Peridynamics for Failure Prediction in the Presence of Material Nonlinearity and Finite Deformation

Abstract

This study examines the failure modeling of materials exhibiting nonlinear behavior and reduced dimension structures using peridynamic (PD) theory. Among the existing PD models, PD constitutive correspondence approach is adopted in the development. PD correspondence approach offers a way to use constitutive equations from classical continuum mechanics by defining a nonlocal deformation gradient tensor. However, using the original definition of deformation gradient leads to spurious oscillations in the solution. This work uses a bond-associated deformation gradient with the peridynamic differential operator to eliminate these oscillations. The numerical modeling assumes the quasi-static loading conditions, and the solution is obtained using the implicit technique with the Intel PARDISO solver using the exact tangent stiffness matrix. PD models are systematically developed for rubber-like materials, polymers exhibiting high stretch, and epoxy adhesives. The force density vectors for rubber materials are derived using the neo-Hookean constitutive equation. The weak form of PD equilibrium is used to impose the boundary conditions directly on the last layer of material points. Stretch-based criterion is used to eliminate interaction during failure simulations. The validity for predicting damage is demonstrated through simulations of experiments concerning progressive damage growth in pre-notched styrene-butadiene rubber sheets. The formulation is then extended for the polymer that can sustain high stretches. Anand’s model and Talamini-Mao-Anand’s model are used to derive force density vectors. The fidelity of this PD model for predicting large deformation, progressive damage, and rupture is established by comparison with experimental measurements of polymer sheets with defects under displacement-controlled tensile loading. To model epoxy adhesives, a viscoelastic material model in the presence of finite deformation is employed to derive the force density vectors. The relaxation modulus for the time-dependent behavior of the viscoelastic material is described in terms of the Prony series. The model performs well in predicting interface failure of lap joint configurations. A new approach is presented to impose traction and displacement boundary conditions while solving for the strong form of PD equilibrium equations without a fictitious boundary layer. The domain is split into inner, outer, and boundary layer regions. In the “interior” region, the equilibrium equations are based on the nonordinary state-based (NOSB) peridynamics. In the “outer” region, the equilibrium equation is derived based on PD differential operator (PDDO). The PD form of traction components based on the PDDO enables the imposition of traction conditions in the actual “boundary layer” region. The displacement constraints are also enforced directly in the real boundary layer. The present approach is free of the unphysical displacement kinks near the boundaries. Also, the displacement predictions maintain the smoothness between the outer and inner regions. The displacement predictions agree well with FE results for all combinations of boundary conditions. The approach is adopted to model the creep behavior of stainless steel at high temperatures. Liu and Murakami's creep damage model is adopted to derive the force density vector. The approach is validated by considering the creep deformation of uniaxial and 2D plane stress stainless steel specimens subjected to a range of constant stress. The results compare well with the experimental measurements and analytical solutions. A generalized PD beam model is formulated based on the Simo-Reissner beam theory. The governing equations are developed based on the form invariance of the first law of thermodynamics under rigid body motion. Nonlocal measures of strain and curvature are defined using the PD differential operator (PDDO). By employing a quadratic strain energy density function for the material response, the present approach is validated by considering numerical examples of beams undergoing large deformation.