Multifield continuum simulations for damaged materials: A bar with voids

This work is based on the formulation of a continuum model with microstructure for the study of the mechanical behavior of microcracked materials. Such a continuum is named multifield continuum because it is characterized by field descriptors accounting for the presence of material internal structure. In particular, the disturbance due to the presence of distributed microcracks in the material is revealed by an additional kinematical field representing the smeared displacement jump over the microcracks. According to the approach of the classical molecular theory of elasticity, the constitutive multifield continuum (macromodel) has been obtained by requiring the energy equivalence with an appropriate discrete micromodel. The stress-strain relations of the continuum have been explicitly identified by selecting the response functions of the interactions of the discrete model and depend on the geometry of the material's internal phases. Attention is here focused on theoretical and numerical investigations on a one-dimensional microcracked bar by varying the microcrack density and size. The effectiveness of the multi-field model, in representing the gross mechanical behavior of such materials with internal structure, is ascertained by comparing the multifield solutions with the numerical solutions obtained by using finite-element simulations for a linear elastic strip having different distributions of voids. © 2011 by Begell House, Inc.