A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response. © 2005 Elsevier Ltd. All rights reserved.

A constitutive description of the inelastic response of ceramics

The objective of the article is to present a unified model for the dynamic mechanical response of ceramics under compressive stress states. The model incorporates three principal deformation mechanisms: (i) lattice plasticity due to dislocation glide or twinning; (ii) microcrack extension; and (iii) granular flow of densely packed comminuted particles. In addition to analytical descriptions of each mechanism, prescriptions are provided for their implementation into a finite element code as well as schemes for mechanism transitions. The utility of the code in addressing issues pertaining to deep penetration is demonstrated through a series of calculations of dynamic cavity expansion in an infinite medium. The results reveal two limiting behavioral regimes, dictated largely by the ratio of the cavity pressure p to the material yield strength σY. At low values of p/σY, cavity expansion occurs by lattice plasticity and hence its rate diminishes with increasing σY. In contrast, at high values, expansion occurs by microcracking followed by granular plasticity and is therefore independent of σY. In the intermediate regime, the cavity expansion rate is governed by the interplay between microcracking and lattice plasticity. That is, when lattice plasticity is activated ahead of the expanding cavity, the stress triaxiality decreases (toward more negative values) which, in turn, reduces the propensity for microcracking and the rate of granular flow. The implications for penetration resistance to high-velocity projectiles are discussed. Finally, the constitutive model is used to simulate the quasi-static and dynamic indentation response of a typical engineering ceramic (alumina) and the results compared to experimental measurements. Some of the pertinent observations are shown to be captured by the present model whereas others require alternative approaches (such as those based on fracture mechanics) for complete characterization. © 2011 The American Ceramic Society.

Material model of lung parenchyma based on living precision-cut lung slice testing.

We describe a novel constitutive model of lung parenchyma, which can be used for continuum mechanics based predictive simulations. To develop this model, we experimentally determined the nonlinear material behavior of rat lung parenchyma. This was achieved via uni-axial tension tests on living precision-cut rat lung slices. The resulting force-displacement curves were then used as inputs for an inverse analysis. The Levenberg-Marquardt algorithm was utilized to optimize the material parameters of combinations and recombinations of established strain-energy density functions (SEFs). Comparing the best-fits of the tested SEFs we found Wpar = 4.1 kPa(I1-3)2 + 20.7 kPa(I1 - 3)3 + 4.1 kPa(-2 ln J + J2 - 1) to be the optimal constitutive model. This SEF consists of three summands: the first can be interpreted as the contribution of the elastin fibers and the ground substance, the second as the contribution of the collagen fibers while the third controls the volumetric change. The presented approach will help to model the behavior of the pulmonary parenchyma and to quantify the strains and stresses during ventilation.

Non linear constitutive models for lattice materials

We use a computational homogenisation approach to derive a non linear constitutive model for lattice materials. A representative volume element (RVE) of the lattice is modelled by means of discrete structural elements, and macroscopic stress-strain relationships are numerically evaluated after applying appropriate periodic boundary conditions to the RVE. The influence of the choice of the RVE on the predictions of the model is discussed. The model has been used for the analysis of the hexagonal and the triangulated lattices subjected to large strains. The fidelity of the model has been demonstrated by analysing a plate with a central hole under prescribed in plane compressive and tensile loads, and then comparing the results from the discrete and the homogenised models. © 2013 Elsevier Ltd.

Finite element modelling of the sismic behaviour of water front structures

Water front structures have suffered significant damage in many of the recent earthquakes. These include gravity type quay walls, vertically composite walls, cantilever retaining walls, anchored bulkheads and similar structures. One of the primary causes for the poor performance of these classes of structures is the liquefaction of the foundation soil and in some instances liquefaction of the backfill soil. The liquefaction of the soil in-front of the quay wall tends to cause large lateral displacements and rotation of the wall. Often such gravity walls are placed on rubble mound deposited onto the sea bed.This paper presents finite element analyses of such a problem in which strength degradation of the foundation soil and the backfill material will be modelled using PZ mark III constitutive model. The performance of the wall in terms of its lateral displacement, vertical settlement and/or the rotation suffered by the wall will be presented. In addition, the contours of the horizontal and vertical effective stresses and the excess pore pressure ratio will be presented at different time instants together with hyrdraulic gradients. Immediately after the earthquake, the hydraulic gradients indicate migration of pore water into the region below the wall, suggesting further softening of the foundation soil below the wall.

Experimental and numerical investigation of fracture mechanics of bitumen beams

This work presents an experimental and numerical investigation to characterise the fracture properties of pure bitumen (the binder in asphalt paving materials). The paper is divided into two parts. The first part describes an experimental study of fracture characterisation parameters of pure bitumen as determined by three-point bend tests. The second part deals with modelling of fracture and failure of bitumen by Finite Element analysis. Fracture mechanics parameters, stress intensity factor, KIC, fracture energy, GIC, and J-integral, JIC, are used for evaluation of bitumen's fracture properties. The material constitutive model developed by Ossa et al. [40,41] which was implemented into a FE code by Costanzi [18] is combined with cohesive zone models (CZM) to simulate the fracture behaviour of pure bitumen. Experimental and numerical results are presented in the form of failure mechanism maps where ductile, brittle and brittle-ductile transition regimes of fracture behaviour are classified. The FE predictions of fracture behaviour match well with experimental results. © 2012 Elsevier Ltd.

Collapse of a composite beam made from ultra high molecular-weight polyethylene fibres

Hot-pressed laminates with a [0/90]48 lay-up, consisting of 83% by volume of ultra high molecular-weight polyethylene (UHMWPE) fibres, and 17% by volume of polyurethane (PU) matrix, were cut into cantilever beams and subjected to transverse end-loading. The collapse mechanisms were observed both visually and by X-ray scans. Short beams deform elastically and collapse plastically in longitudinal shear, with a shear strength comparable to that observed in double notch, interlaminar shear tests. In contrast, long cantilever beams deform in bending and collapse via a plastic hinge at the built-in end of the beam. The plastic hinge is formed by two wedge-shaped microbuckle zones that grow in size and in intensity with increasing hinge rotation. This new mode of microbuckling under macroscopic bending involves both elastic bending and shearing of the plies, and plastic shear of the interface between each ply. The double-wedge pattern contrasts with the more usual parallel-sided plastic microbuckle that occurs in uniaxial compression. Finite element simulations and analytical models give additional insight into the dominant material and geometric parameters that dictate the collapse response of the UHMWPE composite beam in bending. Detailed comparisons between the observed and predicted collapse responses are used in order to construct a constitutive model for laminated UHMWPE composites. © 2013 Elsevier Ltd.

Thermo-hydro-geomechanical simulations of methane gas production from deep sea methane hydrate formations

A new constitutive model called Methane Hydrate Critical State (MHCS) model was conducted to investigate the geomechanical response of the gas-hydrate-bearing sediments at the Nankai Trough during the wellbore construction process. The strength and dilatancy of gas-hydrate-bearing soil would gradually disappear when the bonds are destroyed because of excessively shearing, which are often observed in dense soils and also in bonded soils such as cemented soil and unsaturated soil. In this study, the MHCS model, which presents such softening features, would be incorporated into a staged-finite-element model in ABAQUS, which mainly considered the loading history of soils and the interaction between cement-casing-formation. This model shows the influence of gas-hydrate-bearing soil to the deformation and stability of a wellbore and the surrounding sediments during wellbore construction. At the same time, the conventional Mohr-Coulomb model was used in the model to show the advantages of MHCS model by comparing the results of the two models.