Smeared concept as a general methodology in finite element modeling of physical fields and mechanical problems in composite media

A generalization of the smeared concept for field problems, published in recent papers of the author and his collaborators, is presented in the paper. A composite smeared finite element CSFE is formulated. This generalization can serve as a theoretical background for further applications. A selected numerical example, related to convective-diffusive mass transport within a cancerous tissue, illustrates efficiency and accuracy of the smeared models. Further, a smeared methodology is extended to mechanical problems. A theoretical background is given in detail, with introducing a composite smeared finite element for mechanics CSFEM, which can further be tested and modified. Finally, a consistent derivation is presented for the continuum constitutive tensor corresponding to a fibrous structure.