




Research 


My research has been mainly focused on the mathematical modeling in continuum mechanics, with an emphasis on multiscale mechanics for heterogeneous materials.
Heterogeneous materials, whether natural (e.g. rocks, bones, tissues, muscles),
or manmade (e.g. composite materials, emulsions, electrorheological or magnetorheological materials) exhibit several scales, either in space or in time,
caused by the inhomogeneity, or the complexity of the mechanical process. A major question is the derivation of the macroscale (effective)
properties of the heterogeneous material as a function of the properties of the constituents and of the local geometry; an "averaging" over the microscale yields
the macroscopic constitutive behavior. The associated partial differential equations, have highly oscillating coefficients, and
this averaging translates into the convergence of the solutions.


Book 


C. C. Mei and B. Vernescu, Homogenization Methods for Multiscale Mechanics, World Scientific Publishing Co., 2010.  


Homogenization on Surfaces 


F. Maris, B. Vernescu, Effective leak conditions across a membrane, Complex Variables and Elliptic Equations, 57, 24 (2012) 437453.
D. Onofrei, B. Vernescu, Gconvergence Results for some Spectral Problems Associated to the Neumann Sieve and their Applications, Multi Scale Problems and Asymptotic Analysis, eds. A. Damlamian et. al., GAKUTO International Series, Mathematical Sciences and Applications, 24, (2005) 249260. I. Ionescu, D. Onofrei, B. Vernescu, GammaConvergence for a Fault Model with SlipWeakening Friction and Periodic Barriers, Quarterly for Applied Mathematics, LXIII, 4, (2005) 747778. D. Onofrei, B. Vernescu, Asymptotics of a Spectral Problem Associated to the Neumann Sieve, Analysis and Applications, 3, 1, (2005), 6987.  
Error Estimates in Homogenization 


D. Onofrei, B. Vernescu, Asymptotic analysis of secondorder boundary layer correctors, Applicable Analysis, 91, 6 (2012) 10971110.
D. Onofrei and B. Vernescu, Error Estimates for Periodic Homogenization with non smooth coefficients, Asymptotic Analysis, 54, (2007) 103123.  
Surface Effects in Composite Materials 


R. Lipton and B. Vernescu, Bounds for Cell Wall Permeabilities,
IUTAM Symposium on Synthesis in Bio Solid Mechanics, eds. P. Pedersen and M. P. Bendsoe, Kluver Academic Publishers, (1999), 401406.
R. Lipton and B. Vernescu, Variational Methods, Size Effects and Extremal Microgeometries for Elastic Composites with Imperfect Interface, Mathematical Models and Methods in Appl. Sci., 5, (1995), 11391173, R. Lipton and B. Vernescu, Critical Radius, Size Effects and Extremal Microgeometries for Composites with Imperfect Interface, J. Appl. Physics, 9, (1996), 89648969 R. Lipton and B. Vernescu, Twophase Elastic Composites with Interfacial Slip, Zeitschrift fur Angewandte Mathematik und Mechanik, (ZAMM), 76, 2, (1996), 597 R. Lipton and B. Vernescu, Composites with Imperfect Interface, Royal Society of London Proceedings, 452, (1996), 329358.  
Nonlinear Composite Materials 


S. Jimenez, B. Vernescu and W. Sanguinet, Neutral inclusions: assemblages of spheres,
Int. J. Solids and Structures , 40, 1415, (2013) pp. 22312238.
 
Porous Media 


B. S. Tilley, B. Vernescu and J. Plummer, GeometryDriven Charge Accumulation in Electrokinetic Flows between Thin, Closely Spaced Laminates ,
SIAM J. Appl. Math., 72, 1 (2012) pp. 3960.
B. S. Tilley, B. Vernescu and J. Plummer, Electrokineticallydriven flows in swelling porous media, Proc. 16th National Congress of Theoretical and Applied Mechanics, USNCTAM 2010, June 27July 2, State College, PA. B. Vernescu, Size and DoubleLayer Effects on the Macroscopic Behavior of Clays Recent Advances in Problems of Flow and Transport in Porous Media, eds. J. M. Crolet and M. E. Hatri, Kluver, (1998) 4558. D. Apelian, J. L. Hoffman, B. Vernescu, Deep Bed Filtration of Molten Metals, Proc. International Conference and its Application in Science, Engineering and Industry, H. I. Ene and B. Vernescu, On the Macroscopic Behaviour of Clays, Mathematical Modelling of Flow through Porous Media, eds. Bourgeat, Carrasso, Luckhaus, Mikelic, World Scientific, (1995), 138147. H. I. Ene and B. Vernescu, Viscosity Dependent Behaviour of Viscoelastic Porous Media, Asymptotic Theories for Plates and Shells, eds. R. P. Gilbert and K. Hackl, Pitman Research Notes in Mathematics 319, (1995). B. Vernescu, Asymptotic Analysis for an Incompressible Fluid Flow in Fractured Porous Media, Int. J. Engng. Sci. 28, 9, (1990), 959964. B. Vernescu, Viscoelastic behaviour of a Porous Medium With a Deformable Skeleton, St. Cerc. Mat. 4, 5, (1989), 423440. H. I. Ene and B. Vernescu, Homogenization of a Singular Perturbation Problem, Rev. Roum. Math.Pures et Appl., 30, 10, (1985), 815822.  
Electrorheological Fluids 


B. Vernescu, Multiplescale Analysis of Electrorheological Fluids,
International Journal of Modern Physics B, 16, 1718, (2002), 26432648.
J. Perlak and B. Vernescu, The Effective Yield Stress in Electrorheological Fluids, Rev. Roum. Math. Pures et Appl., 45, 2, (2000), 287299.  
Viscoplastic Materials 


I. R. Ionescu and B. Vernescu, A Numerical Method for a Viscoplastic Problem.
An Application to Wire Drawing,
Int. J. Engng. Sci. 26, 6, (1988), 627633.
I. R. Ionescu, I. Molnar, and B. Vernescu, A Finite Element Model of Wire Drawing. Variational Formulation and Numerical Method Rev. Roum. Sci. Tech. Mech. Appl. 30, 6, (1985), 611622.  
Emulsions 


R. Lipton and B. Vernescu, Homogenization of TwoPhase Emulsions,
Proceedings of the Royal Society of Edinburgh, 124A, (1994) 11191134.
B. Vernescu, On the Convergence of Functionals` Minimum Points, Rev. Roum. Math.Pures et Appl., 30, 8, (1985), 685692.  
Free Boundaries 


R. Stavre and B. Vernescu, Free Boundary Properties in nonHomogeneous Media Fluid Flow, Int. J. Engng. Sci. 27, 4, (1989), 399409.
R. Stavre and B. Vernescu, The Free Boundary Problem for the Anisotropic Dam, Arch. Mech., 40, (1988), 455463. R. Stavre and B. Vernescu, Incompressible Fluid Flow through a nonHomogeneous and Anisotropic Dam, Nonlinear Analysis TMA 9, 8, (1985), 799810. R. Stavre and B. Vernescu, A Free Boundary Problem in Fluid Mechanics, Proc. Conf. Diff. Eqs. ClujNapoca, (1985). 
