Effective Properties of Composite Material Based on Total Strain Energy Equivalence

Wiśniewska, Anna; Hernik, Szymon; Egner, Halina

doi:10.1007/978-3-030-34851-9_11

Cited by 1 publication

(5 citation statements)

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“…From among several physical quantities (strain, stress, elastic strain energy, etc. ), the equivalence of the total strain energy between the real composite configuration and the fictitious quasi-homogeneous configuration is here assumed, which allows determining not only elastic mechanical properties but also inelastic parameters [ 43 ].…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…The total strain energy equivalence (TEE) hypothesis can be described as follows [ 38 , 39 , 42 , 43 , 44 ]:…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Taking into account Equations (2) and (5) and the Hooke law, the elastic stiffness tensor

takes the following form, dependent on the matrix stiffness tensor

and the inclusions volume fraction

[ 38 , 42 , 43 ]:

…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…By the use of the total strain energy equivalence hypothesis, the elastic stiffne sor 𝐸 (𝜉) of a composite material results from the equivalence between elastic energies: 𝑈 = 𝜎 𝜀 = 𝜎 𝜀̃ , Taking into account Equations (2) and ( 5) and the Hooke law, the elastic st tensor 𝐸 (𝜉) takes the following form, dependent on the matrix stiffness tensor 𝐸 and the inclusions volume fraction 𝜉 [38,42,43]:…”

Section: 𝜉 = 𝑑𝑉 𝑑𝑉mentioning

confidence: 99%

“…Additionally, the concentration factors were derived and compared with other homogenization methods, and an optimization problem of an FGM shaft was analyzed with the use of the proposed estimation method. The extension of the method for inelastic material properties of two-component isotropic composites was presented in [ 43 ].…”

Section: Introductionmentioning

confidence: 99%

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Energy Equivalence Based Estimation of Hybrid Composites Mechanical Properties

Wiśniewska

Egner

2023

Materials

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Hybrid composites, usually combining natural and synthetic reinforcing filaments, have gained a lot of attention due to their better properties than traditional two-component materials. For structural applications of hybrid composites, there is a need to precisely determine their mechanical properties on the basis of the mechanical properties, volume fractions, and geometrical distributions of constituent materials. The most common methods, such as the rule of mixture, are inaccurate. More advanced methods, giving better results in the case of classic composites, are difficult to apply in the case of several types of reinforcement. In the present research, a new estimation method is considered, which is simple and accurate. The approach is based on the definition of two configurations: the real, heterogeneous, multi-phase hybrid composite configuration, and the fictitious, quasi-homogeneous one, in which the inclusions are “smeared out” over a representative volume. A hypothesis of the internal strain energy equivalence between the two configurations is formulated. The effect of reinforcing inclusions on the mechanical properties of a matrix material is expressed by functions of constituent properties, their volume fractions, and geometrical distribution. The analytical formulas are derived for an isotropic case of a hybrid composite reinforced with randomly distributed particles. The validation of the proposed approach is performed by comparing the estimated hybrid composite properties with the results of other methods, and with experimental data available in the literature. It is shown that a very good agreement is obtained between experimentally measured hybrid composite properties and their predictions resulting from the proposed estimation method. The estimation errors are much lower than the errors of other methods.

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Section: Theoretical Formulationmentioning

confidence: 99%

“…The total strain energy equivalence (TEE) hypothesis can be described as follows [ 38 , 39 , 42 , 43 , 44 ]:…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Taking into account Equations (2) and (5) and the Hooke law, the elastic stiffness tensor

takes the following form, dependent on the matrix stiffness tensor

and the inclusions volume fraction

[ 38 , 42 , 43 ]:

…”

Section: Theoretical Formulationmentioning