# ADAPTIVE MULTISCALE MODELING AND ANALYSIS OF HETEROGENEOUS MATERIALS

Leitung: | P. Wriggers, I. Temizer |

Jahr: | 2009 |

Ist abgeschlossen: | ja |

**Summary** (download poster)

Computational analysis of microheterogeneous materials in the linear elasticity regime is a well-established field. In this regime, the homogenization method is employed to approximate the effective elastic properties that the heterogeneous material displays on the macroscale, thereby reducing the macroscopic problem to one with standard numerical concerns regarding time and space discretization. However, when the composite displays inelastic and/or finite deformation, there does not exist a closed-form expression for the effective constitutive behavior, so one must resort to computationally expensive homogenization methods that require the solution of embedded problems at selected points of the composite structure. The intensive computational effort required in such schemes is further amplified by the complications that arise near high deformation gradients where homogenization methods may not be applicable, and an explicit analysis of the microstructure may be required. Therefore, in the analysis of a composite structure, multiple levels of resolution are needed: (i) a region where effective elastic properties are employed, (ii) a region where embedded problems are solved, and (iii) a region where explicit microstructural evaluation is required. Efficient solution of fully three-dimensional inelastic finite deformation problems for composite structures requires an adaptive scheme where these three regions are identified in an optimal fashion, based on a criterion that determines the level of resolution needed in a given portion of the macrostructure. Moreover, individual solution schemes for each resolution must be optimized in order to decrease the overall cost of the problem. Development of such computational schemes for the adaptive multiscale analysis of heterogeneous materials is the main purpose of this project.

Support for this project is provided by the German Research Foundation (DFG) under Grant No. WR 19/36.

** Publications**

[1] **I. Temizer, P. Wriggers (2007):** An adaptive method for homogenization in orthotropic nonliner elasticity. Computer Methods in Applied Mechanics and Engineering, 196:3409-3423 ; abstract

[2] **I. Temizer, P. Wriggers (2008):** On a Mass Conservation Criterion in Micro-to-Macro Transitions. Journal of Applied Mechanics, Trans. ASME, 75:054503 (doi: 10.1115/1.2913042) ; abstract

[3] **I. Temizer, P. Wriggers (2008):** On the computation of the macroscopic tangent for multiscale volumetric homogenization problems. Comput. Methods Appl. Mech. Engrg. 198, pp. 495-510 (doi:10.1016/j.cma.2008.08.018) ; abstract

[4] **I. Temizer, P. Wriggers (2009):** An Adaptive Multiscale Resolution Strategy for the Finite Deformation Analysis of Microheterogeneous Structures. Comput. Methods Appl. Mech. Engrg. [submitted]

[5] **I. Temizer, P. Wriggers (2009):** A micromechanically motivated higher-order continuum formulation of linear thermal conduction. Z. Angew. Math. Mech. [submitted]

[6] **I. Temizer, P. Wriggers (2009):** Homogenization in Finite Thermoelasticity. J. Mech. Pyhs. Solids [submitted]