Elastic Contacts of Randomly Rough Indenters with Thin Sheets, Membranes Under Tension, Half Spaces, and Beyond
Martin H. Müser
Abstract
Abstract We consider the adhesion-less contact between a two-dimensional, randomly rough, rigid indenter, and various linearly elastic counterfaces, which can be said to differ in their spatial dimension D . They include thin sheets, which are either free or under equi-biaxial tension, and semi-infinite elastomers, which are either isotropic or graded. Our Green’s function molecular dynamics simulation identifies an approximately linear relation between the relative contact area $$a_{\text {r}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>a</mml:mi> <mml:mtext>r</mml:mtext> </mml:msub> </mml:math> and pressure p at small p only above a critical dimension. The pressure dependence of the mean gap $$u_{\text {g}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>u</mml:mi> <mml:mtext>g</mml:mtext> </mml:msub> </mml:math> obeys identical trends in each studied case: quasi-logarithmic at small p and exponentially decaying at large p . Using a correction factor with a smooth dependence on D , all obtained $$u_{\text {g}}(p)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mtext>g</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> relations can be reproduced accurately over several decades in pressure with Persson’s theory, even when it fails to properly predict the interfacial stress distribution function. Graphical Abstract