Microstructure and elasticity of dilute gels of colloidal discoids

The linear elasticity of dilute colloidal gels formed from discoidal latex particles is quantified as a function of aspect ratio and modeled by confocal microscopy characterization of their fractal cluster...

Random fiber network loaded by a point force

This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.

Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity

PurposeThe goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.Design/methodology/approachThe authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.FindingsThe authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.Originality/valueIn contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

Determination of material properties of a linearly elastic peridynamic material

We investigate the properties of an isotropic linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which considers both length and relative angle changes, and is based on a free energy function proposed in previous work that contains four material constants. To this end, we consider a class of equilibrium problems in mechanics to show that, in interior points of the body where deformations are smooth, the corresponding solutions in classical linear elasticity are also equilibrium solutions in peridynamics. More generally, we show that the equations of equilibrium are satisfied even when two of the four peridynamic constants are arbitrary. Pure torsion of a cylindrical shaft and pure bending of a cylindrical beam are particular cases of this class of problems and are used together with a correspondence argument proposed elsewhere to determine these two constants in terms of the elasticity constants of an isotropic material from the classical linear elasticity. One of the constants has a singularity in the Poisson ratio, which needs further investigation. Two additional experiments concerning bending of cylindrical beam by terminal load and anti-plane shear of a hollow cylinder, which do not belong to the previous class of problems, are used to validate these results.