Finite deformations of elastic–plastic filamentary networks

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.     

Continuum modeling of cell membranes

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.     

Antiplane fracture in a prestressed and prepolarized piezoelectric crystal

The general complex-variable solution to the equations of incrementalantiplane piezoelectricity is used to solve the problem of crackpropagation in a crystal in the presence of an initial stressand electric field. Remote incremental antiplane tractions arespecified and an incremental traction of the same intensityis applied to the crack faces. The initial fields are shownto have a pronounced effect on the near-tip stresses and onthe displacements of the crack faces. Griffith's criterion isused to determine the combination of electromechanical parametersrequired for incipient crack propagation. Received 22 April 2000.