Second-Order Computational Homogenization Scheme Preserving Microlevel C1 Continuity

2014 ◽  
Vol 627 ◽  
pp. 381-384 ◽  
Author(s):  
Tomislav Lesičar ◽  
Zdenko Tonković ◽  
Jurica Sorić
Keyword(s):  
Gradient Elasticity ◽  
Multiscale Model ◽  
Computational Homogenization ◽  
Second Order ◽  
Volume Element ◽  
Homogenization Procedure ◽  
Triangular Finite Element ◽  
Small Strains ◽  
Mesh Density ◽  
Homogenization Scheme

The paper deals with a new second-order computational homogenization procedure for modeling of heterogeneous materials at small strains, whereC1continuity is preserved at the microlevel. The multiscale model is based on the Aifantis theory of gradient elasticity. TheC1two dimensional triangular finite element used for the discretization of macro-and microlevel is described. Contrary to theC1-C0transition, here besides the displacements, the displacement gradients are included into the boundary conditions on the representative volume element (RVE). According to the second order continuum at microlevel, the relevant homogenization relations are derived. Finally, the performance of the algorithms derived is investigated. Dependency of homogenized stresses on mesh density and microstructural parameterlare examined in simple loading cases.

C1 CONTINUITY FINITE ELEMENT FORMULATION IN SECOND-ORDER COMPUTATIONAL HOMOGENIZATION SCHEME

2012 ◽  
Vol 04 (04) ◽  
pp. 1250013 ◽  
Author(s):  
TOMISLAV LESIČAR ◽  
ZDENKO TONKOVIĆ ◽  
JURICA SORIĆ
Keyword(s):  
Finite Element ◽  
Gradient Elasticity ◽  
Computational Homogenization ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Triangular Finite Element ◽  
Patch Tests ◽  
Quadrilateral Finite Element

The paper describes a second-order two-scale computational homogenization procedure for modeling of heterogeneous materials at small strains. The Aifantis theory of linear elasticity has been described and implemented into the two dimensional C1 continuity triangular finite element formulation. The element has been verified on several patch tests and the computational efficiency of numerical integration of the element stiffness matrix has been tested as well. Furthermore, the C1 two dimensional triangular finite element based on full second gradient continuum is formulated and used for the macrolevel discretization in the frame of a multiscale scheme, where the RVE is discretized by the C0 quadrilateral finite element. The application of generalized periodic boundary conditions and the microfluctuation integral condition on RVE has been investigated. The presented numerical algorithms have been implemented into FE software ABAQUS via user subroutines and verified on a pure bending problem. The comparability of RVE size to the length scale parameter of gradient elasticity has been proved, and elastoplastic behavior of heterogeneous material has been also considered. The results obtained show good numerical efficiency of the proposed algorithms.

scholarly journals Determination of macro-scale soil properties from pore-scale structures: model derivation

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170141 ◽  
Author(s):  
K. R. Daly ◽  
T. Roose
Keyword(s):  
Pore Space ◽  
Solid Particles ◽  
Underlying Structure ◽  
Pore Scale ◽  
Homogenization Procedure ◽  
Macro Scale ◽  
Model Derivation ◽  
Scale Structures ◽  
Homogenization Scheme

In this paper, we use homogenization to derive a set of macro-scale poro-elastic equations for soils composed of rigid solid particles, air-filled pore space and a poro-elastic mixed phase. We consider the derivation in the limit of large deformation and show that by solving representative problems on the micro-scale we can parametrize the macro-scale equations. To validate the homogenization procedure, we compare the predictions of the homogenized equations with those of the full equations for a range of different geometries and material properties. We show that the results differ by ≲ 2 % for all cases considered. The success of the homogenization scheme means that it can be used to determine the macro-scale poro-elastic properties of soils from the underlying structure. Hence, it will prove a valuable tool in both characterization and optimization.

Modeling Nanocomposite Piezoresistive Response With Electromechanical Cohesive Zone Material Point Method

2016 ◽  
Author(s):  
Adarsh K. Chaurasia ◽  
Gary D. Seidel
Keyword(s):  
Cohesive Zone ◽  
Large Deformations ◽  
Material Point Method ◽  
Material Point ◽  
Volume Element ◽  
Point Method ◽  
Current Work ◽  
Secondary Field ◽  
Small Strains ◽  
The Matrix

In the current work, the Material Point Method (MPM) is extended to allow for interfacial discontinuities in problems with composite materials using cohesive zone (CZ) techniques. The proposed CZMPM is observed to result in smaller errors in the primary and secondary field variables, especially near the interface, for a given boundary value problem in comparison to the traditional MPM solution. The proposed CZMPM is used to solve an electromechanical test problem with a single fiber in the matrix medium. It is observed that the proposed CZMPM results in smaller local and volume averaged errors. The CZMPM is further used to evaluate the effective piezoresistive response of the nanoscale carbon nanotube (CNT)-polymer composite with electron hopping in between the nanotubes. The observed effective piezoresistive response exhibits features similar to those reported in the literature using finite element techniques for small strains. However, CZMPM allows for large deformations of the nanoscale representative volume element as presented in the current work.

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