# 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 man-made (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.

**PERMEABLE MEMBRANES**

F. Maris, B. Vernescu, Effective Slip for Stokes Flows Across Randomly Leaky Permeable Membranes, Asymptotic Analysis, 86, 1 (2014) pp. 17-48.

F. Maris, B. Vernescu, Effective leak conditions across a membrane, *Complex Variables and Elliptic Equations*, ** 57**, 2-4 (2012) 437-453.

D. Onofrei, B. Vernescu, G-convergence 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) 249-260.

I. Ionescu, D. Onofrei, B. Vernescu, Gamma-Convergence for a Fault Model with Slip-Weakening Friction and Periodic Barriers, * Quarterly for Applied Mathematics*, LXIII, **4**, (2005) 747-778.

D. Onofrei, B. Vernescu, Asymptotics of a Spectral Problem Associated to the Neumann Sieve, * Analysis and Applications*, **3**, 1, (2005), 69-87.

**ERROR ESTIMATES IN HOMOGENIZATION**

D. Onofrei, B. Vernescu, Asymptotic analysis of second-order boundary layer correctors, *Applicable Analysis*, **91**, 6 (2012) 1097-1110.

D. Onofrei and B. Vernescu, Error Estimates for Periodic Homogenization with non- smooth coefficients, *Asymptotic Analysis*, **54**, (2007) 103-123.

**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), 401-406.

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), 1139-1173,

R. Lipton and B. Vernescu, Critical Radius, Size Effects and Extremal Microgeometries for Composites with Imperfect Interface, * J. Appl. Physics*, **9**, (1996), 8964-8969

R. Lipton and B. Vernescu, Two-phase 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), 329-358.

**NONLINEAR COMPOSITE MATERIALS**

S. Jimenez and B. Vernescu, Nonlinear Neutral Inclusions: Assemblages of Coated Ellipsoids, R. Soc. open sci 2015. 2: 140394.

S. Jimenez, B. Vernescu and W. Sanguinet, Neutral inclusions: assemblages of spheres, * Int. J. Solids and Structures* , **40**, 14-15, (2013) pp. 2231-2238.

**POROUS MEDIA**

B. S. Tilley, B. Vernescu and J. Plummer, Geometry-Driven Charge Accumulation in Electrokinetic Flows between Thin, Closely Spaced Laminates , *SIAM J. Appl. Math.*, **72**, 1 (2012) pp. 39-60.

B. S. Tilley, B. Vernescu and J. Plummer, Electrokinetically-driven flows in swelling porous media, *Proc. 16th National Congress of Theoretical and Applied Mechanics,* USNCTAM 2010, June 27-July 2, State College, PA.

B. Vernescu, Size and Double-Layer 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) 45-58.

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), 138-147.

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), 959-964.

B. Vernescu, Viscoelastic behaviour of a Porous Medium With a Deformable Skeleton, * St. Cerc. Mat. 4*, **5**, (1989), 423-440.

H. I. Ene and B. Vernescu, Homogenization of a Singular Perturbation Problem, * Rev. Roum. Math.Pures et Appl.*, ** 30**, 10, (1985), 815-822.

**ELECTRORHEOLOGICAL & MAGNETORHEOLOGICAL FLUIDS**

G. Nika and B. Vernescu, Homogenization for a multi-scale model of magnetorheological suspension, submitted.

B. Vernescu, Multiple-scale Analysis of Electrorheological Fluids, * International Journal of Modern Physics B*, **16**, 17-18, (2002), 2643-2648.

J. Perlak and B. Vernescu, The Effective Yield Stress in Electrorheological Fluids, * Rev. Roum. Math. Pures et Appl.*, **45**, 2, (2000), 287-299.

**EMULSIONS & SUSPENSIONS**

G. Nika and B. Vernescu, Dilute emulsions with surface tension, Quarterly for Applied Mathematics, LXXIV, 1 (2016) pp. 89-111.

F. Maris, Y. Gorb and B. Vernescu, Homogenization for Rigid Suspensions with Random, Velocity-Dependent Interfacial Forces, J. Math. An. Appl., 420, 1 (2014) pp. 632-668.

R. Lipton and B. Vernescu, Homogenization of Two-Phase Emulsions, * Proceedings of the Royal Society of Edinburgh*, **124A**, (1994) 1119-1134.

B. Vernescu, On the Convergence of Functionals` Minimum Points, * Rev. Roum. Math.Pures et Appl.*, **30**, 8, (1985), 685-692.

**HOMOGENIZATION IN INFINITE CYLINDERS**

D. Giachetti, B. Vernescu and M. A. Vivaldi, Asymptotic analysis of singular problems in perforated cylinders, Differential and Integral Equations, 29, 5-6 (2016) pp. 531-562.

P. Donato, S. Mardare and B. Vernescu, Darcy Equations in an Infinite Strip: Do Limits Commute?, Differential and Integral Equations, 26, 9-10 (2013) pp. 949-974.

**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), 627-633.

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), 611-622.

**FREE BOUNDARIES**

R. Stavre and B. Vernescu, Free Boundary Properties in non-Homogeneous Media Fluid Flow, * Int. J. Engng. Sci. 27*, **4**, (1989), 399-409.

R. Stavre and B. Vernescu, The Free Boundary Problem for the Anisotropic Dam, * Arch. Mech.*, **40**, (1988), 455-463.

R. Stavre and B. Vernescu, Incompressible Fluid Flow through a non-Homogeneous and Anisotropic Dam, * Nonlinear Analysis TMA 9*, **8**, (1985), 799-810.

R. Stavre and B. Vernescu, A Free Boundary Problem in Fluid Mechanics, * Proc. Conf. Diff. Eqs.* Cluj-Napoca, (1985