Nonlinear reduced order homogenization of materials including cohesive interfaces

Abstract

The mechanical response of composite materials is strongly influenced by the nonlinear behavior of the interface between the constituents. In order to make reliable yet computationally efficient predictions for such materials, a reduced order model is developed. Conceptual ideas of the NTFA (Michel and Suquet, Int J Solids Struct 40: 6937-6955, 2003, Comput Methods Appl Mech Eng 193:5477-5502, 2004) and of the pRBMOR Leuschner Comput Methods Appl Mech Eng 260:143-154, 2013, Fritzen et al., Comput Methods Appl Mech Eng 278:186-217, 2014) are adopted. The key idea is to parameterize the displacement jumps on the cohesive interfaces by a reduced basis of global ansatz functions. Micromechanical considerations and the potential structure of the constitutive models lead to a variational formulation and reduced equilibrium conditions. The effect of the preanalysis phase on the accuracy is investigated using geometrically optimal training directions. The reduced model is tested for three-dimensional microstructures. Besides the effective stress response, the tension-compression asymmetry and the distribution of the separation of the interface are investigated. Memory savings on the order of 10 5 are realized. The computing time is reduced considerably. asymmetry · Potential-based reduced basis model order reduction (pRBMOR)

Identification of viscoelastic properties from numerical model reduction of pressure diffusion in fluid-saturated porous rock with fractures

“…In this paper, we therefore propose a NMR strategy that significantly reduces the numerical efforts in solving the SVE problems. Our approach is inspired by the Nonuniform Transformation Field Analysis (NTFA), which was initially established for elasto-viscoplastic materials [18,25] and recently extended towards solids with cohesive interfaces [10], generalized standard media [9,27], poroelastic composites [12] and transient heat flow [1], to name only a few application fields. The advancement presented in this paper is that we significantly extend the NMR-methodology that was initially proposed for undamaged poroelastic media in [12] towards pressure diffusion in a hybrid-dimensional formulation.…”

Topology optimization of multiscale elastoviscoplastic structures

“…For this reason, there has been limited research on topology optimization of nonlinear multiscale structures, and the need for a computationally manageable nonlinear multiscale simulation scheme becomes apparent. Intending to alleviate the computational burden in FE 2 , various reduced order models (ROMs) have been proposed for the homogenization of the constitutive properties of elastic (e.g., ) and inelastic materials (e.g., ).…”

“…Aiming at the consideration of dissipative two‐scale materials, different strategies are required in order to allow for the three main tasks: low computing times, low memory consumption, and sufficient accuracy of the nonlinear constitutive response. 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.…”

Computational analysis of damage in hybrid composite structure

“…In this work, a simplistic idea of interfaces was implemented in the modified NTFA scheme. Similar to [16], damage modes are found in the case interface constituents and their behaviour is described in normal and tangential directions (c.f. [47]).…”

“…The next natural step was to extend NTFA to cover more complex material models. Micro-mechanical analysis of composites with pressure-dependent plastic constituents was published in [23,24], crystal visco-plasticity in [17], visco-elasticity in [30], micro-model contains cohesive interface between the constituents in [16].…”