Papers by Keyword: Finite Strain

Abstract: In this paper, macroscopic behavior obtained from crystal plasticity finite element simulations of irregularly shaped 3D and 2D volume elements (VEs) are compared. These morphologically periodic VEs are generated using the open-source software library Voro++. Periodic boundaryconditions are utilized to homogenize the material response employing a prescribed macroscopic deformation gradient tensor. To accelerate the assignment of periodic boundary conditions, a conformalmesh is employed by which periodic couples of faces on the hull of the volume element have identicalmesh patterns. In the simulations, plane strain conditions are assumed, which means that the averagethickness strain in 3D VEs is set to zero. However, grains are allowed to strain in the thickness direction. In the case of 2D VEs, plane strain elements are used. The principal goal of this comparison isto evaluate the accuracy of 2D VEs simulations. In the current study, two kinds of 2D VEs are generated: 1) Slicing 3D VEs normal to the thickness direction, 2) Separately generating 2D VEs. The firstmethod corresponds to sectioning 3D microstructures using EBSD. This approach is generally usedas an assumed more accurate alternative to 2D VEs. Based on the results, there is a large gap betweenthe flow curves of 2D and 3D VEs. Additionally, 2D sectioning of 3D VEs does not necessarily endup in higher precision in material behavior predictions.

Abstract: The deformation of the human breast, especially that of the female, under variable pressure conditions, has been a recent focus for researchers, both in the computational biomechanics, computational biology and the health sector. When the deformation of the breast is large, it hampers suitable cyst tracing as a mammographic biopsy precontrive data. Finite element methods (FEM) has been instrumental in the currently studied practices to trail nodules dislocation. However, the effect of breast material constitution, especially that of a fibrocystic composition, on the biomechanical response of these nodules has gained less attention. The present study is aimed at developing a finite element fibrocystic breast model within the frame of biosolid mechanics and material hyperelasticity to model the breast deformation at finite strain. The geometry of a healthy stress‐free breast is modelled from a magnetic resonance image (MRI) using tissues deformations measurements and solid modelling technology. Results show that the incompressible Neo-Hookean and Mooney-Rivlin constitutive models can approximate large deformation of a stressed breast. In addition to the areola (i.e. nipple base), the surrounding area of the cyst together with its interface with the breast tissue is the maximum stressed region when the breast is subjected to compressive pressure. This effect can lead to an internal tear of the breast that could degenerate to malignant tissue.

Abstract: Finite strain elastoplastic J₂-flow equations are established toward the purpose of automatically, accurately simulating pseudo-elastic effects of SMAs. The uniaxial responses derived from these equations in each loading-unloading cycle exactly produce a closed stress-strain curve of any given shape. Then, any given test data for pseudo-elastic hysteresis loops of SMAs may be accurately fitted by means of a new technique for combining linear spline functions into a unified, smooth interpolating function, in a sense with no need to identify any unknown parameters.

Abstract: Finite strain plastic deformation effects of SMAs are simulated based on finite strain elastoplastic J₂-flow equations, in a direct sense with no reference to any additional variables for phase transition mechanisms. Uniaxial loading-unloading curves of any given shape may be exactly reproduced as uniaxial stress-strain responses of these equations in each loading-unloading cycle. A new technique for combining linear spline functions into a unified, smooth interpolating function is proposed toward the purpose of explicitly, accurately fitting any given test data for both loading and unloading cases.

Abstract: The coiling process under traction is considered, with an incoming residual stress profile (that can be sufficiently compressive to make the strip buckle): a flatness defect. This paper details a 3D non-linear numerical simulation taking into account the contact of the strip on itself, with a perfect contact law. The model relies on elastic behavior at finite strain because of large rotations. Even though the behavior is elastic, the yield Von Mises criterion is computed and gives information about flatness defects (plastic zones are approximated by zones where the yield stress is exceeded). Furthermore, the paper aims at very short computation times. The modeling strategy relies (for each time step) on two analytical sub-steps. Numerical minimization procedure is used in order apply weak boundary conditions. Results are discussed with respect to a comprehensive Finite Element simulation and good agreement is observed.

Abstract: The influence of the crystallographic orientation, the level of axial strain and the test temperature on the progressive cross-section ellipticity of single crystal samples under uniaxial tension is analyzed in order to improve axial strain measurement in experiments. The direct three-dimensional finite element modeling of elasto-plastic deformation process of single-crystal initially cylindrical samples is used with taking into account finite strains, slip mechanisms and necking.

Abstract: This paper presents a consistent theoretical framework for describing the finite poroelasticity with surface effect. The underlying concept of additional pressure that is thought of as an equivalent thermodynamic pressure applying on the pore surface is used to detail the pore pressure. A nonlinear porosity laws is proposed for the finite deformation of porous material. With surface effect consideration, the corresponding constitutive equations are developed. The present model for both the swelling of the matrix and the permeability change of coal induced by adsorption of CO₂ and CH₄ are presented under different pressure conditions. It is shown that the predictions from the model are good agreement with the experimental data of sorption-induced deformation of coals.

Abstract: A two-scale finite element analysis method based on a micro-macro decoupled scheme is applied to an equaled channeling angular extrusion. At first, the macro-scale finite element analysis for one process of an equaled channeling angular extrusion is carried out with a non-liner explicit method to handle the contact and friction between die and bullet. Using the deformation history at a macroscopic material point in this process, the micro-scale finite element analysis is conducted for the multiple processes with a single crystal plasticity and a nonlinear implicit method. As the results, the deformation process of the polycrystalline aggregate during the equaled channeling angular extrusion is numerically reproduced.

Abstract: Rockburst is modeled in this paper by the theory of elastoplastic damage at finite stains. Isotropic damage coupled with elastoplasticity is assumed and multiplicative kinematics in a purely mechanical setting is further applied. Merging the finite strain plasticity framework of Simo and the thermodynamics with internal variables of Lemaitre in definition of damage including processes, the Helmholtz free energy is additively decomposed to characterize the basic mechanism of elasto-plasticity and damage of brittle materials. The numerical simulations for granite burst are conducted by finite element technique.

Abstract: The peculiar properties of shape-memory alloys are the result of a solid/solid phase transformation between different crystallographic structures (austenite and martensite). This paper is concerned with the theoretical prediction of the set of strains that minimize the effective (or macroscopic) energy. Those strains, classically refered to as recoverable strains, play a central role in shape memory effect displayed by alloys such as NiTi or CuAlNi. They correspond to macroscopic strains that can be achieved in stress-free states. Adopting the framework of nonlinear elasticity, the theoretical prediction of stress-free strains amounts to find the austenite/martensite microstructures which minimize the global energy. Closed-form solutions to that problem have been obtained only in few special cases. This paper aims at complementing existing results on that problem, essentially by deriving bounds on the set of stress-free strains.