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, … Show more
“…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 .…”
Section: Setting and Transformation To Fixed Domainmentioning
“…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 .…”
Section: Setting and Transformation To Fixed Domainmentioning
“…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].…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
A general theory of thermodynamically consistent biomechanical-biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and elastic distortion tensors at the interface. The incoherent interface therefore acts as an additional source of internal stress besides allowing for rich growth kinematics. All the biochemicals in the model are essentially represented by nutrient concentration fields, in the bulk and at the interface. A nutrient balance law is postulated which, combined with mechanical balances and kinetic laws, yields an initial-boundary-value problem coupling the evolution of bulk and interfacial growth, on one hand, and the evolution of growth and nutrient concentration on the other. The problem is solved, and discussed in detail, for two distinct examples:annual ring formation during tree growth and healing of cutaneous wounds in animals.
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