J.J. Telega

Plates, laminates and shells : asymptotic analysis and homogenization

Mathematical preliminaries: function spaces, convex analysis, variational convergence. Elastic plates: three-dimensional analysis and effective models of composite plates thin plates in bending and stretching non-linear behaviour of plates moderately thick transversely symmetric plates sandwich plates with soft core. Elastic plates with cracks: unilateral cracks in thin plates unilateral cracks in plates with transverse shear deformation part-through the thickness cracks stiffness loss of cracked laminates comments and bibliographical notes. Elastic-perfectly plastic plates: mathematical complements homogenisation of functional with linear growth homogenisation of plates loaded by forces and moments comments and bibliographical notes. Elastic and plastic shells: linear and non-linear models of elastic shells homogenisation and stiffnesses of thin periodic elastic shells linear approach homogenised properties of thin periodic elastic shells undergoing moderately large relations around tangents perfectly plastic shells. Application of homogenisation methods in optimum design of plates and shells: mathematical complements two-phase plate in bending, Hashin-Shtrikamn bounds two-phase plate Hashin-Shtrikman bounds for the in-plane problem explicit formulae for effective bending stiffnesses and compliances of ribbed plates explicit formulae for effective membrane stiffnesses and compliance s of ribbed plates thin bending two-phase plates of minimum compliance minimum compliance problem for thin plates of varying thickness -application of young measures thin shells of minimum compliances Truss-like Michell continua.

Nonlinear homogenization and its applications to composites, polycrystals and smart materials

Foreword. List of Participants. Titles of Contributed Papers. Invited Lectures. Topology Optimization With The Homogenization And The Level-Set Methods G. Allaire. Thin Films Of Active Materials K. Bhattacharya. The Passage From Discrete To Continuous Variational Problems: A Nonlinear Homogenization Process A. Braides, M.S. Gelli. Approaches To Nonconvex Variational Problems Of Mechanics A. Cherkaev. On G-Compactness Of The Beltrami Operators T. Iwaniec et al. Homogenization And Optimal Design In Structural Mechanics T. Lewinski. Homogenization And Design Of Functionally Graded Composites For Stiffness And Strength R. Lipton. Homogenization For Nonlinear Composites In The Light Of Numerical Simulations H. Moulinec and P. Suquet. Existence And Homogenization For The Problem - div a(x, Du) = F When a(x,) Is A Maximal Monotone Graph In For Every x F. Murat. Optimal Design In 2-D Conductivity For Quadratic Functionals In The Field P. Pedegral. Linear Comparison Methods For Nonlinear Composites P. Ponte Castaneda. Models Of Microstructure Evolution In Shape Memory Alloys T. Roubicek. Stochastic Homogenization: Convexity And Nonconvexity J.J. Telega. Final remarks. Index.

JUSTIFICATION OF A REFINED SCALING OF STIFFNESSES OF REISSNER PLATES WITH FINE PERIODIC STRUCTURE

The aim of this paper is a rigorous justification of the model of linear elastic plates proposed in Ref. 19. Such a model is obtained by rescaling stiffnesses and performing homogenization of a Reissner plate exhibiting fine periodic structure. To prove convergence, when the periodicity parameter tends to zero, the epi-convergence method is applied; the proof of convergence essentially exploits duality arguments. The dual homogenization, based on the principle of the complementary energy, is also studied; the properties of the macroscopic potential are investigated and the dual homogenized (macroscopic) potential is derived.

Homogenization of fissured elastic solids in the presence of unilateral conditions and friction

The objective of this contribution is to find effective properties of hyperelastic bodies weakened by periodically distributed microfissures. Problems investigated are internal Signorinis problems with friction. Two such problems have been studied. The first problem is purely static and the friction law is of the deformational plasticity type. To find the overall properties an implicit variational inequality has been homogenized. The second problem concerns homogenization in the quasi-static case and the sliding rule of the flow law type. The variational formulation is obtained in the form of an implicit variational inequality coupled with a variational inequality. In both cases the macroscopic behaviour is elastic-plastic of nonstandard type.

Electrokinetics in Random Deformable Porous Media

The aim of this contribution is to derive macroscopic equations describing flow of two-ionic species electrolytes through porous piezoelectric media with random, not necessarily ergodic, distribution of pores. Under assumption of ergodicity the macroscopic equations simplify and are obtained by using the Birkhoff ergodic theorem.

Piezoelectricity with polarization gradient: homogenization

Abstract The aim of this paper is to perform homogenization of the equation of linear piezoelectricity with the polarization gradient. We assume that the material coefficients are microperiodic. This assumption can be weakened. One can also consider nonuniform homogenization. Then the homogenized (macroscopic) moduli depend on macroscopic variable.

Variational formulation of the transient motion of a rolling cylinder undergoing plane finite deformations

Abstract This paper is concerned with a variational formulation of the problem of the transient motion of a rolling cylinder undergoing plane finite deformations. Frictionless motion is described by one quasi-variational inequality. If friction is taken into account then the formulation is available in the form of an evolution implicit variational inequality coupled with a quasi-variational inequality.