Aleksander Zubelewicz

STRAIN-SOFTENING BAR AND BEAM : EXACT NON-LOCAL SOLUTION

Using the recently developed imbricate non-local continuum approach. zones of strain softening (distributed micr~racking) which have a tinite size can be modeled. A differential approxi- mation of the averaging integrals for the non-lo4 continuum makes it possible to obtain exact analytical solutions for uniaxial softening in a hdr or for flexural softening in a beam. The ditforential equations of the problem along with the essential and natural boundary conditions and the con- ditions at the interface between the softening and non-softening regions are derived by a variational pro&me based on the principle of virtual work. The faiiure due to strain softening is analyzed as a stability problem. In contrapt to the blunt crack band mod& the si7e of the strain-softening region is treated as an unknown to be solved by stability anal>&. Numerical results show that the size of the strain-softening region is approximately constant. and so is the energy dissipated due to failure. Ductility diagrams. giving the strain :H failure as a function of beam sire and support stitfncss are also crtlculntrd and are found to bc quite similar to those ohlained previously by local analysis with an assumed six of.the snftcning r&n. These conciusion~ lend further support to the use of a blunt crack hand tnodcl for localircd cracking.

Powerless fluxes and forces, and change of scale in irreversible thermodynamics

We show that the dissipation function of linear processes in continuum thermomechanics may be treated as the average of the statistically fluctuating dissipation rate on either coarse or small spatial scales. The first case involves thermodynamic orthogonality due to Ziegler, while the second one involves powerless forces in a general solution of the Clausius–Duhem inequality according to Poincare and Edelen. This formulation is demonstrated using the example of parabolic versus hyperbolic heat conduction. The existence of macroscopic powerless heat fluxes is traced here to the hidden dissipative processes at lower temporal and spatial scales.

Micromechanical study of ductile polycrystalline materials

Abstract A micromechanical model is proposed to study the behavior of ductile polycrystalline materials. The emphasis is focused on the description of the recoverable and irreversible evolution of the materials internal structure. The evolution is used to derive the equivalent stress and strain measures. These theoretical predictions are very appealing when checked with existing experimental data.

Overall stress and strain rates for crystalline and frictional materials

Abstract The paper is concerned with a study of the overall stress and strain rates for crystalline and frictional materials. The method of analysis is based on micro-macro correlations given in the framework of Hills bilinear form. As expected, the overall stress and strain rates differ for the two materials.

Micromechanically based constitutive modeling of crystalline materials

Abstract Overall stress and strain rates for crystalline materials with an “internal structure” are considered. It has been shown that these measures are related to some kinematical constraints which govern the evolution of the internal structure such as development of slip or shear bands within grains and on grain boundaries, growth of voids or microcracks. The overall stress and strain rates provide a framework for a micromechanically based constitutive modeling.

Shale Fracturing for Energy Recovery: Current Issues and Review of Available Analytical and Computational Models

The paper reviews some of the major scientific challenges faced in the field of non-conventional energy production. Particular attention is given to shale rocks, in which the production of hydrocarbons involves hydraulic fracturing, fracture connectivity, multiphase flow, and reactive-transport. In regard to these problems, the paper describes a series of analytical and computational models to study fracturing in quasi-brittle solids and capture failure events in multi-phase geomaterials subjected to simultaneous changes in stress state, fluid pressure, moisture content, thermal and chemical conditions. Advantages and limitations of the different techniques are discussed, setting a vision for a new generation of multi-scale/multi-physical models for shale that can be used to support the optimization of the extraction processes, as well as to address industrial needs and mitigate the risks of environmental hazards, groundwater contamination and induced seismicity.

Fracture model for cemented aggregates

A mechanisms-based fracture model applicable to a broad class of cemented aggregates and, among them, plastic-bonded explosive (PBX) composites, is presented. The model is calibrated for PBX 9502 using the available experimental data under uniaxial compression and tension gathered at various strain rates and temperatures. We show that the model correctly captures inelastic stress-strain responses prior to the load peak and it predicts the post-critical macro-fracture processes, which result from the growth and coalescence of micro-cracks. In our approach, the fracture zone is embedded into elastic matrix and effectively weakens the materials strength along the plane of the dominant fracture.

On Thermodynamic Restrictions in Peridynamics

This note examines restrictions imposed by the second law of ther-modynamics on peridynamics in both the bond-based and thestate-based formulations. Our study was carried out in the frame-work of thermomechanics with internal variables. In bond-basedperidynamics, there are two possible thermomechanical interpre-tations of the dissipation function. One interpretation only admitsa thermodynamic orthogonality of Ziegler, while the other admitspowerless forces within a representation theory of Edelen. Thelatter interpretation is admissible in state-based peridynamics.Since the dissipation function of peridynamics is set up in velocityspace, a link to statistical mechanics of irreversible phenomenadoes not appear possible. [DOI: 10.1115/1.4006945]