Boris Jeremić

Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone

Nanoindentation has been widely used to study bone tissue mechanical properties. The common method and equations for analyzing nanoindentation, developed by Oliver and Pharr, are based on the assumption that the material is linearly elastic. In the present study, we adjusted the constraint of linearly elastic behavior and use nonlinear finite element analysis to determine the change in cancellous bone material properties caused by bisphosphonate treatment, based on an isotropic form of the Mohr-Coulomb failure model. Thirty-three canine lumbar vertebrae were used in this study. The dogs were treated daily for 1 year with oral doses of alendronate, risedronate, or saline vehicle at doses consistent, on a mg/kg basis, to those used clinically for the treatment of post-menopausal osteoporosis. Two sets of elastic modulus and hardness values were calculated for each specimen using the Continuous Stiffness Measurement (CSM) method (E(CSM) and H(CSM)) from the loading segment and the Oliver-Pharr method (E(O-P) and H(O-P)) from the unloading segment, respectively. Youngs modulus (E(FE)), cohesion (c), and friction angle (phi) were identified using a finite element model for each nanoindentation. The bone material properties were compared among groups and between methods for property identification. Bisphosphonate treatment had a significant effect on several of the material parameters. In particular, Oliver-Pharr hardness was larger for both the risedronate- and alendronate-treated groups compared to vehicle and the Mohr-Coulomb cohesion was larger for the risedronate-treated compared to vehicle. This result suggests that bisphosphonate treatment increases the hardness and shear strength of bone tissue. Shear strength was linearly predicted by modulus and hardness measured by the Oliver-Pharr method (r(2)=0.99). These results show that bisphosphonate-induced changes in Mohr-Coulomb material properties, including tissue shear cohesive strength, can be accurately calculated from Oliver-Pharr measurements of Youngs modulus and hardness.

International Benchmark on Numerical Simulations for 1D, Nonlinear Site Response (PRENOLIN): Verification Phase Based on Canonical Cases

PREdiction of NOn‐LINear soil behavior (PRENOLIN) is an international benchmark aiming to test multiple numerical simulation codes that are capable of predicting nonlinear seismic site response with various constitutive models. One of the objectives of this project is the assessment of the uncertainties associated with nonlinear simulation of 1D site effects. A first verification phase (i.e., comparison between numerical codes on simple idealistic cases) will be followed by a validation phase, comparing the predictions of such numerical estimations with actual strong‐motion recordings obtained at well‐known sites. The benchmark presently involves 21 teams and 23 different computational codes. We present here the main results of the verification phase dealing with simple cases. Three different idealized soil profiles were tested over a wide range of shear strains with different input motions and different boundary conditions at the sediment/bedrock interface. A first iteration focusing on the elastic and viscoelastic cases was proved to be useful to ensure a common understanding and to identify numerical issues before pursuing the nonlinear modeling. Besides minor mistakes in the implementation of input parameters and output units, the initial discrepancies between the numerical results can be attributed to (1) different understanding of the expression “input motion” in different communities, and (2) different implementations of material damping and possible numerical energy dissipation. The second round of computations thus allowed a convergence of all teams to the Haskell–Thomson analytical solution in elastic and viscoelastic cases. For nonlinear computations, we investigate the epistemic uncertainties related only to wave propagation modeling using different nonlinear constitutive models. Such epistemic uncertainties are shown to increase with the strain level and to reach values around 0.2 (log_(10) scale) for a peak ground acceleration of 5  m/s^2 at the base of the soil column, which may be reduced by almost 50% when the various constitutive models used the same shear strength and damping implementation.

A model for elastic-plastic pressure sensitive materials subjected to large deformations

Abstract Development of a finite deformation elasto-plastic model for pressure sensitive materials is presented. The chosen model, which has its roots in the MRS-Lade material model is influenced by recent developments. The thermodynamic consequences of introducing non-associative yielding (both deviatoric and volumetric) and hardening⧸softening characteristics are assessed. The consistently linearized Algorithmic Tangent Stiffness (ATS) tensor is presented. This tensor is used in the constitutive driver as a key feature of the efficient iterative procedure for satisfying equilibrium in the case of stress (or mixed) control. The chosen model is calibrated using data from experiments conducted in a Directional Shear Cell (DSC) , which has been used extensively at the University of Colorado at Boulderto investigate the behavior of pressure sensitive materials under deformations of large magnitude.

Application of the p-version of the finite element method to elastoplasticity with localization of deformation

In this paper we discuss the use of the p-version of the finite element method applied to elastoplastic problems that exhibit sharp (but continuous) deformation gradients. The deformation theory of deviatoric, linearly hardening elastoplasticity with an iterative, displacement based finite element framework is used. The focus of this work is on assessing the applicability of the p-version to the analysis of localized deformation with continuous strain and displacement fields. Presented examples demonstrate that the method can be used reliably with a proper finite element mesh design. Possible extensions of the work are also discussed.

