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New micromechanical model in time domain for linear viscoelastic composites with ellipsoidal reinforcements

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Abstract

An innovative micromechanical approach developed directly in the time domain is presented for aging linear viscoelastic heterogeneous materials. The viscoelastic behavior is described by a relaxation kernel of a Volterra integral type. Using the technique of Green's function, a new integral formulation is developed to obtain two integral equations in the heterogeneous viscoelastic problem. Applying the inclusion Eshelby model, a new concentration equation gives the average strain of the inclusion. The model presents the exact solution of the strain field for anisotropic aging viscoelastic ellipsoidal inclusion embedded in an isotropic aging viscoelastic matrix. The model is evaluated by comparisons with the existing results of the literature, either analytically or numerically. The effective relaxation behavior of a two-phase composite is obtained using a Mori-Tanaka homogenization scheme. The shape effect and the viscoelastic behavior of inclusion are analyzed to illustrate the method's capabilities providing time-domain accurate numerical results with reduced processing time and no large memory space for numerical computing.

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The authors are grateful to the French Ministry of Higher Education for financial supports.

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  1. Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, 57000, Metz, France

    Florence Dinzart, Luan Mayk Torres-Costa & Hafid Sabar

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  1. Florence Dinzart
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Dinzart, F., Torres-Costa, L.M. & Sabar, H. New micromechanical model in time domain for linear viscoelastic composites with ellipsoidal reinforcements. Acta Mech 233, 2009–2029 (2022). https://doi.org/10.1007/s00707-022-03208-4

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