•Functionally graded materials (FGM) beams under bilateral constraints•Experimental testing and theoretical and numerical validations•Systemic study on the influences of geometric and material ...parameters•Material topology for optimization of material functions
In recent years, the study of Functionally graded materials (FGM) opened exciting new venues for the control and manipulation of engineered materials and structures. In this study, we investigate bilaterally constrained FGM beams with programmable material functions. The FGM beams are fabricated using 3D printing techniques, and tested t understand the behavior of structural instability (i.e., postbuckling) under the bilateral confinements. Theoretical and numerical models are developed to investigate the postbuckling response, and the results are compared to experimental observations with satisfactory agreements. Material topology optimization is then carried out to investigate the influences of the material functions on the release of the stored energy during the bucking mode transitions in the FGM beams. It is found that stored energy variations can be used to optimize the material functions, which allows for the guided design of bi-walled FGM beams with well-defined controllability over the structural instability. The reported bilaterally constrained FGM beams with optimized material functions can be used in a multitud of different applications.
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In the framework of integral constitutive relations for linear isotropic viscoelastic media with difference-type kernels in the case of a non-relaxing volume, we propose possible experimental setups ...for determining the kernels of the Ilyushin operators
, supplementing the known methods. One of them is based on the use of a sample of an auxiliary viscoelastic solid, the material functions of which are related to the creep function and bulk modulus of the initial material. Similar schemes of the experimental setup are also proposed for finding the kernels of the operators
, which are conjugate to
in a certain sense.
A class of constitutive relations is considered that connect symmetric stress and small strain tensors in three-dimensional space using an isotropic potential tensor nonlinear function of a rather ...general form. Various definitions of tensor nonlinearity are given and their equivalence is shown. From the standpoint of the mathematical apparatus of the theory of tensor nonlinear functions, the interpretation of the Poynting effect known in experimental mechanics and similar phenomena has been carried out. It is proved that these effects are not necessarily the result of the tensor nonlinearity of the defining relations, but may be due to the dependence on one of the material functions on the quadratic invariant, which is absent, for example, in the physically linear case. From here conclusions are drawn about the order of smallness of these effects. The possibility of modeling the Poynting effect by tensor-linear defining relations is discussed.
In the theory of constitutive relations, isotropic quadratic nonlinear tensor functions modeling media with second-order effects, in particular, with misalignment of the force and kinematic tensors, ...are considered. It is very interesting to consider tensor functions with a scalar potential relating two symmetric deviators of rank two. In this case, the potentiality conditions are integrated, and it is shown that the first integral contains two arbitrary functions of the quadratic invariant of the tensor argument and one arbitrary function of the cubic invariant. A tensorially nonlinear generalization of the rigid-viscoplasticmodel (a two-contact Binghamsolid) is carried out.
This paper deals with the development and application of a three-dimensional material model for the simulation of early-age cracking of concrete. The starting point is the determination of the ...intrinsic material function for the fracture energy of early-age concrete. For this purpose, results of beam bending tests reported in Proceedings of the SEM/RILEM International Conference on Fracture of Concrete and Rock. Houston, Texas, USA: 1987. p. 409 are employed. The intrinsic material function serves as input for the calibration of the Rankine fracture criterion formulated in the framework of chemoplasticity. Finally, the developed 3D material model is employed for a chemomechanical analysis of a roller-compacted-concrete dam. The temperature fields and the field of the degree of hydration required for this analysis are obtained from a preceding thermochemical analysis of the dam.
The mathematical model proposed earlier by the author for materials tensor which is due to nonlinearity of plastic changes, loss of the internal relations and the accumulation of damage to the ...structure, shows the consent of the theory with experimental data, for example, gray cast iron. The model was not able to accurately reflect the peculiarity of aluminum and other materials, which are anomalously high values of the ratio of the transverse deformation at plastic strength. Mentioned alloys currently attract the attention of many scientists who give with the help of metallographic analysis convincing evidence of the fact that internal processes include mechanisms "self-healing " defects.The objective is to improve the original model for gelatinous plastic materials. The analysis of experimental researches have shown that the tensor nonlinearity these environments attributed to the strong dependence of the volume deformations and medium voltage, as the level of strain and stress. For their description from the original equations (Reiner) already allocated other equations for dilatancy. The latter, as a component of the volumetric strain, can be both positive and negative. This preserves the nonlinear coupling between the deviators. For more accurate descriptions of all the strains and stresses imposed additional options, since the dependence of the main characteristics and dilatancy of stress vary significantly. The material functions and all constants are defined makroelementa.It is shown that the parameter characterizing the process of self-organization patterns, is rapidly increasing function of the deformation. Changes also mean stress, reflecting the nonlinear growth of the number of additional connection with the decrease in volume deformations. It is possible to assume that such behavior of dilatancy in strain, close to destroy, can cause loss of balance between the dissipative process and the process of its self-organization and outwardly manifested, "running necks". The development of this theme can be not only useful for specialists dealing with the physics internal structural processes accompanying the plastic deformation, but also to attract achieve physicists on improvement of the developed model.
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