A Simple Numerical Implementation Of The Arrudaboyce Viscoplatic Model To Reproduce The Mechanical Behavior Of Uhmwpe

Abstract

Bioengineering and biomechanics are areas of growing interest in the scientific and
engineering research community. Computational biomechanics is a relatively new discipline in which
scientists pretend to use computational and mathematical tools to model and predict biomechanical
events and phenomena using the finite element method as a primary tool. In this context, appropriate
selection, development and robust implementation of constitutive models for biological tissues and
biomaterials seems to be a challenging task. The role of constitutive models is crucial to achieve
realistic numerical simulations. A highly popular material for biomedical applications is UHMWPE
(ultra high molecular weight polyethylene). UHMWPE is a though material with the highest impact
strength of any thermoplastic ever made, on the other hand, it is quite difficult to find a constitutive
model capable to reproduce all the phenomenological features that can be observed in simple uniaxial
tests of this material .
Recent publications show that the Arruda-Boyce constitutive model is capable to reproduce the
mechanical behavior of UHMWPE quite accurately. While the Arruda-Boyce viscoplastic constitutive
model is quite popular in the area polymer mechanics there are not much works referring to its
computational implementation. The physically inspired mathematical structure of Arruda-Boyce
viscoplastic model offers a few particularities that make its mathematical treatment and numerical
implementation quite difficult. With the awareness of the potential drawbacks and inconveniences that
can be found in the numerical implementation of this constitutive model, a simple implementation of
the Arruda-Boyce constitutive model is presented in this work. The implementation is done by means
of a explicit integration algorithm coded in a UMAT subroutine for ABAQUS finite element software.