Generalized “grid” continuum description as a tool for proposing multi-scale material models

AbstractTo describe materials with more complex microstructure, generalization of the standard continuum theory is proposed. The key idea consists in dividing the studied body onto a set of small but finite cells. The state of the microstructure withineachcell is described by an additional field that may be discontinuous or highly oscillating. Hence, non-trivial effects of microstructure can be involved in resulting material models. The theory is illustrated on atwo-scale hyperelasticmodel of amaterialwithprestressat the reference state.Non-trivial character of the mechanical responsecaused by a collapse of micro-constituents motivates us to design an engineering material with similar properties