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Computational Mechanics

Computational mechanics emphasizes the development of mathematical models representing physical phenomena and applies modern computing methods to analyze these phenomena.

It draws on the disciplines of physics, mechanics, mathematics and computer science, and encompasses applying numerical methods to various problems in science and engineering. The general scope of work in computational mechanics includes fundamental studies of multiscale phenomena and processes in civil engineering, from kilometer-scale problems to a much finer scale up to and including the nano-scale.

Current research in computational mechanics dealing with kilometer-scale problems includes numerical simulation of folding and fracturing of sedimentary rock strata using combined elastoplastic-damage continuum theory along with enhanced finite element (FE) methods for shear localization analysis, as well as simulation of regional-scale earthquake fault nucleation and propagation using a finite deformation stick-slip law with a variable coefficient of friction. 

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Research dealing with meter-scale problems includes development of constitutive models for new high-performance materials such as ductile fiber-reinforced concrete and modeling of nonlinear response of structural systems that use high-performance composite materials. Research on problems dealing with a much finer scale includes theoretical and numerical investigation into the micromechanics of porous media using coupled Lattice-Boltzmann (LB)/FE simulations of fluid flow hydrodynamics through micron-scale pores in rocks.

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Measurement and calibration are key to a successful development of computational algorithms and numerical models at different scales. Light Detection and Ranging (LiDAR) technology, including laser scanning, GPS and digital imagery, provides high-resolution topographic data to constrain kilometer-scale fold models and decameter-long, centimeter-thickness fractures. At the other end of the spectrum lie the advances of 3D digital imaging of lab specimens using X-ray computed tomography with micron-scale resolution.

Combined with traditional testing of centimeter- and meter-scale lab specimens, numerical models can now reach a level of mathematical sophistication commensurate with our ability to measure relevant response variables. A great challenge in computational mechanics research is bridging the different scales without sacrificing resolution. For example, effort is underway to bridge the gap between continuum-scale and atomistic molecular dynamics through combining the particle-based LB approach with the continuum-based FE method to model the fluid flow hydrodynamics through porous rocks.

For a computational technique to be competitive, it is essential to consider not only the spatial and temporal discretization procedures but also how the equations will be solved. While it is generally acknowledged that parallel supercomputing offers considerable promise for solving large problems of practical interest, it is important to recognize that new algorithms and data structures have to be developed to exploit the new discretization methods and attack the intrinsic difficulties of the problem being addressed. Adaptive and stabilized solution schemes based on error estimation also provide unique challenges for solver technology. Current work in our group involves the development of new solution algorithms for multiscale statics and dynamics problems related to parallel and distributed computing.