A continuum membrane model for small deformations of a spider orb-web

•A model for the small deformations of a spider orb-web is proposed for the first time.•The mechanical model is a structured continuum membrane with a given pre-stress state.•The free transverse vibration is studied in detail for a supported circular orb-web•The accuracy in describing a real discrete orb-web is numerically investigated.•The model will be useful for studying the mechanisms for capturing prey.

In this paper we propose a continuum membrane model for the infinitesimal deformation of a spider web. The model is derived in the simple context of axially-symmetric webs formed by radial threads connected with circumferential threads belonging to concentric circles. Under suitable assumption on the tensile pre-stress acting in the referential configuration, the out-of-plane static equilibrium and the free transverse and in-plane vibration of a supported circular orb-web are studied in detail. The accuracy of the model in describing a discrete spider web is numerically investigated.