyzed. The stress distributions are obtained along the interface for various elastic modulus gradients. The calculations are performed in the commercial finite element software Abaqus using a user material (UMAT) subroutine to control the dependence of Young's modulus on the radial position. The UMAT code is shared in the paper. The results reveal that the decreasing elastic modulus toward the perimeter of the punch can be used to significantly reduce the normal stress magnitudes in the singularity domain, which leads to stronger adhesion. The increase in the adhesion strength is characterized numerically. The effect of Poisson's ratio is also analyzed.