Visualizing tensor fields in geomechanics

The study of stress and strains in soils and structures (solids) help us gain a better understanding of events such as failure of bridges, dams and buildings, or accumulated stresses and strains in geological subduction zones that could trigger earthquakes and subsequently tsunamis. In such domains, the key feature of interest is the location and orientation of maximal shearing planes. This paper describes a method that highlights this feature in stress tensor fields. It uses a plane-in-a-box glyph which provides a global perspective of shearing planes based on local analysis of tensors. The analysis can be performed over the entire domain, or the user can interactively specify where to introduce these glyphs. Alternatively, they can also be placed depending on the threshold level of several physical relevant parameters such as double couple and compensated linear vector dipole. Both methods are tested on stress tensor fields from geomechanics.

Soil Uncertainty and Its Influence on Simulated G/Gmax and Damping Behavior

In this paper, recently developed probabilistic elastoplasticity was applied in simulating cyclic behavior of clay. A simple von Mises elastic–perfectly plastic material model was used for simulation. Probabilistic soil parameters, elastic shear modulus (Gmax) and undrained shear strength (su), needed for the simulation were obtained from correlations with the standard penetration test (SPT) N-value. It has been shown that the probabilistic approach to geo-material modeling captures some of the important aspects—the modulus reduction, material damping ratio, and modulus degradation—of cyclic behavior of clay reasonably well, even with the simple elastic–perfectly plastic material model.

Line search techniques for elasto‐plastic finite element computations in geomechanics

In this paper we present a globally convergent modification of Newtons method for integrating constitutive equations in elasto-plasticity of geomaterials. Newtons method is known to be q-quadratically convergent when the current solution approximation is adequate. Unfortunately, it is not unusual to expend significant computational time in order to achieve satisfactory results. We will present a technique which can be used when the Newton step is unsatisfactory. This scheme can be considered as a modified version of the traditional concept of backtracking along the Newton direction if a full Newton step provides unsatisfactory results. The method is also known as line search technique. The technique is applied to the fully implicit Newton algorithm for a hardening or softening general isotropic geomaterials at the constitutive level. Various solution details and visualizations are presented, which emerge from the realistic modelling of highly non-linear constitutive behaviour observed in the analysis of cohesionless granular materials. Copyright

Object-Oriented Approach to Hyperelasticity

Abstract.This paper describes the application of an Object-Oriented Paradigm (OOP) to the implementation of a hyperelastic constitutive driver. The C11 programming language used in our implementation leads to an efficient and readable program. It will be shown that object-oriented implementation naturally follows from analytical developments in isotropic hyperelasticity. Examples of classes developed and results from a number of large deformation hyperelastic numerical test are presented.

Forward and backward probabilistic simulations in geotechnical engineering

To account for non-uniformity and uncertainties in soil parameters, in recent years, civil engineering practice and in particular, geotechnical engineering practice has seen an increasing emphasis on probabilistic treatment to data and subsequent simulation/design. Consistent development of a probabilistic framework for geotechnical simulation/design will not only provide a rational way to address our confidence (or lack thereof) in simulated/designed behavior, but also, it will empower engineers to demonstrate the need for more, uniform data of soil properties, to develop novel site characterization techniques, and to design geotechnical systems that will (probably) achieve best performance. This paper discusses the influence of uncertainties in soil properties on seismic ground motions. Both spatial and point-wise uncertainties – natural variability, testing and transformation uncertainty – in soil properties are identified and consistently propagated through the governing equations of geomechanics, in evaluating the complete probabilistic behavior of the response. Recently developed probabilistic elasto-plasticity and stochastic elastic-plastic finite element method are used for this purpose. Also discussed is setting up of the forward uncertainty propagation problem as an optimization problem in inversely solving for site characterization details from a given probabilistic behavior of the response.

Numerical Modeling and Simulation of Soil Lateral Spreading Against Piles

In this paper we present methodology to numerically simulate behavior of piles in liquefiable soils. In addition to that, simulation examples involving laterally spreading soil with and without piles are presented as well. These simulation examples are also used to investigate the so called pile pinning effects where pile (is trying to) resist liquefied soil lateral spreading. Prediction of behavior of piles in laterally spreading grounds is also used to investigate effects a geomechanics phenomena of voids - pore fluid volume/pressure redistribution has on behavior of such systems. Presented work constitutes another step in our effort to develop high fidelity models and simulation tools for use in performance based design of infrastructure objects.