Effects of Voids in Tensile Single-Crystal Cu Nanobeams

Molecular dynamic simulations of defect nanosized beams of single-crystal Cu, loaded in displacement controlled tension until rupture, have been performed. The defects are square-shaped, through-the-thickness voids of different sizes, placed centrally in the beams. Three different cross section sizes and two different crystallographic orientations are investigated. As expected, the sizes of the beam cross section and the void as well as the crystal orientation strongly influence both the elastic and the plastic behaviors of the beams. It was seen that the strain at plastic initiation increases with beam cross section size as well as with decreasing void size. It is further observed that the void deformed in different ways depending on cross section and void size. Sometimes void closure, leading to necking of the beam cross section followed by rupture occurred. In other cases, the void elongated leading to that the two ligaments above and below the void ruptured independently

Modelling of Granular Materials

The aim of this doctoral study is to develop and implement a material model for granular materials. The course of this work was concentrated upon a non-associated plasticity model with yield surface and the flow potential expressed in terms of the mean stress p and the third stress invariants I3. The plastic work hardening in the model depends upon both plastic volumetric and deviatoric strain increments in order to model dilatancy before the ultimate state. The calibration procedure that captures the principal features of the stress-strain and axial to volume strain relations is developed and all six material parameters in the model are determined from the data of one standard triaxial test. An efficient implicit integration algorithm, for granular material models including I3-plasticity, is developed and implemented as a user defined material behaviour in a commercial finite element code. The implemented algorithm is utilized to study the difference in strength and stress distribution between rigid and flexible footings resting on a surface of sand and the differences between two and three dimensional simulations of strip and square footings. The material behaviour for a two-component soil system consisting of sand and gravel particles is studied micromechanically and then the global response is investigated. The dependance of the strain localization phenomenon on the particle form and the effects of dilantcy are studied. For many geotechnical purposes in practice the soil foundations contain not only soil but also water. In order to include the influence of flowing water on soil, the material model for dry soil is incorporated in a binary mixture model. The mixture model is formulated by eliminating the supply terms due to interactions and hence these terms do not need to be constituted. The model is implemented and incorporated into the finite element code and simulations of footing resting on water saturated sand have been performed

Three-Dimensional Finite Element Analysis of Footing Resting on Sand

Numerical analysis, such as the finite element method is the most used computational procedure for nonlinear deformation and strength analysis of structures. In order to obtain meaningful results the material behaviour must be described and simulated accurately. Another important element in order to perform the simulation is a robust and accurate numerical integration algorithm. The present paper is focused on three-dimensional numerical simulation of footing resting on sand. The complex nature of soil behaviour, depending on void ratio and stress state is highly non-linear and it is modeled with a non-associated plasticity model developed by Krenk (2000). The model has been implemented as a user-defined mechanical material behavior in ABAQUS finite element code using an implicit integration algorithm with explicit update of the hardening parameter, presented in Ahadi & Krenk (2003). The implemented subroutine is used to study the deformation and strength behaviour of sand subjected to load with flexible footing. Both strip footing under plain strain conditions and three dimensional square footing are analyzed. The simulations are performed using large strains in order to account for geometrical nonlinearities. The deformation behaviour, vertical stress distribution and the settlement beneath the footing from the strip and the square footings are compared

FE-Implementation of Elasto-Plastic Model for Granular Materials and Analysis of Foundations

The non-associated plasticity model is utilized to simulate a three dimensional nonlinear finite element analysis on sand. The model is a three-dimensional generalization of the Cam-Clay model with yield- and flow potential functions expressed in a common format, but with different shapes and hardening rule depending on both the shear and volumetric stains, which enables modelling of dilation. The model has been implemented as a user-defined mechanical material behavior in ABAQUS finite element code using an implicit integration algorithm with explicit update of the hardening parameter. The implemented subroutine UMAT in ABAQUS is verified by carrying out a triaxial test on single element and comparing the result to the experimental data and implementation in the high level language MATLAB. The implemented subroutine is used to study the influence of the rigidity of the footing. Simulation with both absolute rigid and absolute flexible footings are carried out and the deformation behaviour, the differences in vertical and contact stress distributions beneath the footing are presented. In addition the effects of using large strains are investigated by simulating a flexible strip footing resting on sand and comparing the deformation behaviour to the small strain solution.

Implementation and evaluation of a binary mixture model and three-dimensional FE-analysis of water saturated soil

A binary mixture model for soils has been formulated and analyzed. In the model one of the constituents is soil and the other constituent an incompressible liquid. The effects of water are included by formulating a mixture model is formulated as an extension of an existing non-associated elasto-plastic material model for granular materials. This paper is focused on the balance of momentum equations of the mixture model, primarily to avoid the difficulties arising when the interaction terms between the constituents needs to be formulated and constituted. Considering the momentum balance of the mixture as an extension of the balance equation of the soil constituent, it is supplemented with body forces, stresses and flow effects from the water constituent. These supplemented terms are evaluated and analyzed. An alternative way of deriving equation of motion for the fluid is also presented. The computer algorithm for integrating the constitutive relation of dry sand is supplemented and numerical simulations with a finite element code are carried out. It is shown that although the mixture model consists of two constituents, it is possible to include the existence of voids and a system with three constituents, i.e. water unsaturated soil, can be analyzed. Results from single element tests and simulations of a flexible footing resting on a surface of water saturated sand are presented

Constitutive modeling of friction materials

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Model representation of sand tests

A non-associated plasticity model for friction materials was presented by Krenk (1999) and an efficient calibration procedure developed by Ahadi & Krenk (1999). The ability of the model to represent the behaviour of sand was verified by calibrating the model from different sets of triaxial drained tests for both loose and dense sand performed at different confining pressures. This paper is a collection of calibration and prediction examples. The model was calibrated according to the procedure described in Ahadi & Krenk (1999) and results were compared to experimental data from Borup & Hedegaard (1995) and Ibsen & Jakobssen (1996). The obtained material parameters indicate that the shear modulus $G$ should increase with the mean stress, while the increase of the bulk stiffness should be less than linear. The dependency on mean stress is studied by fitting a power law function for both $G$ and $kappa$. Finally prediction for undrained (constant volume) test at different initial pressures are presented with material parameter determined from drained triaxial test data