Computational modelling of isotropic multiplicative growth. (English) Zbl 1188.74059

Summary: The changing mass of biomaterials can either be modelled at the constitutive level or at the kinematic level. This contribution attends on the description of growth at the kinematic level. The deformation gradient will be multiplicatively split into a growth part and an elastic part. Hence, in addition to the material and the spatial configuration, we consider an intermediate configuration or grown configuration without any elastic deformations. With such an ansatz at hand, contrary to the modelling of mass changes at the constitutive level, both a change in density and a change in volume can be modelled.
The algorithmic realisation of this framework within a finite element setting constitutes the main contribution of this paper. To this end the key kinematic variable, i.e., the isotropic stretch ratio, is introduced as internal variable at the integration point level. The consistent linearisation of the stress update based on an implicit time integration scheme is developed. Basic features of the model are illustrated by means of representative numerical examples.


74S05 Finite element methods applied to problems in solid mechanics
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids