Multiresolution Continuum Theory and Dislocation Density Based Constitutive Relations

Abstract: In classical description, the mechanical state of a material point depends on the variables defined at this point solely. It can integrate and catch some aspects of the material’s microstructure by conventional homogenization method. The application of the conventional continuum assumption results in a simplified description of the system which makes the large scale simulation of the material more efficient but at the expense of a loss of information at small length scales. Localization is a phenomena where a large degree of deformation occurs in highly concentrated regions. The conventional continuum theory with strain softening can not give the convergent solution as the size of the localization zone is completely determined by the mesh discretization. The multiresolution continuum theory (MRCT) is a higher order continuum theory where additional kinematic variables supplementing the conventional macroscopic displacement field are added to account for deformations at several distinct length scales. The direct inclusion of the length scale parameters in the material’s constitutive equations remedies the convergence problem. In crystalline materials the initiation of plastic flow and subsequent permanent plastic deformation is attributed to the presence and movement of dislocations and also the interactions between the dislocation themselves and different kinds of obstacles, inclusions, second phase particles and grain boundaries etc. Some of these defects can alsolead to damage initiation in the materials. For example, the stresses developed at the dislocation pile-ups contribute to the initiation of the microvoids and microcracks. A dislocation density based damage model has been developed and combined with a physically based flow stress model. They are calibrated and validated for 316L stainless steel at different temperatures and strain rates. These models have been implemented into the macroscopic material description of the MRCT element.