Efficient and Robust Explicit and Implicit Integration Schemes for the Arruda-Boyce Viscoplatic Model?.

I. TOMAS; ADRIÁN CISILINO; P FRONTINI

San Luis

Congreso; Métodos Numéricos y sus Aplicaciones ENIEF2008,; 2008

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.