Classification of Constitutive Equations for Dissipative Materials—General Review

2023

Materials

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.

Section: Introductionmentioning

confidence: 99%

Energy Equivalence Based Estimation of Hybrid Composites Mechanical Properties

Wiśniewska

2023

Materials

“…The need for homogenization is due to the fact that although the components of the composite are most often homogenous, the final composite material is heterogeneous. The approach of mechanical equivalence between the real and fictitious material configurations, typically applied in continuum damage mechanics issues [1] was lately broaden to a general multi-dissipative material modelling by Egner and Ryś [2,3,4]. This method allows us to describe both the elastic and plastic behaviour of the material, thanks to the use of the framework of thermodynamics of irreversible processes with internal state variables.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Functionally Graded Structural Members by Means of New Effective Properties Estimation Method

Wiśniewska

2019

Materials

An innovative method of effective composite mechanical properties estimation is applied to optimize the distribution of reinforcement in a functionally graded structural element. The concept is based on the assumption of the mechanical equivalence between two configurations: The real heterogeneous composite configuration and the fictitious quasi-homogeneous one. It allows to obtain the analytical formulae describing the dependence of the effective elastic composite properties on the volume fraction of reinforcing inclusions. As an example of application, a circular bar subjected to torsion is considered.

“…where r k corresponds to isotropic expansion of the yield surface, k ij affects translatoric displacements of the yield surface, l k ijpq is a hardening tensor of the fourth order which includes varying lengths of axes and rotation of the yield surface, and g k ijpqmn describes changes of the curvature of the yield surface (distortion) related to kth dissipative phenomenon (cf. Egner and Egner, 2015;Kowalsky et al, 1999). ð…”

Section: Introductionmentioning

confidence: 99%

Total energy equivalence in constitutive modeling of multidissipative materials

International Journal of Damage Mechanics

Ryś

2016

In the present work, the total energy equivalence hypothesis was applied in constitutive modeling of engineering materials. The approach originally developed for damaged materials, was extended to modeling not only damage but also other dissipative phenomena, like phase transformation, in a consistent manner. The proposed model was examined by means of parametric studies to show its ability to reflect different experimentally observed features of real materials.