Boundary viscoelasticity theory at finite deformations and computational implementation using isogeometric analysis

Abstract

Use of surface elasticity theory has experienced a prolific growth recently due to its utility in understanding the mechanics of nanomaterials and soft solids at small scales. Various extensions of surface elasticity theory have been proposed. The main objective of this contribution is to formulate a finite deformation theory for boundary viscoelasticity in principal stretches by accounting for strain-dependent boundary stresses. We present a model that utilizes a nonlinear evolution law and thus is not restricted to the states that are close to the thermodynamic equilibrium. Boundary contributions include both surface and curve effects wherein boundary elasticity as well as boundary tension are accounted for. The boundary constitutive models are formulated such that fluid-like and solid-like viscoelastic behavior of boundaries are considered. A geometrically exact computational framework using isogeometric analysis inherently suited to account for boundaries is developed. Equipped with the theoretical and computational framework, the influence of boundary viscoelasticity on the material response is illustrated. Non-equilibrium counterpart of surface tension is introduced and its effects are elucidated via examples. Through numerical examples, various applications of the bulk–boundary coupled formulation which require further investigation are highlighted.