Constitutive Modelling

The typical shear behaviour of rock joints has been studied under a constant normal load (CNL) or zero normal stiffness condition, but recent studies have shown that this boundary condition may not replicate more practical situations, and that constant normal stiffness (CNS) is a more appropriate boundary condition to describe the stress-strain response of field joints. In addition to the effect of boundary conditions, the shear behaviour of a rough joint also depends on its surface properties and the initial stress acting on its interface. Despite this, exactly how these parameters affect the shear behaviour of joints is not fully understood because the stress-strain response of joints is governed by non-uniform asperity damage and the resulting gouge that accumulates on their interfaces. Therefore, an attempt has been made in this study to predict the complete shear behaviour of rough joints incorporating the asperity deformation under CNS conditions. In order to validate this analytical model, a series of CNS shear tests were conducted on rough tensile (natural) joints and their replicas at a range of initial normal stresses that varied from 0.4 to 1.6 MPa. Comparisons between the predicted shear behaviour and the experimental results show close agreement.

This paper presents the numerical results obtained from the finite element analyses of the superplastic forming (SPF) of Al–Ti alloys. The models are used to optimise the process and predict forming times in terms of deformed shapes, stress–strain distributions and ...

Interventions in historic brick buildings require an exhaustive analysis of the current characteristics of bricks in order to establish the role performed by these elements in the buildings. This study presents the results of an experimental analysis of the compressive strength of brick specimens extracted from different buildings built in the 19th and 20th centuries in the province of Zamora (Spain). The study analyses specimens with very different characteristics to compare results from different masonry units and manufacturing processes. Specimens are classified into four groups according to their macroscopic and microscopic analyses. Compressive strength results are correlated to the above classification and to the results of density, absorption and open porosity of the samples. The compressive strength results present high variation between clay bricks (9.2–64.4 N/mm2) and between samples extracted from the same brick due to the heterogeneity of the material. Correlations betwe...

The results of a simple geotechnical benchmark problem, an embankment on soft clay, are presented and discussed. The problem has been simulated with several constitutive models: models that are commonly used for practical geotechnical engineering problems, as well as advanced models developed by SCMEP Network partners. These advanced constitutive models account for initial and induced anisotropy, destructuration and creep or combinations of these features. The comparisons highlight the effects of these features on soft clay response and demonstrate the differences between alternative constitutive modelling approaches.

Creep tests are carried out under tension, pure torsion, and combined tension and torsion at an elevated temperature of 523K for pure copper and 423K for an aluminium alloy. Different creep and rupture properties of the materials are observed throughout the deformation process under the different stress states. The effects of stress states on primary creep, secondary creep, the failure

In the present study we consider an adaptation of Nguyen’s model [G.D. Nguyen, A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, D.Phil. Thesis, Dept. of Engng. Sci., University of Oxford, 2005] for brittle materials to the case of ductile rupture. We focus our attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework. We demonstrate the capability of the model to generate mesh-independent results and to follow the rupture process very close to failure. Rupture analysis of thin plates of different geometry is presented (symmetric double notch-edged specimen, asymmetric double notch-edged specimen, double notch-edged specimen containing a hole). Further modifications are outlined required to simulate crack growth and paths under the conditions of creep and fatigue.

Experimental results of in vivo measurements to characterize the mechanical behaviour of human uterine cervices are documented. Aspiration experiments were performed on eight uteri in vivo, before vaginal/abdominal hysterectomy, and four uteri were also tested ex vivo, approximately 1.5h after extraction. The reproducibility of the mechanical data from the in vivo aspiration experiments has been analysed. For an introduced "stiffness parameter" the organ specific SD is 22%, so that the proposed experimental procedure allows detections of 30% changes with respect to a reference value of the stiffness parameter. A comparison of in vivo and ex vivo data from the same organ has shown that: (i) the ex vivo mechanical response of the uterine cervix tissue does not differ considerably from that observed in vivo; (ii) some differences can be identified in tissue pre-conditioning with ex vivo showing a stronger history dependence with respect to in vivo; (iii) the differences in the time dependence of the mechanical response are not significant and might be masked by the variability of the measured data. This study represents a first step of a clinical application aiming at analysing the mechanical response of normal cervical tissue at different gestational ages, and identifying the mechanical properties that characterize pathologic conditions such as cervical insufficiency leading to preterm delivery.

In the present study we consider an adaptation of Nguyen’s model [G.D. Nguyen, A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, D.Phil. Thesis, Dept. of Engng. Sci., University of Oxford, 2005] for brittle materials to the case of ductile rupture. We focus our attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework. We demonstrate the capability of the model to generate mesh-independent results and to follow the rupture process very close to failure. Rupture analysis of thin plates of different geometry is presented (symmetric double notch-edged specimen, asymmetric double notch-edged specimen, double notch-edged specimen containing a hole). Further modifications are outlined required to simulate crack growth and paths under the conditions of creep and fatigue.

The response to mechanical loading of the thermosetting resin system RTM-6 has been investigated experimentally as a function of strain rate and a constitutive model has been applied to describe the observed and quantified material behaviour. In order to determine strain rate effects and to draw conclusions about the hydrostatic stress dependency of the material, specimens were tested in compression and tension at strain rates from 10−3 to 104 s−1. A Standard screw-driven tensile machine was used for quasi-static testing, with an ‘in house’ hydraulic rig and Hopkinson bars for medium and high strain rates, respectively. At all rates appropriate photography and optical metrology have been used for direct strain measurement, observation of failure and validation of experimental procedures. In order to enable the experimental characterisation of this brittle material at very high rates in tension, a novel pulse shaping technique has been applied. With the help of this device, strain rates of up to 3800 s−1 have been achieved while maintaining homogeneous deformation state until specimen fracture in the gauge section of the tensile specimens. The yield stress and initial modulus increased with increasing strain rate for both compression and tension, while the strain to failure decreased with strain rate in tension. An existing constitutive model, the Goldberg model has been extended in order to take into account the nonlinear strain rate dependence of the elastic modulus. The model has been validated against 3-point impact bending tests of prismatic RTM-6 beams.