A multiscale analysis of the mechanical behavior of bovine Haversian cortical bone is presented in the frame-work of linear elasticity. Cortical bone displays a complex microstructure that includes four phases: Haversian canals, osteons, cement lines, and interstitial bone. Based on close experimental observations, a Monte Carlo algorithm is implemented to build the natural bone composite microstructure. To represent the hierarchical nature of bone, the algorithm incorporates macroscopic morphological components, such as its porosity and osteonal volume fraction, as well as microscopic parameters, such as the characterized distributions of the osteons diameters. Bone local mechanical properties are measured by nanoindentation and microextensometry. The three-dimensional microstructures are discretized by a finite element method in order to evaluate the representative volume element of bovine cortical bone. The numerical model calculates the macroscopic bulk and material Young’s moduli and describes the local stress and strain. How geometrical or mechanical factors affect bone failure is investigated through a comparison of the macroscopic anisotropy and local strain to experimental data.

Jets that emanate from high density porous liners are most widely used for penetration into Earth materials. These shaped-charges differ from those that contain solid copper liners in three major aspects: the porosity, the usually higher initial density, and the very short standoff in which they typically operate. Because penetration depth is commonly very difficult to increase by means of high density solid liners, it is important to understand the benefit of using porous liners in utilization of high density materials. The models published so far to describe the performance of jets formed by porous liners are based on the modification of the virtual origin model to suit this special case, which limits the accuracy of their predictions. Here we present a more general analysis that does not depend on the virtual origin assumption. Our study employs the SCAN semi-analytical code into which a new model for porous jet behavior is incorporated. It is used to explain the benefit of using this type of liner for oil-well penetration, hence penetration into low density targets, as opposed to penetration into hard steel.

The two-dimensional Mandel-type problem geometry is well-known to bio-geomechanicians for testing rocks, cartilages, and bones with solutions in Cartesian coordinates for rectangular specimens or polar coordinates for cylindrical and disk samples. To date, all existing solutions are only applicable to single-porosity and single-permeability models, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fracture. This paper extends the plane strain and axisymmetric Mandel-type solutions from single-to dual-porosity and dual-permeability poromechanics. The solutions are presented in explicit analytical forms and account for arbitrary time-dependent external loading conditions, e.g., cyclic and ramping. The derived analytical solutions and results exhibit general behaviors characterized by two time scales. Stresses, pore pressures, and displacements are plotted for various time scale ratios to illustrate the interplaying effects of permeability and stiffness contrast of both porous regions, in addition to the interporosity exchange, on the overall responses of the system. Also, examples with realistic loading conditions for laboratory testing or field simulation such as cyclic and ramping are provided to demonstrate the engineering applications of the presented dual-poroelastic formulation and solutions.

The intention of this study is to predict the fatigue-safe long life behavior of elastoplastic porous materials subjected to zero-tension fluctuating load. It is assumed that the materials contain a dilute amount of voids (less than 5%) and obey Gurson’s model of plastic yielding. The question to be answered is what would be the highest allowable stress amplitude that a porous material can endure (the “endurance limit”) when undergoing an infinite number of loading/unloading cycles. To reach the answer we employ the two shakedown theorems: (a) Melan’s static shakedown theorem (“elastic shakedown”) for establishing the lower bound to fatigue limit and (b) Koiter’s kinematic shakedown theorem (“plastic shakedown”) for establishing its upper bound. The two bounds are formulated rigorously but solved with some numerical assistance, mainly due to the nonlinear pressure dependency of the material behavior and the complex description of the plastic flow near stress-free voids. Both bounds (“dual bounds”) are adjusted to capture Gurson-like porous materials with noninteractive voids. General residual stresses (either real or virtual) are presented in the analysis. They are assumed to be time-independent as generated, say, by permanent temperature gradient between void surfaces and remote material boundaries. Such a situation is common, for instance, in ordinary porous sleeves (used in space industry and alike). A few experiments agree satisfactorily with the shakedown bounding concept.

Two models for predicting the stress-strain curve of porous NiTi under compressive loading are presented in this paper. Porous NiTi shape memory alloy is considered as a composite composed of solid NiTi as matrix and pores as inclusions. Eshelby’s equivalent inclusion method and Mori-Tanaka’s mean-field theory are employed in both models. Two types of pore connectivity are investigated. One is closed cells (model 1); the other is where the pores are interconnected to each other forming an open-cell microstructure (model 2). We also consider two different shapes of pores, spherical and ellipsoidal. The stress-strain curves of porous shape memory alloy with spherical pores and ellipsoidal pores are compared. It is found that the ellipsoidal shape assumption is more reasonable than the assumption of spherical pores. Comparison of the stress-strain curves of the two models shows that use of open-cell microstructure (model-2) makes the predictions more agreeable to the experimental results of porous NiTi whose microstructure exhibits open-cell microstructure.

