I am Dr. Brad Darrall, a mechanical engineer and graduate of the University at Buffalo. I currently hold the position of teaching assistant professor at the University at Buffalo. Aside from teaching I am also an avid researcher, with strengths in theory, formulations, and computational methods for multiphysics problems, micromechanics, and quantum mechanics. In addition to my strong academic base I am also a life long musician, most recently playing with the band Imperial Brown.
I have done a great deal of research work in the field of couple stress mechanics, a continuum theory that bridges the gap between classical mechanics and molecular dynamics, ideal for micro- and nanomechanics. Related to this I have also done significant work in the fields of flexoelectricity, also known as size-dependent piezoelectricity, and size-dependent thermoelasticity. For all cases I have developed finite element methods, variational principles, and analyzed many interesting problems. Currently I am working on furthering a set of experiments with the aim at measuring couple stress effects, as well as developing 3d simulation approaches.
Another field of research that I have contributed to is variational approaches to dynamic mechanics problems. A new type of stationary action principle, coined convolved action principles, or sometimes mixed convolved action principles, resolve difficulties associated with many, or all, efforts to develope time-dependent variational principles based on the original Hamilton's principle. These new action principles have many distinct advantages over their predecessors, both theoretically and computationally. Interestingly, I have been able to apply these new action principles to both classical, and quantum mechanics with great success, which seems to be an area of great interest moving forward. Corresponding to these new variational methods, I have also developed novel time-space finite element methods.
In the future, I hope to draw from my previous research experience to make significant contributions in the fields of nanomechanics, quantum mechanics, complex multiphysics problems, and numerical methods.
My greatest drive in life is learning; a day without learning something new is a wasted day. Having said that there is an intimate bond between learning and teaching, and I am glad to be able to call teaching my career.
Courses I have experience teaching:
Intro to MATLAB and Linear Algebra (EAS230)
Structural Analysis (MAE315)
Fluids and Thermal Lab (MAE338)
Intermediate Dynamics (MAE345)
Applied Math for Engineers (MAE376)
Darrall, B.T., “Convolved energy variational principle in heat diffusion”, Int. J. Heat Mass Transf, 175, 121315 (2021).
Pedgaonkar, A., Darrall, B.T., Dargush, G.F., “Mixed displacement and couple stress finite element method for anisotropic centrosymmetric materials”, Eur. J. Mech. A-Solids, 85, 104074 (2021).
Darrall, B.T., Dargush, G.F. “Variational principle and time-space finite element method for dynamic thermoelasticity based on mixed convolved action”, Eur. J. Mech. A-Solids, 71, 351-364, (2018).
Darrall, B.T., Dargush, G.F. “Mixed Convolved Action Variational Methods for Poroelasticity”, J. Appl. Mech., 83.9, 091011, (2016).
Dargush, G.F., Apostolakis, G., Darrall, B.T., Kim, J. “Mixed convolved action variational principles in heat diffusion”, Int. J. Heat and Mass Transfer, 100, 790-799, (2016).
Darrall, B.T., Dargush, G.F. “Mixed convolved action principles for dynamics of linear poroelastic conitinua”, ASME, IMECE2015-53163, Houston, TX, November 2015.
Dargush, G.F., Darrall, B.T., Kim, J., Apostolakis, G. “Mixed convolved action principles in linear continuum dynamics”, Acta Mech., 226, 4111-4137 (2015).
Darrall, B.T. “Variational and 2D finite element formulations for size-dependent elasticity and piezoelectricity”, M.S. Thesis, University at Buffalo, The State University of New York (2015).
Darrall, B.T., Hadjesfandiari, A.R., Dargush, G.F. “Size-dependent piezoelectricity: A 2D finite element formulation for electric field-mean curvature coupling in dielectrics”, Eur. J. Mech. A-Solids, 49, 308-320 (2015).
Darrall, B.T., Dargush, G.F., Hadjesfandiari, A.R. “Finite element Lagrange multiplier formulation for size-dependent skew-symmetric couple-stress planar elasticity”, Acta Mech., 225, 195-212 (2014).
Many more to be posted soon!