Estimating the poroelastic properties of cracked materials

We present a comparative study of the ability of some micromechanics estimates to predict the overall properties of heterogeneous materials. We focus mainly on cracked materials, for which this task is difficult and many estimates fail. We study particularly the interaction direct derivative estimate, proposed by Zheng and Du, which is an approximation of the generalized self-consistent scheme, but has the very convenient property to be always explicit. A modified version of this estimate, called full-range IDD by Zheng and Du, yields good results when comparing all poromechanical coefficients predicted by the estimate to finite element simulations of a 2D cracked material in plane strain, up to crack density factors of 1 for aligned cracks and 0.60 for randomly oriented cracks. The accuracy of finite element computations of the overall moduli is also commented by plotting the convergence of the average of the properties as well as the confidence intervals on these averages.     

The elasto-plastic indentation of a half-space by a rigid sphere

Using the finite element method, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.     

Quasi-static deformation of a multilayered poroelastic half-space by two-dimensional buried sources

Summary The fully coupled Biot quasi-static theory of fluid-infiltrated porous materials is used to study the two-dimensional plane strain deformation of a multilayered poroelastic half-space by internal sources. Pure compliance formulation, in which the stresses and the pore pressure are taken as the basic state variables, is used. Displacements are then obtained by integrating the coupled constitutive relations and the fluid flux from the Darcy law. The problem is formulated in terms of the propagator matrices. Simplified explicit expressions for the elements of the 6 × 6 propagator matrix are obtained. The propagator matrix is also used to obtain explicit expressions for the surface displacements and fluid flow due to a line force and a fluid injection source buried in a poroelastic half-space.     

Spherical indentation of a transversely isotropic elastic half-space reinforced with a thin layer

The frictionless spherical indentation test is considered for a transversely isotropic elastic half-space reinforced with a thin layer whose flexural stiffness is negligible compared to its tensile stiffness. It is assumed that the deformation of the reinforcing layer can be treated as the generalized plane stress state. Closed-form analytical approximate equations for the maximum contact pressure, contact radius, and contact force are presented. The isotropic case is considered in detail.     

Dynamic responses of a pile embedded in a layered poroelastic half-space to a harmonic axial loading

The dynamic response of a single pile embedded in a layered poroelastic half-space to an axial harmonic load is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in a layered poroelastic half-space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile subjected to a harmonic axial load is constructed. The proposed model is validated by comparing a special case of our model with an existing result. Based on numerical results of this paper, it is concluded that the presence of a stiffer or a softer middle layer in the layered half-space will affect the impedance of the pile considerably and the inhomogeneity of the half-space will enhance the pore pressure significantly.     

Interaction between internal loading and surface indentation for a transversely isotropic elastic half-space

Summary An analytical solution is given for the axisymmetric indentation problem of a half-space loaded by internal forces. Closed form results are presented for an interior point force and a flat-ended indenter. The interaction between internal and external loadings is discussed using numerical results and graphs.With 2 Figures     

The indentation of a half-space of hexagonal elastic material by a circular punch of arbitrary end-profile

Summary The problem is considered of the indentation by a smooth rigid punch of a half-space composed of linear elastic material of hexagonal symmetry whose plane boundary is parallel to the basal planes. The case is considered in which the area of contact between the punch and the half-space is circular, the end of the punch with is in contact with the half-space having an arbitrary profile. An integral equation is formulated and solved for the boundary value of the normal displacement in the half-space, and an expression is derived for the distribution of pressure under the punch.     

Particle modeling of polymeric material indentation study

This paper presents a further application of a newly modified particle modeling (PM) for the simulation of dynamic fragmentation of another polymeric material, vinyl ester, subject to an impact of a rigid indenter after the previous study of nylon-6, 6 [Wang G, Al-Ostaz A, Cheng AH-D, Mantena PR. Particle modeling of a polymeric material (nylon-6, 6) due to the impact of a rigid indenter. Comput Mater Sci [in press]]. A two-layer particle interaction scheme (nearest-second neighboring particle interaction) is still adopted to eliminate a mesh bias in the direction of fracture propagation in a regular lattice model with uniform axial linkage technique. The effective bond stiffness with this new interaction network is addressed to preserve the associated material’s physical property, i.e., Young’s modulus. The modeling results compare favorably with the according experimental observations, in terms of the time-dependent load and energy profiles, the deflection value at the peak of the load, and the indenter drop speed versus time, etc. Failure strain is found to be a critical factor affecting the prediction accuracy. Via this study, it exhibits again that particle modeling can be used as an alternative tool for dynamic fracture problems.     

