A. Konstantinidis

Hydraulic behavior and contaminant transport in multiple porosity media

The hydraulic behavior and contaminant transport of aquifers containing distinct families of fractures are investigated by using the multiple porosity continuum model. We consider that the conditions are such that a horizontal 2D flow takes place. By writing the continuity of mass (including exchange terms between the various families of fractures) and Darcys law for each family of fractures, macroscopic equations for both confined and unconfined flow are obtained. A classification procedure and geometrical idealization of the individual fractures for each family is proposed which enables the calculation of the exchange coefficients. Equations for the description of the contaminant transport in the field scale for both confined and unconfined aquifer are developed. It turns out that the adequate formulation of the macroscopic equations and their sink-source term depends on whether the aquifer investigated is confined or unconfined, and also on the value of an nondimensional parameter describing the transfer process at the microscopic scale (connection Peclet number). Numerical investigation of representative problems offers some insight into the behavior of double and triple porosity aquifers.

Strain gradient and wavelet interpretation of size effects in yield and strength

Abstract The problem of yield stress and ultimate strength dependence on the specimen size is considered. This dependence, in otherwise geometrically similar specimens, is herein interpreted on the basis of gradient plasticity and wavelet analysis which introduce an internal length scale in the stress vs. strain relation. In particular, gradient plasticity within a simple strength of materials approach and wavelets within a simple scale-dependent constitutive equations approach, are used to derive expressions for the yield stress and the ultimate strength of solid bars subjected to torsion and bending. It is shown that these expressions depend on the size of the specimen. When the dimensions of the specimen become comparable to the internal length scale, size effects become important, while for larger specimens such dependence becomes negligible. Comparisons of the theoretical predictions to available experimental data are given.

Determination of Poisson’s Ratio by Spherical Indentation Using Neural Networks—Part I: Theory

When studying analytically the penetration of an indenter of revolution into an elastic half-space use is commonly made of the fraction E r =E/(I - v 2 ). Because of this, only E r is determined from the indentation test, while the value of v is usually assumed. However, as shown in the paper, if plastic deformation is involved during Ioading, the depth-load trajectory depends on the reduced modulus and, additionally, on the Poisson ratio explicitly. The aim of the paper is to shown, with reference to a simple plasticity model exhibiting linear isotropic hardening, that the Poisson ratio can be determined uniquely from spherical indentation if the onset of plastic yield is known. To this end, a loading and at least two unloadings in the plastic regime have to be considered. Using finite element simulations, the relation between the material parameters and the quantities characterizing the depth-load response is calculated pointwise. An approximate inverse function represented by a neural network is derived on the basis of these data.

Recent Developments in Gradient Plasticity—Part II: Plastic Heterogeneity and Wavelets

Wavelet analysis is used for describing heterogeneous deformation in different scales. Slip step height experimental measurements of monocrystalline alloy specimens subjected to compression are considered. The experimental data are subjected to discrete wavelet transform and the spatial distribution of deformation in different scales (resolutions) is calculated. At the finer scale the wavelet analyzed data are identical to the experimental measurements, while at the coarser scale the profile predicted by the wavelet analysis resembles the shear band solution profile provided by gradient theory in agreement with experimental observations. The different data sets provided by wavelet analysis are used to train a neural network in order to predict the spatial distribution of strain at resolutions higher than those possible by the available experimental probes. In addition, applications of wavelet analysis to interpret size effect data in torsion and bending at the micron scale are examined by deriving scale-dependent constitutive equations which are used for this purpose.

Scale-dependent constitutive relations and the role of scale on nominal properties

Abstract Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.

Roughening and pinning of interface cracks in shear delamination of thin films

We investigate the roughening of shear cracks running along the interface between a thin film and a rigid substrate. We demonstrate that short-range correlated fluctuations of the interface strength lead to self-affine roughening of the crack front as the driving force (the applied shear stress/stress intensity factor) increases towards a critical value. We investigate the disorder-induced perturbations of the crack displacement field and crack energy, and use the results to determine the crack pinning force and to assess the shape of the critical crack. The analytical arguments are validated by comparison with simulations of interface cracking.

Nucleation of interfacial shear cracks in thin films on disordered substrates

We formulate a theoretical model of the shear failure of a thin film tethered to a rigid substrate. The interface between film and substrate is modeled as a cohesive layer with randomly fluctuating shear strength/fracture energy. We demonstrate that, on scales large compared with the film thickness, the internal shear stresses acting on the interface can be approximated by a second-order gradient of the shear displacement across the interface. The model is used to study one-dimensional shear cracks, for which we evaluate the stress-dependent probability of nucleation of a critical crack. This is used to determine the interfacial shear strength as a function of the film geometry and statistical properties of the interface.

Size Effects in Tension: Gradient Internal Variable and Wavelet Models

A gradient internal variable model and a gradient-based wavelet analysis are employed to interpret size effects in uniaxial tension o f smooth un-notched specimens. This task could not be addressed within the standard strain gradient theory because macroscopic strain gradients are absent for this type o f loading. It turns out that both approaches can be used to model such size effects quite satisfactorily.

Size Effects on Tensile Strength and Fracture Energy In Concrete: Wavelet vs. Fractal Approach

The problem of size effect on tensile strength and fracture energy of brittle, heterogeneous and disordered materials is considered within two, apparently different approaches: one based on wavelets and scaledependent constitutive relations and another based on fractal arguments. Using wavelet analysis, scaledependent constitutive relations are derived from an underlying gradient formulation. By varying the scale parameter, size effects in tensile strength and fracture energy can be captured. Using fractal analysis, a fractal dimension of the damaged material surface which the stress acts upon is defined and a corresponding sizedependent tensile strength and fracture energy is obtained. These two approaches are then compared. Both of them give results with similar trend and their divergence emerges only in the limit of infinitesimally small specimens, where different deformation mechanisms and random responses may prevail.

Correlating the internal length in strain gradient plasticity theory with the microstructure of material

The internal length is the governing parameter in strain gradient theories which among other things have been used successfully to interpret size effects at the microscale. Physically, the internal length is supposed to be related with the microstructure of the material and evolves during the deformation. Based on Taylor hardening law, we propose a power-law relationship to describe the evolution of the variable internal length with strain. Then, the classical Fleck–Hutchinson strain gradient theory is extended with a strain-dependent internal length, and the generalized Fleck–Hutchinson theory is confirmed here, by comparing our model predictions to recent experimental data on tension and torsion of thin wires with varying diameter and grain size. Our work suggests that the internal length is a configuration-dependent parameter, closely related to dislocation characteristics and grain size, as well as sample geometry when this affects either the underlying microstructure or the ductility of the material.