Multiscale modeling solid mechanics

In the next sections, the multiscale modeling methods are presented from the different disciplines perspectives. Clearly one could argue that overlaps occur, but the idea here is to present the multiscale methods from the paradigm from which they started. For example, the solid mechanics internal state variable theory includes mathematics, materials science, and numerical methods. However, it clearly started from a solid mechanics perspective and the starting point for mathematics, materials science, and numerical methods has led to other different multiscale methods. 

Not mentioned in this review but certainly important to multiscale modeling related to solid mechanics are topics, such as self-assemblies, thin films, thermal barrier coatings, patterning, phase transformations, nanomaterials design, and semiconductors, all of which have an economic motivation for study. Studies related to these types of materials and structures require multiphysics formulations to understand the appropriate thermodynamics, kinetics, and kinematics. 

VAN DER HoEF, M. A., VAN SiNT AnNALAND, M., DeEN, N. G. KUIPERS, J. A. M. 2008 Numerical simulation of dense gas-solid fluidized beds a multiscale modeling strategy. Annual Review of Fluid Mechanics 40, Al-10. 

FIGURE 1.5 Multiscale modeling in computational pharmaceutical solid-state chemistry. Here DEM and FEM are discrete and finite element methods MC, Monte Carlo simulation MD, molecular dynamics MM, molecular mechanics QM, quantum mechanics, respectively statistical approaches include knowledge-based models based on database analysis (e.g., Cambridge Structure Database [32]) and quantitative structure property relationships (e.g., group contributions models [33a]). 

While multiscale modeling is still in its infancy, its promise is such that considerable efforts should be devoted to its development in the years to come. A few examples have started to appear in the literature. In the case of solid materials, the challenge of coupling atomistic phenomena (e.g., the tip of a crack) with mechanical behavior (e.g., crack propagation and failure) over macroscopic domains has been addressed by several authors. In the case of fluids, molecular-level structure (e.g., the conformation of DNA molecules in solution) has been... 

In this chapter, we have discussed three levels of modeling for dense gas-solid flows, with the emphasis on the technical details of each of the models, which have not been published elsewhere. Up till now, the models have mainly been used to obtain qualitative information, that is, to acquire insight into the mechanisms underlying the gas-solid flow structures. However, the ultimate objective of the multiscale approach is to obtain quantitative... 

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

L.E. Shilkrot et al Multiscale plasticity modeling Coupled atomistics and discrete dislocation mechanics. J. Mech. Phy. Solids 52, 755-787 (2004)... 

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