Tangential-displacement effects in the wedge indentation of an elastic half-space – an integral-equation approach

The idea of considering tangential-displacement effects in a classical elastostatic contact problem is explored in this paper. The problem involves the static frictionless indentation of a linearly elastic half-plane by a rigid wedge, and its present formulation implies that the tangential surface displacements are not negligible and should thus be coupled with the normal surface displacements in imposing the contact zone boundary conditions. L.M. Brock introduced this idea some years ago in treating self-similar elastodynamic contact problems, and his studies indicated that such a formulation strongly influences the contact-stress behavior at half-plane points making contact with geometrical discontinuities of the indentor. The present work again demonstrates, by studying an even more classical problem, that the aforementioned considerations eliminate contact-stress singularities and therefore yield a more natural solution behavior. In particular, the familiar wedge-apex logarithmic stress-singularity encountered within the standard formulation of the problem (i.e. by avoiding the tangential displacement in the contact boundary condition) disappears within the proposed formulation. The contact stress beneath the wedge apex takes now a finite value depending on the wedge inclination angle and the material constants. By utilizing pertinent integral relations for the displacement/stress field in the half-plane, an unusual mixed boundary-value problem results whose solution is obtained through integral equations.     

Computational modeling of growth

The present contribution is dedicated to the computational modeling of growth phenomena typically encountered in modern biomechanical applications. We set the basis by critically reviewing the relevant literature and classifying the existing models. Next, we introduce a geometrically exact continuum model of growth which is not a priori restricted to applications in hard tissue biomechanics. The initial boundary value problem of biomechanics is primarily governed by the density and the deformation problem which render a nonlinear coupled system of equations in terms of the balance of mass and momentum. To ensure unconditional stability of the required time integration procedure, we apply the classical implicit Euler backward method. For the spatial discretization, we suggest two alternative strategies, a node-based and an integration point–based approach. While for the former, the discrete balance of mass and momentum are solved simultaneously on the global level, the latter is typically related to a staggered solution with the density treated as internal variable. The resulting algorithms of the alternative solution techniques are compared in terms of stability, uniqueness, efficiency and robustness. To illustrate their basic features, we elaborate two academic model problems and a typical benchmark example from the field of biomechanics.     

On the smoothness of the surface deformation profile due to the indentation of an elastic half-space

Although the surface deformation concept has been used in the nanoindentation study, there is a lack of investigation on the smoothness of the surface deformation profile. We find that the surface deformation profile is continuous while its first order derivative is continuous only for incomplete and critical complete contact situations. The presented result may be used to make more realistic assumptions on the surface deformation in the nanoindentation modeling.     

Computational modeling of a carbon nanotube-based DNA nanosensor

During the last decade the design of biosensors, based on quantum transport in one-dimensional nanostructures, has developed as an active area of research. Here we investigate the sensing capabilities of a DNA nanosensor, designed as a semiconductor single walled carbon nanotube (SWCNT) connected to two gold electrodes and functionalized with a DNA strand acting as a bio-receptor probe. In particular, we have considered both covalent and non-covalent bonding between the DNA probe and the SWCNT. The optimized atomic structure of the sensor is computed both before and after the receptor attaches itself to the target, which consists of another DNA strand. The sensor's electrical conductance and transmission coefficients are calculated at the equilibrium geometries via the non-equilibrium Green's function scheme combined with the density functional theory in the linear response limit. We demonstrate a sensing efficiency of 70% for the covalently bonded bio-receptor probe, which drops to about 19% for the non-covalently bonded one. These results suggest that a SWCNT may be a promising candidate for a bio-molecular FET sensor.     

Computational modeling of gas-surface interaction

In this study, a new computational modeling of the gas-surface interaction is proposed to explain the results of the scattering experiments of molecular beams from solid surfaces, especially from industrial surfaces. The characteristic feature of the model is to settle the adsorbed gas layer and the collision layer which involve adsorbed molecules and surface molecules, respectively. Incident molecules experience force due to the gas-solid potential gradient, changing their trajectories which is computed by Molecular Dynamics method. The gas molecules are scattered from the surfaces after collisions with adsorbed or surface molecules. The simulated results are compared with the experimental ones: i.e., flux distributions, TOF spectra and the average energy of scattered molecules.     

Computational modeling of explosive-filled cylinders

A time-dependent, two-dimensional, finite-difference code can be used to model fragmenting cylinders. Strictly hydrodynamic treatment of the casing material generally overpredicts the final fragment velocity. A more definitive final fragment velocity is predicted when the casing material is treated as an elastic-plastic material, but the final fragment velocities occur at unrealistically high cylindrical expansion ratios. To remove some of these objections and, at the same time, model the casing motion more realistically, a gas leakage model has been developed to simulate explosive gas leakage around fragments after casing breakup. Comparisons have been made between code calculations and experimental data. The experimental data include different length-to-diameter ratios, natural and discrete fragmenting cylinders, different charge-to-casing mass ratios, and different initiation postures. The gas leakage model predicts definitive final fragment velocities in excellent agreement with the experimental data.     

