A novel continuum–discrete multiscale coupling method for strain localization of lipid bio-membrane under tension

A novel continuum–discrete multiscale coupling (CDMC) method is proposed for lipid bio-membrane to deal with its strain localization problems. This approach differs from classical continuum methods, in which the constitutive models are determined on the basis of macroscale phenomenological experiments. In this multiscale model, the moving least squares (MLS) approximation is used for linking the fully discrete coarse-grained particle model and the corresponding higher-order continuous solid model, and bridging the microscale and macroscale deformation fields. From the numerical point of view, this method can freely select the degree of freedom of a system. Based on the proposed CDMC method, a variationally consistent meshless computational scheme is constructed for simulating the strain localization of lipid bio-membrane sheets. The strain localization behaviors of lipid bio-membrane sheets under tension are simulated by the proposed CDMC method. The effectiveness and accuracy of this method are confirmed comparing with full particle simulations.