Thermomechanics of Phase Transitions in Classical Field Theory

The Nonlinear Theory of Elastic Shells with Phase Transitions

“…In analogy to the problem of thermodynamic equilibrium of 3D elastic bodies undergoing a phase transition [2,3], the position of the phase interface C within M can be established from the variational principle δI = 0. The principle states that among all possible values of translations, rotations, and positions of the phase interface curve C the actual solution renders the functional (22) stationary.…”

Mathematical Modeling of Morphogenesis in Living Materials

“…(99). The leading order incrementŜ can be derived by differentiating the constitutive equation in Eq.…”

“…For matters of generality, we assume that generic mass fluxes m − and m + may exist between the volumes and the moving interface 4 . Therefore, by applying the transport and divergence theorems in a system with a non-material discontinuity [99], the surface mass balance takes the following form:…”

Continuous bodies with thermodynamically active singular sharp interfaces

“…Here, we will not consider possible limiting processes leading to sharp-interface models when the thickness of the interfacial layer tends to zero. We refer the reader to [2,3,7,12,30,31].…”

“…They can be met in many situations and applications in physics, mechanics, chemistry, biology covering the behavior of solids, fluids and gases. We exemplarily refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and to the references therein. Two immiscible fluids divided by a thin film, the aforementioned ice melting (Stefan problem; see e.g.…”