Wave propagation in cracked elastic slabs and half-space domains—TBEM and MFS approaches

In this paper, the traction boundary element method (TBEM) and the method of fundamental solutions (MFS), formulated in the frequency domain, are used to evaluate the 3D scattered wave field generated by 2D empty cracks embedded in an elastic slab and a half-space. Both models overcome the thin-body difficulty posed when the classical BEM is applied.The crack exhibits arbitrary cross section geometry and null thickness. In neither model are the horizontal formation surfaces discretized, since appropriate fundamental solutions are used to take them into consideration.The TBEM models the crack as a single line. The singular and hypersingular integrals that arise during the TBEM model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. The results provided by the proposed TBEM model are verified against responses provided by the classical BEM models derived for the case of an empty cylindrical circular cavity.The MFS solution is approximated in terms of a linear combination of fundamental solutions, generated by a set of virtual sources simulating the scattered field produced by the crack, using a domain decomposition technique. To avoid singularities, these fictitious sources are not placed close to the crack, and the use of an enriched function to model the displacement jumps across the crack is unnecessary.The performances of the proposed models are compared and their limitations are shown by solving the case of a C-shaped crack embedded in an elastic slab and a half-space domain.The applicability of these formulations is illustrated by presenting snapshots from computer animations in the time domain for an elastic slab containing an S-shaped crack, after applying an inverse Fourier transformation to the frequency domain computations.     

Measurement and modeling of gas transfer in cracked mortars

The research aims at better understanding the parameters controlling air flow through cracked cementitious material elements. Rizkalla et al. proposed a model that describe gas transport in a cracked concrete element subjected to a pressure gradient. The model includes a flow coefficient, n and a friction coefficient, k that must be determined experimentally. Equations giving the values of n and k were proposed by experimentally analysing air leakage through multi-cracked reinforced concrete panels. This paper aims at validating the model proposed by Rizkalla et al. by analysing the air flow in a single defined crack generated in mortar samples (normal- and high-strength). A permeability cell was developed to measure airflow through a single cracks under controlled conditions. The results confirm the validity of Rizkalla's model. The approach based on single crack measurements has show that, for all the considered cases, airflow in cracks was largely laminar. This lead to a simplification of Rizkalla model and the development of a simple equation that gives air flow as a function of crack geometry, pressure gradient and friction coefficient only. No effect of type of mortar matrix was found on the airflow through a crack.     

A thin cracked layer bonded to an elastic half-space under an antiplane concentrated load

The antiplane elasticity problem for a thin cracked layer bonded to an elastic half-space under an antiplane concentrated load is considered. The fundamental solution is obtained as a rapidly convergent series in terms of the complex potentials via iterations of Möbius transformation. The singular integral equation with a logarithmic singular kernel is derived to model a crack problem that can be solved numerically in a straightforward manner. The dimensionless mode-III stress intensity factors obtained for various crack inclinations and crack lengths are discussed in detail and provided in graphic form. A strip problem with an arbitrarily oriented crack is also considered.     

Computational modeling of material aging effects

Summary Progress is being made in our efforts to develop computational models for predicting material property changes in weapon components due to aging. The first version of a two-dimensional lattice code for modeling thermomechanical fatigue, such as has been observed in solder joints on electronic components removed from the stockpile, has been written and tested. The code does a good qualitative job of presenting intergranular and/or transgranular cracking in a polycrystalline material when undergoing thermomechanical deformation. Algorithms to couple codes at different length-scales were also exercised. The current progress is an encouraging start for our long-term effort to develop multi-level simulation capabilities for predicting age-related effects on the reliability of weapons.     

Lattice modeling of chloride diffusion in sound and cracked concrete

Reinforced concrete structures are frequently exposed to aggressive environmental conditions. Most notably, chloride ions from sea water or de-icing salts are potentially harmful since they promote corrosion of steel reinforcement. Concrete cover of sufficient quality and depth can ensure protection of the steel reinforcement. However, it is necessary to study the effects of material heterogeneity and cracking on chloride ingress in concrete. This is done herein by proposing a three-dimensional lattice model capable of simulating chloride transport in saturated sound and cracked concrete. Means of computationally determining transport properties of individual phases in heterogeneous concrete (aggregate, mortar, and interface), knowing the concrete composition and its averaged transport properties, are presented and discussed. Based on numerical experimentation and available literature, a relation between the effective diffusion coefficient of cracked lattice elements and the crack width was adopted. The proposed model is coupled with a lattice fracture model to enable simulation of chloride ingress in cracked concrete. The model was validated on data from the literature, showing good agreement with experimental results.