Surface growth in deformable solids using an Eulerian formulation

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, which mass is added the boundary continuum body ambient medium or within body. In contrast bulk growth interior, description requires addition new particles challenging for standard formulations solids that are meant situations with fixed amount material. Recent approaches handle this have used time-evolving reference configurations. work, an Eulerian approach problem formulated, enabling side-stepping issue constructing configuration. However, raises complementary challenge determining stress response solid, typically deformation gradient not immediately available formulation. To resolve this, introduces additional kinematic descriptors, namely relaxed zero-stress and elastic deformation; gradient, these important advantage they required satisfy compatibility. The resulting model has only density, velocity, as variables setting. introduction formulation provides whereby material can bring its own information. Loosely, "brings configuration" through specification enables, e.g., modeling non-normal using normal velocity simple prescribing conditions.