Point forces in elasticity equation and their alternatives in multi dimensions

Deep dermal wounds induce skin contraction as a result of the traction forcing exerted by (myo)fibroblasts on their immediate environment. These are cells that responsible for regeneration collagen is necessary integrity We consider several mathematical issues regarding models simulate forces (myo)fibroblasts. Since size (e.g. (myo)fibroblasts) much smaller than domain computation, one often considers point forces, modelled Dirac Delta distributions boundary segments to cells. In current paper, we treat directed normal cell and toward centre. it can be shown there exists no smooth solution, at least not in H1 solutions governing momentum balance equation, analyse convergence quality approximation. Furthermore, expected finite element problems get necessitate scrutinize alternative model formulations, such use smoothed distributions, or so-called particle approach well ‘hole’ where cellular through (natural) conditions. this investigate attempt quantify conditions consistency between various approaches. This has resulted into error analyses L2-norm numerical solution based Galerkin principles entail Lagrangian basis functions. The paper also addresses well-posedness terms existence uniqueness. analysis been performed linear steady-state (hence neglecting inertia damping) equations under assumption Hooke’s law.