Continuous bodies with thermodynamically active singular sharp interfaces

Abstract

The subject of this comprehensive study is the general (mathematical) modeling of sharp (i.e. two-dimensional) interfaces without and with their own thermodynamical activity. We provide essential tools for the modeling of body-interface systems. Important items of the kinematics of singular (moving) interfaces as well as balance equations at interfaces will be addressed. Problems connected with material representation will be discussed. Special interfacial balances for mass, impulse, angular momentum, energy, mass of a tracer and of entropy will be considered including the discussion of special cases. As an illustrative example, a continuous model for a body with loss of material (e.g. due to mechanical treatment) will be developed in the framework presented.

Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations

“…Note that, if we neglect the dissipation and if we have equal densities and heat capacities in both phases (or, a bit more general, ⟦ ρ c d ⟧ = 0), equation reduces to the usual Stefan condition . More complex interface conditions then equations , would arise, if the interface were allowed to be thermodynamically active thereby requiring us to formulate separate balance equations for surface stress and surface heat, we refer to .…”

Biological growth in bodies with incoherent interfaces

“…Whereas mass is added in the bulk material during volumetric growth [9,13,25] (e.g., in soft tumorous and arterial tissues), it accretes on to the free surface of the body during surface growth [8,12,27] (e.g., in hard horn and bone tissues). On the other hand, mass addition can also happen at a material or a non-material interface within the body [7,11,33], as is the case with ring formation in trees, healing of cutaneous animal wounds, growth of animal nails, etc. In fact, interfacial growth models can also provide a viable framework for studying problems in surface growth, e.g., by considering the external source to be the bulk body on one side of the interface [12] or by assuming the interface to be between a bulk substrate and a growing two-dimensional film [16,22].…”

“…in hard horn and bone tissues). On the other hand, mass addition can also happen at a material or a non-material interface within the body [9][10][11], as is the case with ring formation in trees, healing of cutaneous animal wounds, growth of animal nails, etc. In fact, interfacial growth models provide a viable framework for studying problems in 2018 The Author(s) Published by the Royal Society.…”