Nonuniform transformation field analysis of materials with morphological anisotropy

Abstract

Abstract. The effective properties of metal matrix composites with particulate reinforcement are investigated using the nonuniform transformation field analysis (NTFA) developed by Michel and Suquet (2003). In particular the effect of the particle morphology on the effective mechanical response is examined in detail. For that, an existing periodic three-dimensional mesh generation technique for particulate composites is extended to allow for anisotropic morphologies. It is shown that the effects induced by the anisotropic particles can be captured by the NTFA. Additionally, the load partitioning between reinforcement and matrix material is investigated and a good agreement to full-field computations is attained with the NTFA.

Topology optimization of multiscale elastoviscoplastic structures

“…Recently, the authors have presented a ROM for this problem class that is computationally feasible, yet sufficiently accurate: the potential‐based reduced basis model order reduction (pRBMOR, ). The pRBMOR extends general ideas of the nonuniform transformation field analysis (NTFA; ) to a broader class of microscopic constitutive models. The key idea of the pRBMOR is the approximation of the internal state variables of the dissipative material by a reduced basis.…”

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

“…Note that, by simultaneous use of parallel computing and ROM [22], a further reduction in computational time can be achieved in multiscale analysis [23]. Most of the existing ROMs constructed using reduction strategies such as Proper Orthogonal Decomposition (POD) [24,25], Proper Generalized Decomposition (PGD) [26][27][28], material map model [29,30], eigendeformation-based reduction [31,32], Nonuniform Transformation Field Analysis (NTFA) [33][34][35][36], and Numerical EXplicit Potentials (NEXP) [37,38] are developed intending to represent the effective constitutive law of nonlinear heterogeneous materials.…”

TFA-based Homogenization for Composites Subjected to Coupled Damage-friction Effects

“…The Transformation Field Analysis (TFA) can be considered an interesting and effective homogenization technique for solving the nonlinear micro-mechanical homogenization problem [4][5][6][7]9,15]. Particular interest arise in the evaluation of the macroscopic constitutive response of heterogeneous materials when its constituents are characterized by damaging phenomena and when decohesion between the constituents occurs [1,8,13].…”