Modelling framework for mass-growth

•Hyper-elasticity and plasticity theory are merged suitably to produce a modelling framework for mass-growth of matter.•Stimulus of mass-growth builds in an elastic stage of deformation followed by a stage that involves plastic-like flow.•A hyper-elasticity-type of constitutive equation is also derived which includes explicit contribution of mass-growth.•The end of the elastic-like stage of mass-growth is marked through satisfaction of a yield condition for mass-growth.•The efficiency of the new modelling framework is illustrated thought a relatively simple example application.

This study adopts a simple and rather known concept which suggests that stimulus of mass-growth may be built up in a elastic-like stage of mass-growth deformation, followed immediately afterwards by a stage of growth that may involve features of plastic flow. Such an analogy between known solid mechanics and mass-growth concepts suggests that the end of an elastic-like stage of mass growth can be marked through the satisfaction of a certain yield condition for mass-growth. This paper illustrates a manner in which hyper-elasticity and plasticity theory of solids may merge in order to produce such a suitable framework for modelling mass-growth features of matter, in general, or soft material tissue, in particular. In this context, it derives a new type of hyper-elasticity-type of constitutive equation which includes explicit contribution of mass-growth, and illustrates the efficiency of this new modelling framework through a relatively simple example application.