Boundary Element Crystal Plasticity Method

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1740003
Author(s):  
Ivano Benedetti ◽  
Vincenzo Gulizzi ◽  
Vincenzo Mallardo
Keyword(s):  
Grain Boundary ◽  
Boundary Element ◽  
Crystal Plasticity ◽  
Boundary Integral Equations ◽  
Voronoi Tessellation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Approach ◽  
Rate Dependent ◽  
Individual Grains

A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.

Boundary Element Method Analysis of Three-Dimensional Thermoelastic Fracture Problems Using the Energy Domain Integral

2005 ◽  
Vol 73 (6) ◽  
pp. 959-969 ◽  
Author(s):  
R. Balderrama ◽  
A. P. Cisilino ◽  
M. Martinez
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Auxiliary Function ◽  
Boundary Integral ◽  
Crack Advance ◽  
Domain Integral ◽  
Energy Domain ◽  
Element Method

A boundary element method (BEM) implementation of the energy domain integral (EDI) methodology for the numerical analysis of three-dimensional fracture problems considering thermal effects is presented in this paper. The EDI is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains, temperatures, and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations. Special emphasis is put on the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of the crack front with free surfaces. Several examples are analyzed to demonstrate the efficiency and accuracy of the implementation.

scholarly journals Development of boundary-element time-step scheme in solving 3D poroelastodynamics problems

2018 ◽  
Vol 183 ◽  
pp. 01042 ◽  
Author(s):  
Igor Vorobtsov ◽  
Aleksandr Belov ◽  
Andrey Petrov
Keyword(s):  
Boundary Element ◽  
Solid Phase ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Discrete Analogue ◽  
Boundary Integral ◽  
Step Method ◽  
Time Step ◽  
Element Scheme ◽  
Runge Kutta

The development of time-step boundary-element scheme for the three dimensional boundaryvalue problems of poroelastodynamics is presented. The poroelastic continuum is described using Biot’s mathematical model. Poroelastic material is assumed to consist of a solid phase constituting an elastic formdefining skeleton and carrying most of the loading, and two fluid phases filling the pores. Dynamic equations of the poroelastic medium are written for unknown functions of displacement of the elastic skeleton and pore pressures of the filling materials. Green’s matrices and, based on it, boundary integral equations are written in Laplace domain. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. Boundary element scheme is based on time-step method of numerical inversion of Laplace transform. A modification of the time-step scheme on the nodes of Runge-Kutta methods is considered. The Runge-Kutta scheme is exemplified with 2-and 3-stage Radau schemes. The results of comparing the two schemes in analyzing a numerical example are presented.

scholarly journals NUMERICAL ANALYSIS OF THE DYNAMICS OF THREE-DIMENSIONAL ANISOTROPIC BODIES BASED ON NON-CLASSICAL BOUNDARY INTEGRAL EQUATIONS

2021 ◽  
Vol 83 (1) ◽  
pp. 76-86
Author(s):  
A.A. Belov ◽  
A.N. Petrov
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Classical Approach ◽  
Classical Boundary ◽  
Nonclassical Formulation

The application of non-classical approach of the boundary integral equation method in combination with the integral Laplace transform in time to anisotropic elastic wave modeling is considered. In contrast to the classical approach of the boundary integral equation method which is successfully implemented for solving three-dimensional isotropic problems of the dynamic theory of elasticity, viscoelasticity and poroelasticity, the alternative nonclassical formulation of the boundary integral equations method is presented that employs regular Fredholm integral equations of the first kind (integral equations on a plane wave). The construction of such boundary integral equations is based on the structure of the dynamic fundamental solution. The approach employs the explicit boundary integral equations. The inverse Laplace transform is constructed numerically by the Durbin method. A numerical solution of the dynamic problem of anisotropic elasticity theory based on the boundary integral equations method in a nonclassical formulation is presented. The boundary element scheme of the boundary integral equations method is built on the basis of a regular integral equation of the first kind. The problem is solved in anisotropic formulation for the load acting along the normal in the form of the Heaviside function on the cube face weakened by a cubic cavity. The obtained boundary element solutions are compared with finite element solutions. Numerical results prove the efficiency of using boundary integral equations on a single plane wave in solving three-dimensional anisotropic dynamic problems of elasticity theory. The convergence of boundary element solutions is studied on three schemes of surface discretization. The achieved calculation accuracy is not inferior to the accuracy of boundary element schemes for classical boundary integral equations. Boundary element analysis of solutions for a cube with and without a cavity is carried out.

