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Publication 21-CNA-006
Surface Growth in Deformable Solids using an Eulerian Formulation Kiana Naghibzadeh Noel J. Walkington Kaushik Dayal In this work, an Eulerian approach to this problem is formulated, enabling the side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduces additional kinematic descriptors, namely the relaxed zero-stress deformation and the elastic deformation; in contrast to the deformation gradient, these have the important advantage that they are not required to satisfy kinematic compatibility. The zero-stress deformation and the elastic deformation are used to eliminate the deformation gradient from the formulation, with the evolution of the elastic deformation shown to be governed by a transport equation. The resulting model has only the density, velocity, and elastic deformation as variables in the Eulerian setting. The proposed method is applied to simplified examples that demonstrate non-normal growth and growth with boundary tractions. The introduction in this formulation of the relaxed deformation and the elastic deformation provides a description of surface growth whereby the added material can bring in its own kinematic information. Loosely, the added material “brings in its own reference configuration” through the specification of the relaxed deformation and the elastic deformation of the added material. This kinematic description enables, e.g., modeling of non-normal growth using a standard normal growth velocity and a simple approach to prescribing boundary conditions. Get the paper in its entirety as 21-CNA-006.pdf |