Continuum and Multiscale Modeling of Rubber Toughened Glassy Polymers at Finite Strains

Other conference contribution, 2019

Over recent years, the modeling of heterogenous multi-phase materials has been a topic of extensive
research by the scientific community. Among other approaches, computational homogenizationbased
multiscale modeling has emerged as an effective way to relate the macroscopic behaviour of
materials with their underlying heterogeneous microstructure by continuous interchange of
information between scales. Under the key assumption of the principle of separation of scales, the
hierarchically coupled multi-scale finite element method is based on the nested solution of two
coupled boundary value problems: (i) at the macroscale, where the material’s macroscopic response
is sought, and (ii) at the microscale, where computations are conducted over representative volume
elements in order to account for microstructural phenomena in the macroscopic response, through
an homogenization procedure.
A considerable effort has been made by the scientific community to develop constitutive models
that are able to accurately describe the deformation behaviour of polymeric based materials.
Concerning their fracture thoughness, it is well known that glassy polymers show brittle behaviour,
particulary under specific conditions such as low temperatures and high strain rates. One important
and well-known technique to improve their fracture toughness is termed rubber toughnening, which
consists in dispersing rubbery particles in the polymeric matrix in order to hinder the propagation of
microfractures. Associated with these rubbery particles is the phenomenon of internal cavitation,
meaning that they will behave as voids during the deformation of the rubber toughened polymer.
In the present contribution, a continuum constitutive model is developed in order to predict the
behaviour of porous polymeric materials. This model fully couples the finite strain elastoviscoplastic
constitutive model proposed by Mirkhalaf et al. [1] with the yield surface of the wellknown
micromechanical void growth model proposed by Gurson [2]. A first order homogenizationbased
multiscale model [3] is then employed to critically assess the predictive ability of the
developed continuum model, through several numerical comparisons between the continuum
approach and the homogenized response of a voided representative volume element.