Boundary Element Formulation for Numerical Surface Wave Modelling in Poroviscoelastisity

2016 ◽  
Vol 685 ◽  
pp. 172-176 ◽  
Author(s):  
Leonid Igumnov ◽  
S.Yu. Litvinchuk ◽  
A.A. Belov ◽  
A.A. Ipatov
Keyword(s):  
Boundary Element ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Dynamic Responses ◽  
Element Formulation ◽  
Weakly Singular Kernel ◽  
Viscoelastic Parameters ◽  
Viscoelastic Effects ◽  
Biot’S Equations

Problems of the poroviscodynamics are considered. Theory of poroviscoelasticity is based on Biot’s equations of fluid saturated porous media under assumption that the skeleton is viscoelastic. Viscoelastic effects of solid skeleton are modeled by mean of elastic-viscoelastic correspondence principle, using such viscoelastic models as a standard linear solid model and model with weakly singular kernel. The fluid is taken as original in Biot’s formulation without viscoelastic effects. Boundary integral equations method is applied to solve three-dimensional boundary-value problems. Boundary-element method with mixed discretization and matched approximation of boundary functions is used. Solution is obtained in Laplace domain, and then Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. An influence of viscoelastic parameters on dynamic responses is studied. Numerical example of the surface waves modelling is considered.

Simulation of Crack Tip Plasticity Using 3D Crystal Plasticity Theory

2011 ◽  
Vol 291-294 ◽  
pp. 1057-1061
Author(s):  
Wen Hui Liu ◽  
Hao Huang ◽  
Zhi Gang Chen ◽  
Da Tian Cui
Keyword(s):  
Finite Element ◽  
Grain Boundary ◽  
Crystal Plasticity ◽  
Three Dimensional ◽  
Crack Tip ◽  
Plasticity Theory ◽  
Plastic Work ◽  
High Angle ◽  
Rate Dependent ◽  
Crystal Plasticity Theory

To investigate the plasticity distribution of microstructurally small crack tip in FCC crystals, the crack tip opening displacment(CTOD), crack tip plastic zone and maximum plastic work for stationary microstructurally small cracks were calculated with the three dimensional crystal plasticity finite element theory, which was implemented in the finite element code ABAQUS with the rate dependent crystal plasticity theory code as user material subroutine. Results show that crystallographic orientation has significant influence on CTOD and maximum plastic work. The CTOD and maximum plastic work in hard orientation are larger than that in soft orientaion under the displacement controlled boundary condition, which means that crack in hard orientation is more likely to extend than that in soft orientaion. The high-angle grain boundary shows a tendency to reduce crack extension, and the dislocation ahead of the crack tip becomes blocked by high-angle grain boundary.

scholarly journals Boundary Element Modeling of Dynamic Bending of a Circular Piezoelectric Plate

2018 ◽  
Vol 183 ◽  
pp. 01025
Author(s):  
Leonid Igumnov ◽  
Ivan Markov ◽  
Alexandr Konstantinov
Keyword(s):  
Boundary Element ◽  
Mechanical Response ◽  
Initial Conditions ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Element Formulation ◽  
Laplace Domain ◽  
Piezoelectric Plates

Accurate modelling of a coupled dynamic electro-mechanical response of circular piezoelectric plates under various loading conditions is of particular importance. Piezoelectric plates are not only basic structural elements, but with certain considerations can be conveniently fit for numerical simulation of piezoelectric sensors and transducers. In this work, a Laplace domain direct boundary element formulation is applied for dynamic analysis of three-dimensional linear piezoelectric moderately thick circular plates. Zero initial conditions, vanishing body forces and the absence of the free electrical charges are assumed. Weakly singular expressions of Laplace domain boundary integral equations for the generalized displacements are employed. Spatial discretization is based on the nodal collocation method. Mixed boundary elements are implemented. The geometry of the elements, generalized displacement and generalized tractions are represented with different shape functions: quadratic, linear and constant, accordingly. Integral expressions of the three-dimensional Laplace domain piezoelectric displacement fundamental solutions are used. After solving the problem on a set of Laplace transform parameter values, time-domain solutions are retrieved from the corresponding Laplace domain solutions by employing a numerical inversion routine. Numerical example is provided to show reliability and accuracy of the proposed boundary element formulation.

