Thiebaud Richeton - Stress partitioning and effective behavior of N-phase laminates in anisotropic elasticity from a fast explicit method

jtcam:8506 - Journal of Theoretical, Computational and Applied Mechanics, March 30, 2022 - https://doi.org/10.46298/jtcam.8506
Stress partitioning and effective behavior of N-phase laminates in anisotropic elasticity from a fast explicit method

Authors: Thiebaud Richeton

In this work, a fast explicit method, easy to implement numerically, is proposed in order to compute the effective behavior and the distribution of stresses in a general N-phase laminate made of parallel, planar and perfectly bonded interfaces. The solutions are exact for a homogeneous far-field loading and work for an arbitrary number of phases, a general linear anisotropic elasticity, as well as different uniform thermal and plastic strains in the phases. A simple direct analytical formula is also derived to compute the stress in a given phase once the effective behavior of the laminate is known. Moreover, the correctness of the proposed method is checked by comparisons with finite element simulation results on a same boundary value problem, showing excellent agreements. An application of the method is performed for a near-β titanium alloy with elongated grains, by comparing the level of internal stresses for different elastic loadings within a N-phase laminate made of 100,000 orientations and a 2-phase laminate of equal volume fraction with maximal elastic contrast. Interestingly, the maximum von Mises stress of the 2-phase laminate is always the lowest, which is explained by a volume fraction effect. Finally, comparisons with elastic self-consistent models considering oblate spheroidal grains of different aspect ratios are performed.


Published on: March 30, 2022
Accepted on: February 14, 2022
Submitted on: September 20, 2021
Keywords: laminate,anisotropic elasticity,incompatibility stresses,effective behavior,composite structure,[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph],[SPI.MAT]Engineering Sciences [physics]/Materials,[PHYS.MECA]Physics [physics]/Mechanics [physics]


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