Multiscale Peridynamics Analysis of Nanocomposites and Energetic Materials Using Nonlocal and Local Interface Models

Abstract

Interface modeling is a critical aspect in any multi-material system modeling. Even a small change in the interface model may lead to significant changes in material behavior of the microscale, and these changes may transfer up to higher scales influencing the strain and stress fields, and damaging behavior in the macroscale material. This work focuses on the effects of different interface models in nanocomposites composed of carbon nanotubes in polymer matrix materials and their applications as nanocomposite binders in energetic materials. These material systems include materials that span multiple scales from nano to macroscale, and thus require a detailed multiscale analysis. A hierarchical multiscale framework is employed here, where the effective material properties from subscales are obtained by solving the subscale boundary value problem. The information obtained from the subscale simulations are transferred up to higher scales to be used as input properties. A nonlocal continuum mechanics framework known as peridynamics is used to perform the computational simulations. Peridynamics uses integro-differential equations for conservation laws instead of partial differential equations as in the classical continuum mechanics. This makes it possible for peridynamics to inherently account for nonlocal effects such as damage initiation, crack growth, and crack branching without any modifications such as element deletion, adaptive mesh refinement, using enrichment functions and so on, which are commonly used in other numerical methods. Peridynamics is a particle-based method where the particles are allowed to interact with other particles within their horizon which serves as a cut-off distance for forming particle-to-particle bonds and therefore defines the extent of nonlocality. Peridynamics has different formulations regarding the bond interactions. A bond-based peridynamics framework is used here. A verified and validated in-house code is used for the simulations. The simulations for the carbon nanotube and nanofiber-based nanocomposites, and for nanocomposite bonded energetic materials start from the microscale and range up to the macroscale. For only the carbon nanotube-polymer nanocomposites, the interfaces include the CNT-polymer interfaces. For the energetic materials, the interfaces consider the CNT-polymer interfaces in the microscale and the grain-nanocomposite binder interfaces in the mesoscale. Peridynamics, being a nonlocal continuum mechanics method, by default will have nonlocal interfaces. The material systems investigated in this work first use different nonlocal interfaces in peridynamics which consider the bond between two particles at the interface to be connected in series or in parallel. The nonlocal interface model in peridynamics makes it challenging to control the interface properties and leads to fuzzy interfaces, i.e. interfaces of finite thickness. In this work, a local cohesive interface model is implemented in the peridynamics framework. Cohesive zones were originally used for modeling the growth of cracks by introducing cohesive forces that hold the crack surfaces together, thereby removing the stress singularity problem in linear elastic fracture mechanics. The idea of cohesive zones are applied to peridynamics interfaces, which introduces locality into the nonlocal framework. This interface model does not only remove the nonlocality at the peridynamics interfaces, but it leads to a higher fidelity interface model that is controllable by the user. The differences between the nonlocal and local interfaces are studied in detail in different scales and for different material systems. Implementing a local model into a nonlocal framework brings some challenges, namely obtaining and calibrating the cohesive interface properties for the materials used, the numerical problems with material interpenetration in extreme compression, and very small time steps that are required to resolve the material response. Some remedies are proposed for the problems encountered. The cohesive zone model used in this work can have different functional forms in normal and tangential direction to reflect differences in opening mode and frictional sliding behaviors.