An Elastic and Elasto-Plastic Mixed Analysis Using Overlaying Mesh Method.

Image-based multi-scale modelling strategy for complex and heterogeneous porous microstructures by mesh superposition method

“…The governing equations of C and ABC written in a strong form are as follows. For details, refer to the paper [18] which is rewritten in the appendix of this paper:…”

“…Moreover, the second superscript means sub domains A, AB or C. n AB is a normal line along the boundaries of A , AB , C in consideration of the direction C is evaluated only by that of the local model. Note that if material constants in the local model of C are zero, and the body force is ignored, it means that C is a physical pore as in the following equations [17,18] (see also appendix):…”

“…If C sets in touch with AB , the displacement of a global model correlates with that of a local model. It means that the desired microscopic modelling by a local model is not achieved because we cannot derive from equations ( 16) to (18).…”

“…For general purposes, Nakasumi et al [17] mathematically proved that when the local model with a hole represented by the inner boundary of the model is superimposed onto a homogenized global model, the global model framed by the inner boundary is equivalent to a physical hole. They derived generalized formulation to be applied to filling material components [18].…”