UB - University at Buffalo, The State University of New York UB Mechanical and Aerospace Engineering
photo of Deborah Chung

Computational and Applied Mechanics


Affiliated Faculty

Research Summaries

Modeling and Simulation Based Risk Management of Geophysical Mass Flows

This ongoing long term project involves the development of algorithms and tools for distributed high-end simulation of mass flow (avalanche type – mudflow, block and ash, debris, snow) hazard events, using the best available and suitable newly developed schemes; a major outcome of this project is the TITAN toolset incorporating the best available numerical methodology (parallel and adaptive finite volume) and physical modeling for hazardous geophysical mass flows. Current and future work in this effort will include the incorporation of uncertainty into the parameters and inputs used for these computations.

A.PATRA. Sponsor: NSF and NASA

Mixed variational methods for dynamics problems

A series of novel mixed variational methods are under development for a broad range of coupled dynamical problems in engineering mechanics. In particular, the concept of Mixed Convolved Action resolves a long-standing problem in mechanics by providing a single scalar functional for dissipative dynamical systems. The new method involves fractional calculus and the convolution of convolutions to define an action that recovers all of the governing differential equations, initial conditions and boundary conditions of the problem. A series of Mixed Lagrangian Formulations (MLF) also are under development with G. Apostolakis for dynamic thermomechanics, bringing these problems into a variational framework for the first time. Another focus is on defining robust numerical solutions for problems involving deterioration and damage in structural, solid mechanics and material science.

Size-dependent continuum mechanics

Theoretical formulations are being developed with A. Hadjesfandiari for size-dependent continuum mechanics that resolve the major issues of indeterminacy and inconsistency that plague all previous formulations. The key discoveries in this work involve the definition of couple stresses and mean curvatures as skew-symmetric, energy conjugate measures. In addition to the general theory, corresponding boundary element, finite element and finite difference methods also are under development . Furthermore, all of these formulations extend in a natural way to a wide range of size-dependent coupled problems.


Computational methods linking variational and integral equation methods

The theory of boundary eigensolutions has been developed in collaboration with A.R. Hadjesfandiari. This theory provides an alternative view to characterize the solution of boundary value problems and creates a fundamental link between variational and integral equation methods. As a consequence, several new computational mechanics formulations have also been developed that are particularly attractive for the systematic solution of non-smooth problems involving cracks, notches and bimaterial interfaces. Boundary element methods for generalized fracture mechanics and multiscale analysis of engineering composites are presently under development.


Computational methods for multi-hazard design

Robust computational approaches are under development for multi-hazard design and decision support based upon evolutionary methodologies. These new approaches explicitly account for environmental uncertainty and incorporate both engineering and sociotechnical aspects of the problem. One research thread of the current work focuses on the evolutionary seismic design and retrofit of structures using passive energy dissipation systems. A second innovative research thrust is directed toward the development of a general computational methodology for organizational modeling and complex decision processes. The initial application of this approach addresses seismic retrofit decisions in hospitals and other critical healthcare organizations.

G. DARGUSH, D.J. ALESCH, W.J. PETAK, S. DOGRUEL, G. APOSTOLAKIS and O. LAVAN. Funding has been provided by MCEER and NSF.

Passively damped structural systems


A mechanics-based approach was developed for passively damped structural systems. This approach provides an important theme for the book written with T.T. Soong entitled Passive Energy Dissipation Systems in Structural Engineering published by Wiley. The book includes both a synthesis and critique of existing work on a wide range of PED systems. Although emphasis is placed on a mechanics-based presentation of fundamentals, numerous design and implementation issues are also addressed. Since its publication in 1997, this text has been cited numerous times in the archival literature. A Chinese translation was released in 2005. In addition, a new book co-authored with Z. Liang, G.C. Lee and J. Song, entitled Structural Damping: Applications in Seismic Response Modification, was published by Taylor & Francis in 2011.

Computational Modeling of Soft Tissue

The biomechanical modeling of the tissue of arteries or heart valves is critical to determine the stress experienced by the tissue that can cause damages, tissue remodeling, or failure/rupture. However, modeling of tissue behavior requires computational methods capable of handling large deformations and non-linear material behavior. We have developed and implemented a finite element (FE) method for large deformation of tissue with non-linear, anisotropic material behavior, e.g., see here. The FE solver is coupled with our flow solver to carry out fluid-structure interaction simulations of arteries and heart valves. These simulations are used to identify the problem areas and ways to resolve them.

Efficient probability of failure calculations for composite materials

Standard criteria exist for calculating the failure of composite materials, and these criteria can be cast in probabilistic formulations. But for high reliability loading states, there is a very large computational burden in running sufficient Monte Carlo simulations to ensure accurate results. The “importance sampling” is a variance reduction technique which can be used in such high reliability conditions by first maximizing the joint pdf of the strengths, subject to the constraint of the failure envelope. Sampling is done in the region where failure is most likely, and the inherent bias for this sampling is corrected during the sampling process. The goal is to be able to calculate the reliability to a high degree of precision with many fewer samples than required for standard Monte Carlo sampling.


Accurate tests for strength of bimaterial interfaces

There are problems producing a uniform stress state so that the tensile (mode I) strength and fracture of a bimaterial interface can be properly evaluated. In particular, there can be stress singularities where the interface intersects the edge of the sample. The basic theory relies on the curvature of the interface to avoid the stress singularity, and such samples have been used to injection mold two polymeric materials with greatly differing moduli together. We will explore the use of this technique for the technologically useful metal-polymer interfaces such as Al and Cu with epoxy or other thermoset polymers.

Vibration of trapezoidal membranes

Rectangular membranes (planar structures without bending stiffness) are typically used in very low Reynolds number applications such as micro-air vehicles (MAV’s). There are solutions for the natural frequencies and flutter of rectangular membranes, but it is considerably more likely that the application to MAV’s will involve non-rectangular, specifically trapezoidal, planforms. This work will explore the application of Galerkin’s method to this non-linear problem in a trapezoidal domain.




  • UB MAE Research

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    MAE researchers have developed advanced computational techniques for Fire Simulation and multi-phase reacting turbulent flows.

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    UB MAE researchers in computational mechanics have developed a high fidelity volcanic landslide simulator to aid geologists in mapping the hazard areas at locations such as the island of Montserrat.

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    A Level Set Embedded Interface Method has been developed at Compuational Fluid Dynamics Laboratory to simulate Conjugate heat transfer for irregular geometries

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    MAE's Laser Flow Diagnostic Laboratory is a leader holographic particle image velocimetry, a three-dimensional, next generation flow diagnostics tool.

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    MAE's Automation, Robotics, and Mechatronics Laboratory is conducting research both on the theoretical formulation and experimental validation of such novel mechatronic systems as multi-robot collaboration.

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    The nonlinear estimation group is developing techniques for propagating uncertainties through nonlinear dynamical systems for better forecasting and output uncertainty characterization.

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    Study of Non-premixed flame-wall interaction using vortex ring configuration is done for the first time at the Computational Fluid Dynamics Laboratory.

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