arXiv subjects

Shahed Rezaei

Publications and source records attributed to Shahed Rezaei.

21 records · Page 2Linked to original sources

arXiv2021

An anisotropic cohesive fracture model: advantages and limitations of length-scale insensitive phase-field damage models

The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the idea introduced in \cite{REZAEI2021a} for direction-dependent fracture energy and also anisotropic PF damage models based on structural tensors. The cohesive PF damage formulation used in the current contribution is motivated by the works of \cite{LORENTZ201120, wu2018, GEELEN2019}. The results of the latter models are shown to be insensitive with respect to the length scale parameter for the isotropic case. This is because they manage to formulate the fracture energy as a function of diffuse displacement jumps in the localized damaged zone. In the present paper, we discuss numerical examples and details on finite element implementations where the fracture energy, as well as the material strength, are introduced as an arbitrary function of the crack direction. Using the current formulation for anisotropic cohesive fracture, the obtained results are almost insensitive with respect to the length scale parameter. The latter is achieved by including the direction-dependent strength of the material in addition to its fracture energy. Utilizing the current formulation, one can increase the mesh size which reduces the computational time significantly without any severe change in the predicted crack path and overall obtained load-displacement curves. We also argue that these models still lack to capture mode-dependent fracture properties. Open issues and possible remedies for future developments are finally discussed as well.

cs.CE↗

arXiv2021

Lossless Multi-Scale Constitutive Elastic Relations with Artificial Intelligence

The elastic properties of materials derive from their electronic and atomic nature. However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless and lossless transition of the constitutive description of the elastic response of materials between these two scales has been so far elusive. Here we show how this problem can be overcome by using Artificial Intelligence (AI). A Convolutional Neural Network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corresponding elasticity tensor, calculated from Molecular Statics (MS), as output. Trained with the atomistic data, the CNN model captures the size- and pore-dependency of the material's elastic properties which, on the physics side, can stem from surfaces and non-local effects. Such effects are often ignored in upscaling from atomistic to classical continuum theory. To demonstrate the accuracy and the efficiency of the trained CNN model, a Finite Element Method (FEM) based result of an elastically deformed nanoporous beam equipped with the CNN as constitutive law is compared with that by a full atomistic simulation. The good agreement between the atomistic simulations and the FEM-AI combination for a system with size and surface effects establishes a new lossless scale bridging approach to such problems. The trained CNN model deviates from the atomistic result by 9.6\% for porosity scenarios of up to 90\% but it is about 230 times faster than the MS calculation and does not require to change simulation methods between different scales. The efficiency of the CNN evaluation together with the preservation of important atomistic effects makes the trained model an effective atomistically-informed constitutive model for macroscopic simulations of nanoporous materials and solving of inverse problems.

cond-mat.mtrl-sci↗

arXiv2017

Mixed timestepping schemes for nonsmooth mechanics with high frequency damping

This work deals with the integration of nonsmooth flexible multibody systems with impacts and dry friction. We develop a framework which improves a non-impulsive trajectory of state variables by impulsive correction after each time-step if necessary. This correction is automatic and is evaluated on the same kinematic level as the piecewise non-impulsive trajectory. The resulting overall mixed timestepping scheme is consistent with respect to impacts and friction as well as benefits from advantages of the base integration schemes used to calculate the approximation inside the time-step. Therefore, we compare the generalized-$α$ method, the Bathe method and the ED-$α$ method.

math.NA↗