A numerical boundary integral equation analysis for standard linear viscoelastic media made of functionally graded materials

Abstract

Background: Although structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures. Methods: In the present paper, a 2D boundary element formulation capable of modeling time-dependent functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity in terms of the displacements is developed to solve 2D problems of the exponentially graded viscoelasticity. The FGM concept can be applied to various materials, for structural and functional purposes. In this model, only Green functions of the nonhomogeneous elastostatic problems are needed with material properties that vary continuously along a given dimension. Results and Conclusions: Results reveal that the boundary element approach can successfully be employed for the present complicated problem for arbitrary time histories of the applied loads and arbitrary boundary conditions, without the need to use relaxation functions or mathematical transformations.

Glucose‐derived superabsorbent hydrogel materials based on mechanically‐interlocked slide‐ring and triblock copolymer topologies

“…The hydrogels were tested directly after gelation without undergoing any drying/rehydration processes 82 . The indentation studies were performed with the load functions: approaching with 2 μm/s in 5 s, loading with 5 μm/s in 20 s, holding with 0 μm/s in 180 s, unloading with −5 μm/s in 20 s, and retracting with −2 μm/s in 5 s. The samples were analyzed using a load relaxation model which was usually used for biphasic samples containing a liquid phase suspended in a solid matrix (e.g., water swollen in polymer networks) 83 . As expected, ABA/PR hydrogel synthesized at a higher concentration shows a greater slope in the force‐displacement curve (Figure 6D).…”

Delamination fracture analysis of an elastic-plastic functionally graded multilayered beam

“…Functionally graded materials are new composites developed in the last 30 years (Ashrafi and Shariyat 2014;Bohidar et al 2014;Butcher et al 1999;Gasik 2010;Hirai and Chen 1999;Ivanov and Stoyanov 2011;Lu et al 2009;Maganti and Nalluri 2015;Mohammadiha and Ghariblu 2016;Mortensen and Suresh 1995;Nemat-Allal et al 2011;Neubrand and Rödel 1997;Suresh and Mortensen 1998). They are made by mixing of two or more material constituents in different ratios in different parts of a structural member in order to get optimum performance to external loads.…”