Eveline Baesu

Incremental behaviour of hyperelastic dielectrics and piezoelectric crystals

Abstract. The equations describing the behaviour of a hyperelastic dielectric under pre-existing mechanical and electrical fields are derived. The associated differential system is shown to be self-adjoint. This property, in turn, is used to establish the equivalence of linear static and dynamic stability criteria.

Continuum modeling of cell membranes

Abstract In this paper, we develop a finite-deformation model for cell membranes with a view toward characterizing the local mechanical response of membranes in atomic force microscope (AFM) experiments. The membrane is modeled as a 2-D fluid continuum endowed with bending resistance. The general theory is used to obtain equations that describe axisymmetric equilibrium states. The membrane is assumed to enclose a fluid medium, which transmits hydrostatic pressure to the membrane, and a point load is applied at the pole to simulate an AFM probe. Both types of loading are associated with a potential and the problem is then cast in a variational setting. The equilibrium equations and boundary conditions are obtained by applying standard variational procedures, resulting in a pair of coupled fourth-order differential equations to be solved for the shape of the meridian. Further refinements associated with global constraints on the enclosed volume and contact with a rigid substrate are introduced, and a solution strategy is proposed which relies on an iterative scheme for calculating the associated Lagrange multipliers.

Finite deformations of elastic–plastic filamentary networks

Abstract Finite elastic–plastic deformation of a thin sheet formed by several families of perfectly flexible extensible fibers is described using an idealized theory in which the fibers are assumed to be continuously distributed to form a surface. The constitutive properties of the surface are deduced directly from those of the constituent fibers. The equilibrium equations are cast in rate form and associated rate potentials are derived. Physically plausible sufficient conditions for the existence of an exact dual extremum principle are proposed and used to prove uniqueness of solutions. Yielding and plastic flow criteria for individual fibers are given in a strain-space setting and adapted to model the elastic–plastic response of the sheet as a whole.

Fracture Criteria for Pre-stressed and Pre-polarized Piezoelectric Crystals

Griffiths notion of energy-release rate is extended to the linearized incremental theory of pre-stressed and pre-polarized piezoelectric crystals under suitable restrictions on the pre-existing fields.

A treatment of internally constrained elastic–plastic materials

Abstract A treatment of internally constrained elastic–plastic materials is presented in the context of the Lagrangian strain-space formulation of the theory of finitely deforming elastic–plastic materials. A general type of internal constraint, represented by a smooth scalar-valued function of Lagrangian strain and a list of plastic variables, is considered. At fixed values of the plastic variables, the constraint equation determines a smooth hypersurface (the constraint manifold) imbedded in six-dimensional strain space. This manifold moves about and changes its shape as the deformation progresses. Adopting an approach introduced by Casey and Krishnaswamy for thermoelastic materials, the imbedded elasticity of elastic–plastic materials and the internal constraint are used to induce an equivalence relation on the set of unconstrained elastic–plastic materials. A unique constrained elastic–plastic material is then associated with each equivalence class of unconstrained materials, and a characterization of the constrained material is obtained from the properties of the corresponding unconstrained ones.

A class of exact solutions for a 3D filamentary continuous medium

A theory for a three-dimensional (3D) continuum composed of continuously distributed fibers is presented. General results are derived concerning kinematics, a constitutive equation, the uniqueness of the solution to the equilibrium equations, and convexity conditions. A class of exact solutions is obtained that contains, as a particular case, all homogeneous deformations.

A continuum model for two-dimensional fiber networks

Elastic-plastic deformation of a continuum formed by continuously distributed fibers is described. Applications to the mechanical characterization of nanofibers, and to biological materials such as cellular cytoskeleton and tissue scaffolds are indicated.