Jurica Sorić^*, Tomislav Lesičar, Zdenko Tonković

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 915-934, 2021, DOI:10.32604/cmes.2021.014142

Abstract The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach. The scale transition methodology in the multiscale framework is described. The structure at the macrolevel is discretized by the triangular C¹ finite elements obeying nonlocal continuum theory, while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable. The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity. The macrolevel softening is governed by… More >

Jurica Sorić*, Tomislav Lesičar, Filip Putar, Zdenko Tonković

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 181-183, 2019, DOI:10.32604/icces.2019.04554

Abstract The paper deals with the novel multiscale approaches for modelling of both quasi-brittle and ductile damage responses of heterogeneous materials. The damage is induced at the microstructural level and, after the homogenization procedure, it is included in the constitutive stiffness of the material point at macrolevel. The derived algorithms are implemented into the finite element software ABAQUS. The new two-scale transition procedures have been verified on the standard benchmark examples. More >

Hiroshi Kadowaki¹, Wing Kam Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 269-282, 2005, DOI:10.3970/cmes.2005.007.269

Abstract A method to derive governing equations and elastic-plastic constitutive relations for the micropolar continuum model is proposed. Averaging procedures are operated over a surrounding sub-domain for each material point to bridge a discrete microstructure to a macro continuum model. Material parameters are determined by these procedures. The size of the sub-domain represents the material intrinsic length scale, and it is passed into the macroscopic governing equation so that the numerical solution can be regularized for analyses of failure phenomena. An application to a simple granular material model is presented. More >

D. Chrupalla¹, J. Kreikemeier¹, S. Berg², L. Kärger³, M. Doreille⁴, T. Ludwig⁴, E. Jansen², R. Rolfes², A.Kling¹

CMC-Computers, Materials & Continua, Vol.32, No.3, pp. 159-176, 2012, DOI:10.3970/cmc.2012.032.159

Abstract In this paper, a loose coupling multiscale modeling technique for the detailed numerical analysis of critical areas in composite structures is presented. It is used to describe the global (macroscopic) behaviour of composite structures taking into account the effects of local phenomena. This is done by indirectly connecting the global and local FE-models. Prescribed displacements are assigned to the local boundaries in the transition from the global to local modeling level. The local-to-global transition is realized by assigning averaged local stresses to the respective global Gauss points and by updating the global tangent stiffness operator. To illustrate the feasibility of… More >

Paul R. Dawson¹, Donald E. Boyce², Ronald Rogge³

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.2, pp. 123-142, 2005, DOI:10.3970/cmes.2005.010.123

Abstract Computational mechanics provides a powerful environment for modeling the evolution of material structure during deformation processes and for associating that evolution with changes to the mechanical properties. In this paper, we illustrate a two-scale formulation that links the mechanical loading applied at the scale of a component (the continuum scale) to the responses of the material at the scale of the crystals that comprise it (the crystal scale). Employing the capabilities offered by computational mechanics, we can better understand how heterogeneity of deformation arising at both the continuum and crystal scales influences the behaviors observed experimentally. Such an understanding is… More >