A multiscale model is formulated and used to characterize the duration and amplitude of temperature peaks (i.e., hot spots) at intergranular contact surfaces generated by shock compaction of the granular high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). The model tracks the evolution of both bulk variables and localized temperature subject to a consistent thermal energy localization strategy that accounts for inelastic and compressive heating, phase change, and thermal conduction at the grain scale (grain size ∼ 50 μ m ). Steady subsonic compaction waves having a dispersed two-wave structure are predicted for mild impact of dense HMX (porosity ∼ 19 % ), and steady supersonic compaction waves having a discontinuous solid shock followed by a thin compaction zone are predicted for stronger impact. Short duration hot spots having peak temperatures in excess of 900 K are predicted near intergranular contact surfaces for impact speeds as low as 100 m ∕ s ; these hot spots are sufficient to induce sustained combustion as determined by a two-phase thermal explosion theory. Thermal conduction and phase change significantly affect hot-spot formation for low impact speeds ( ∼ 100 m ∕ s ) , whereas bulk inelastic heating dominates the thermal response at higher speeds resulting in longer duration hot spots. Compressive grain heating is shown to be largely inconsequential for the range of impact speeds considered in this work ( 100 ⩽ u p ⩽ 1000 m ∕ s ) . Predictions for the variation in inelastic strain, pressure, and porosity through the compaction zone are also shown to qualitatively agree with the results of detailed mesoscale simulations.

A porothermoelastic solution of the general problem of the inclined borehole in a transversely isotropic porous material is presented herein and compared with the isotropic porothermoelastic solution. The governing equations are outlined for the case of general anisotropy and specialized for a transversely isotropic poroelastic material under nonhydrostatic and nonisothermal in situ conditions. A superposition scheme is employed to obtain the analytical solutions within the isotropic and transversely isotropic poromechanics theory. The borehole generator is assumed to coincide with the material axis of symmetry, in the case of transverse isotropy, yet subjected to a three-dimensional state of stress. A systematic analysis has been carried out to evaluate the effect of the anisotropy of the poromechanical material parameters as well as the thermal material properties on stress and pore pressure distributions and the potential impact on the overall stability of deep wellbore drilling.

The effect of liquid viscosity, surface tension and strain rate on the deformation behavior of partially saturated granular material was studied over a ten order of magnitude range of capillary number (the ratio of viscous to capillary forces). Glass spheres of average size 35 microns were used to make pellets of 35% porosity and 70% liquid saturation. As the capillary number increased, the failure mode changed from brittle cracking to ductile plastic flow. This change coincided with the transition from strain-rate independent flow stress to strain-rate dependent flow stress noted previously [Iveson, S. M., Beathe, J. A., and Page, N. W., 2002, “The Dynamic Strength of Partially Saturated Powder Compacts: The Effect of Liquid Properties,” Powder Technol. , 127 , pp. 149–161]. This change in failure mode is somewhat counter-intuitive, because it is the opposite of that observed for fully saturated slurries and pastes, which usually change from plastic to brittle with increasing strain rate. A model is proposed which predicts the functional dependence of flow stress on capillary number and also explains why the flow behavior changes. When capillary forces dominate, the material behaves like a dry powder: Strain occurs in localized shear planes resulting in brittle failure. However, when viscous forces dominate, the material behaves like a liquid: Shear strain becomes distributed over a finite shear zone, the size of which increases with strain rate. This results in less strain in each individual layer of material, which promotes plastic deformation without the formation of cracks. This model also explains why the power-law dependency of stress on strain rate was significantly less than the value of 1.0 that might have been expected given that the interstitial liquids used were Newtonian.

A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.

The emergence of two-phase instability is investigated analytically for the axisymmetric cylinders made of a pervious solid matrix with pores filled with an interstitial fluid. General analytical solutions are derived for a broad range of constitutive models, and are illustrated for a few specific types of solids. For particular combinations of stresses and material moduli, saturated hypoelastic and elastoplastic solids are found to undergo two-phase instability, whereas their dry solid matrices remain stable. Two-phase instability can emerge within stable single-phase solids due to the interaction between solid matrix and fluid flow. The present analysis provides general analytical solutions useful for investigating the instabilities of axisymmetric soil samples subjected to the undrained triaxial tests of geomechanics.

Radiation loading on a vibrating structure is best described through its radiation impedance. In the present work the modal acoustic radiation impedance load on an infinitely long cylindrical source harmonically excited in circumferentially periodic (axially independent) spatial pattern, while positioned concentrically within a fluid cylinder, which is embedded in a fluid-saturated unbounded elastic porous medium, is computed. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation (White, J. E., 1983, Underground Sound Application of Seismic Waves, Elsevier, Amsterdam, Fig. 5.29, p. 183), is of practical importance with a multitude of possible applications in seismo-acoustics and noise control engineering. The formulation utilizes the Biot phenomenological model to represent the behavior of the sound in the porous, fluid-saturated, macroscopically homogeneous and isotropic surrounding medium. Employing the appropriate wave-harmonic field expansions and the pertinent boundary conditions for the given boundary configuration, a closed-form solution in the form of an infinite series is developed and the resistive and reactive components of modal radiation impedances are determined. A numerical example for a cylindrical surface excited in vibrational modes of various order, immersed in a water-filled cavity which is embedded within a water-saturated Ridgefield sandstone environment, is presented and several limiting cases are examined. Effects of porosity, frame stiffness, source size, and the interface permeability condition on the impedance values are presented and discussed.

Shakedown analysis, and its more classical special case of limit analysis, basically consists of “direct” (as distinct from time-stepping) methods apt to assess safety factors for variable repeated external actions and procedures which provide upper bounds on history-dependent quantities. The issues reviewed and briefly discussed herein are: some recent engineering-oriented and cost-effective methods resting on Koiter’s kinematic theorem and applied to periodic heterogeneous media; recent extensions (after the earlier ones to dynamics and creep) to another area characterized by time derivatives, namely poroplasticity of fluid-saturated porous media. Links with some classical or more consolidated direct methods are pointed out.