Continuum damage mechanics: combining thermodynamics with a thoughtful characterization of the microstructure

We formulate a macroscopic description of the mechanics of damaged materials. To represent the microstructure, the distribution of crack sizes is captured by way of the Minkowski functionals, or so-called quermass integrals, while a second-rank tensor is used to describe the average orientation of the cracks. A two phase-type approach is adopted to distinguish elastically strained material from unstrained regions in the wake of the cracks. Using nonequilibrium thermodynamic techniques, the driving force for the growth of the microcracks is naturally identified. In particular, Griffith's law is generalized to assemblies of polydisperse crack sizes. Due to the detailed characterization of the microstructure, we are also able to account for the plastic zones at the rims of the cracks that are known to hamper the crack growth, and to discuss possible forms of the damage parameter. The presented approach separates in a transparent fashion the incorporation of fundamental thermodynamic and mechanic principles on one hand, from the specification of the material and details of the crack formation and growth on the other han

A simple method for the determination of refractive indices of (rough) transparent solids

Simple methods for the determination of refractive indices of transparent polymers and inorganic and organic solids of irregular geometry or with scratched or corrugated surfaces are rare. A classical procedure is based on the invisibility of a body immersed in a liquid with the same refractive index as that of the body. In order to avoid the laborious procedure connected with the search for a liquid with matching refractive index and to find an approach which is independent of the observation by eye, we describe here a modified immersion method which allows the ready determination of the refractive index of solids. The present method is based on the interpolation of the maximum transmission (nTmax) of a solid immersed in liquids with different, typically non-matching, refractive indices. Illustrations with quartz glass, crown glass and poly(vinylidene fluoride) (PVDF) films showed that nTmax can be determined with a reproducibility of ± 0.003. By comparison with refractive indices determined by ellipsometry, it was concluded that the refractive index of a solid can be determined with the modified immersion method within an accuracy better than ± 0.01 when systematic errors resulting from the fit method are also taken into consideratio

Surface viscoelasticity in model polymer multilayers: From planar interfaces to rising bubbles

International audienceIn the present work a polymeric transient viscoelastic network is used as a model system to investigate several fundamentals of interfacial viscoelasticity and non-linear behavior, in simple shear, compression and for simple mixed deformations. A supramolecular polymer bilayer, characterized by long but finite relaxation times, is created at the water-air interface using a layer-by-layer assembly method. The possibility of studying the individual layers starting from an unstrained reference state enabled the independent quantification of the equilibrium ther-modynamic properties, and the viscoelastic response of the bilayer could be studied separately for shear and compressional deformations. Time-and frequency-dependent material functions of the layer were determined in simple shear and uniform compression. Moreover, a quasi linear neo-Hookean model for elastic interfaces was adapted to describe step strain experiments on a viscoelastic system by allowing the material properties to be time-dependent. The use of this model made it possible to calculate the response of the system to step deformations. Within the linear response regime, both stress-strain proportionality and the superposition principle were investigated. Furthermore, the onset of non-linear behavior of the extra stresses was characterized in shear and for the first time in pure compression. We conclude by investigating the multilayer system in a rising bubble setup and show that the neo-Hookean model is able to predict the extra and deviatoric surface stresses well, up to moderate deformations

Generation of Porous Particle Structures using the Void Expansion Method

The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller "void-particles". Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles' mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure

The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February 2012

Test Model Coverage Analysis under Uncertainty

In model-based testing (MBT) we may have to deal with a non-deterministic model, e.g. because abstraction was applied, or because the software under test itself is non-deterministic. The same test case may then trigger multiple possible execution paths, depending on some internal decisions made by the software. Consequently, performing precise test analyses, e.g. to calculate the test coverage, are not possible. This can be mitigated if developers can annotate the model with estimated probabilities for taking each transition. A probabilistic model checking algorithm can subsequently be used to do simple probabilistic coverage analysis. However, in practice developers often want to know what the achieved aggregate coverage, which unfortunately cannot be re-expressed as a standard model checking problem. This paper presents an extension to allow efficient calculation of probabilistic aggregate coverage, and moreover also in combination with k-wise coverage