Boundary Element Analysis of Three-Dimensional Water Wave-Structure Dynamic Interaction Problems

1988 ◽  
Vol 110 (2) ◽  
pp. 131-139 ◽  
Author(s):  
N. Tosaka ◽  
K. Kakuda
Keyword(s):  
Boundary Element ◽  
Water Wave ◽  
Eigenvalue Problems ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Wave Structure ◽  
Coupled System ◽  
Dynamic Interaction ◽  
Boundary Integral ◽  
Structure Dynamic

Water wave-structure dynamic interaction problems are treated as eigenvalue problems of the coupled system by means of the boundary element method. The coupled system for a large-sized ocean structure is modelized generally with the three-dimensional continuum mechanics. The boundary integral equations of the coupled system are derived by the weighted residual method and related fundamental solutions. The solving scheme for the discretized equations is discussed in detail. Numerical examples of the three-dimensional problem are given to show the validity of the present method through the comparison with other results.

Comparative Analysis of 3D Viscoelastic and Poroelastic Dynamic Boundary-Element Modelling

2014 ◽  
Vol 709 ◽  
pp. 186-189
Author(s):  
L.A. Igumnov ◽  
A.A. Ipatov ◽  
E.A. Lebedeva
Keyword(s):  
Boundary Value Problems ◽  
Boundary Element ◽  
Integral Transform ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Three Dimensional ◽  
Maxwell Model ◽  
Boundary Integral ◽  
Weakly Singular Kernel ◽  
Dynamic Boundary

3D dynamic boundary-value problems of linear viscoelasticity and poroelasticity are considered. Laplace integral transform and its numerical inversion are used. Classical viscoelastic models, such as Maxwell model, KelvinVoigt model, standard linear solid model, and model with weakly singular kernel (Abel type) are considered. Boundary integral equations (BIE) method is developed to solve three-dimensional boundary-value problems. A numerical modelling of wave propagation is done by means of boundary element approach.

scholarly journals Stress Analysis of Three-Dimensional Media Containing Localized Zone by FEM-SGBEM Coupling

2011 ◽  
Vol 2011 ◽  
pp. 1-27
Author(s):  
Jaroon Rungamornrat ◽  
Sakravee Sripirom
Keyword(s):  
Stress Analysis ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Numerical Technique ◽  
Computational Cost ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Element Method

This paper presents an efficient numerical technique for stress analysis of three-dimensional infinite media containing cracks and localized complex regions. To enhance the computational efficiency of the boundary element methods generally found inefficient to treat nonlinearities and non-homogeneous data present within a domain and the finite element method (FEM) potentially demanding substantial computational cost in the modeling of an unbounded medium containing cracks, a coupling procedure exploiting positive features of both the FEM and a symmetric Galerkin boundary element method (SGBEM) is proposed. The former is utilized to model a finite, small part of the domain containing a complex region whereas the latter is employed to treat the remaining unbounded part possibly containing cracks. Use of boundary integral equations to form the key governing equation for the unbounded region offers essential benefits including the reduction of the spatial dimension and the corresponding discretization effort without the domain truncation. In addition, all involved boundary integral equations contain only weakly singular kernels thus allowing continuous interpolation functions to be utilized in the approximation and also easing the numerical integration. Nonlinearities and other complex behaviors within the localized regions are efficiently modeled by utilizing vast features of the FEM. A selected set of results is then reported to demonstrate the accuracy and capability of the technique.

Sign in / Sign up

Export Citation Format

Share Document