Quasi static and dynamic problems in strain gradient (granular) micromechanics

This work presents a comprehensive continuum theory for 2D strain gradient materials that accounts for a class of dissipation phenomena. The continuum description is constructed by means of a reversible placement function and irreversible damage and plastic functions. In addition to specifying expressions for elastic and dissipation energies, we postulate a hemi-variational principle to derive strain gradient Partial Dierential Equations (PDEs), boundary conditions (BCs), and Karush-Kuhn-Tucker (KKT) type conditions. Unlike previous models, our approach does not assume ow rules, and plastic deformation can be derived through the placement function. The derived PDEs and BCs govern the evolution of the placement descriptor, while the KKT conditions govern the damage and plastic variables. To demonstrate the applicability of our model, we conduct numerical experiments on homogeneous cases, which do not require Finite Element simulations. We investigate the induced anisotropy of the response and demonstrate the coupling between damage and plasticity evolution. Using nite element method this work analyzes the mechanical behavior of materials with granular microstructures in two dimensions using a strain-gradient continuum approach based on micromechanics. We account for tensioncompression asymmetry of grain-assembly interactions and microscale damage while linking the continuum scale to the grain-scale mechanisms. Overall, our approach captures microstructural-size-dependent eects and provides a comprehensive understanding of the mechanical behavior of materials with granular microstructures. It has been showed that a granular micromechanics approach can lead to load-path dependent continuum models. In this study, we extend this approach by introducing an intrinsic 2nd gradient energy storage mechanism in the grain-grain interaction, similar to a pantographic micromechanism. We homogenize the approach and determine the macro-scale mechanical behavior, varying the averaged intergranular distance and the stiness associated with the pantographic term. Results show that the inclusion of the pantographic term allows for successful modeling and netuning of the desired thickness of the localization zone. Furthermore, we demonstrate that the complex mechanics of load-path dependency can be predicted through micromechanical eects and the introduced pantographic term. Given approach could be used not only in quasi-static but also in dynamic problem. This work presents a dynamic model for the propagation of fractures in materials subjected to strain gradients. The proposed model accounts for the eects of material heterogeneity and microstructure on the fracture behavior by incorporating a strain gradient term into the governing equations. The model is based on a continuum mechanics framework and uses a variational formulation to derive the equations of motion. The numerical implementation is carried out using the nite element method, and the results are validated against experimental data from literature. The simulations show that the strain gradient has a signicant eect on the fracture patterns and propagation velocity, especially in materials with small length scales. This work provides a valuable tool for predicting and analyzing fracture behavior in microstructured materials, with potential applications in the design of advanced materials and structures.