Abstract
Computational homogenization allows to let the macroscopic constitutive behavior of materials emerge from microscale simulations without loss of generality with respect to microstructure and microscale constitutive response. Although computationally demanding, computational homogenization works very well for the hardening response of materials where the macroscopic stress and strain fields are smooth. However, in case of softening materials, when localization of deformation takes place, special care is needed to ensure objectivity of the method. In this paper, a generic multiscale computational homogenization approach for modeling onset and propagation of cracks in heterogeneous materials that is capable of considering various microscale mechanisms is presented. The common acoustic tensor bifurcation criterion is reinforced by an additional condition to help detect the localization mode more robustly. After the onset of macroscale localization, a key scale transition parameter is needed to translate the macroscopic displacement jump to an averaged strain over the micromodel domain. Then the macroscale crack is governed by a homogenized traction-separation relation evaluated from the underlying micromodel in which micro-failure accumulates. The scale transition parameter is studied for a range of different scenarios and endowed with a geometrical interpretation. Various numerical tests have been performed to confirm the objectivity and validity of the framework. The framework is generic in the sense that no assumptions on the microscale constitutive or kinematic representation of material failure are made in the scale transition. The framework is also highly compatible with the first order computational homogenization, which minimizes the additional complexity of adding macroscopic crack growth to the computational implementation.
Highlights
Synthetic composite materials such as concrete and fibre-reinforce polymers are widely used in a variety of engineering sectors due to their superior mechanical performance and/or excellent durability compared to traditional single-component materials
Discrete macroscopic crack onset and propagation for heterogeneous materials are derived from the micromodel in which the underlying microstructure undergoes accumulating micro-fracture failure
The key scale transition parameter which serves as a numerical characteristic length is examined and endowed with a geometrical interpretation which leads to a proper computing method
Summary
Synthetic composite materials such as concrete and fibre-reinforce polymers are widely used in a variety of engineering sectors due to their superior mechanical performance and/or excellent durability compared to traditional single-component materials. Based on the introduced failure-zone averaging technique which guarantees the objectivity of softening RVEs, Nguyen et al (2011) and Nguyen et al (2012a) proposed a continuous-discontinuous CH framework to model the transition of microscopic diffusive damage to macroscopic cohesive failure for tensile cracking problems. Instead of resorting to cohesive models, Khoei and Saadat (2019) proposed a CH framework which adopts non-local damage model on both scales for the purpose of regularization through establishing an additional transition relation for non-local damage terms These CH models have been successful in dealing with multiscale strain localization problems. The current contribution presents a generic CH framework which is tailored to dealing with macroscopic crack onset and propagation for heterogeneous materials without restrictive assumptions on the microscopic failure processes and remains as less intrusive to the existing code as possible. Generality with respect to micromodel formulation is illustrated by including plasticity in the micromodel
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