Modelling framework for mass-growth II: The general case

• This is an extension of the mass-growth modelling framework proposed in Soldatos (2013).
• It models a mass-growth stage in which elastic and plastic deformations take place simultaneously.
• It postulates that the rate of plastic deformation influences the strain energy density for growth.
• It does not anticipate a-priori the rule that elastic and plastic deformations are assembled.
• Instead, it enables specification of that rule through the solution of a growth problem of interest.

The mass-growth modelling framework proposed in Soldatos (2013) is extended to consider an intermediate and, essentially, more general stage during which pseudo-elastic and pseudo-plastic mass-growth take place simultaneously. This “mixed” mass-growth stage is based on the postulation that the strain energy density for mass-growth depends not only on the deformation gradient and the state of pre-stress, but also on the rate of plastic deformation. The rate of total deformation may be thought of as composed by elastic and plastic parts, but the rule according which those parts are assembled is not specified in an a-priori manner. It is instead left to be determined through the solution of the particular mass-growth problem of interest. Still though, either of the purely pseudo-elastic and purely pseudo-plastic mass-growth stages considered in Soldatos (2013) may be obtained as particular cases of the present formulation. Uniform mass-growth of a pre-stressed solid cube (Soldatos, 2013) is again engaged in a pilot, example application where, however, the cube is now assumed to grow in the implied mixed, pseudo-elastic–plastic manner. All unknown quantities involved in this application are identified in a complete manner. It is thus verified that the proposed, mixed stage of growth may be further thought of as an overlap between consecutive pseudo-elastic and pseudo-plastic stages of mass-growth.