Peridynamics model of viscoelasticity for beams and lattice structures

Abstract

This paper concerns the development of peridynamics beam viscoelasticity theory to model creep deformation in beams and lattice structures. The idea here is to employ Simo’s hypothesis on deformation field in the three-dimensional viscoelastic constitutive equations and integrate over the cross-sectional area which leads to the reduced form of viscoelastic constitutive equations in terms of the force and moment resultants. Two evolution equations for internal variables emerge which are coupled with the beam viscoelastic constitutive equations. This provides a general framework where every material point in the beam has 6 + 6p number of degrees of freedom, viz., three displacement components, three incremental rotation components, and six components of two vector internal variables with p being the number of the internal variables. Time marching scheme and the update formulae for force and moment resultants and internal variables are developed. Numerical implementation strategy using the Newton-Raphson method is discussed in detail. Extensive numerical simulations and validation studies are carried out on creep deformation of cantilever beams, frame structures, truss-frames, and lattice structures, and creep failure of compression-torsion lattice which establish the effectiveness of the proposed method.