Boundary Element Calculations for Normal Contact of Soft Materials With Tensed Surface Membrane

Weike Yuan,Gangfeng Wang

doi:10.3389/fmech.2020.00057

Abstract

This work considers the non-adhesive frictionless contact problem of soft materials with surface being tensed by equi-biaxial tension. The boundary element method based on Fast Fourier Transform and conjugate gradient algorithm is extended to deal with this problem. By comparing with existing analytical solutions for the axisymmetric contact between a rigid parabolic indenter and an elastic half space with constant membrane/surface tension, our numerical simulations are validated having great accuracy and efficiency. Then, with this numerical tool, we further calculate the contact responses of a soft substrate indented by a smooth indenter with general quadric profile and a rough indenter with self-affine fractal surface, respectively. Some nontrivial contact behavior resulted from the presence of membrane tension are demonstrated and discussed.

Highlights

Many physiological systems can be modeled as the layer-foundation structure, and generally, the mechanical properties of surface layer differ from those of bulk interior
This paper aims to extend the mature Fast Fourier Transform (FFT)-based boundary element method (BEM) for the calculation of normal contact of material with membrane/surface tension
The FFT-based boundary element method is extended for normal contact of soft material, of which the surface is tensed by equi-biaxial tension

Summary

Introduction

Many physiological systems can be modeled as the layer-foundation structure, and generally, the mechanical properties of surface layer differ from those of bulk interior. It is assumed that the surface membrane thickness is small so that its bending rigidity can be neglected. Argatov and Sabina (2012) treated the surface layer as a reinforced membrane under generalized plane stress state. They hypothesized that no pre-tension exists in the membrane, and the flexural stiffness is negligible compared with the in-plane tensile stiffness. Such modeling method was employed in the deformation analysis of anisotropic articular cartilage (Argatov and Mishuris, 2016)

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