6 Bipolar Electrochemistry for Synthesis

Bipolar electrochemistry has gained remarkable interest in recent years, especially in the fields of materials science and organic electrosynthesis. This is due to the interesting features of this particular electrochemical technology, such as the contactless nature of the electrochemical reactions, the use of low concentrations of supporting electrolytes, and the synergetic action of electrophoresis and electrolysis. In this chapter, the most important contributions regarding bipolar electrochemistry for the electrosynthesis of novel functional materials are reviewed. These contributions include the most traditional industrial applications and bipolar reactors for electroorganic synthesis, as well as innovative approaches for the fabrication of anisotropic materials and gradient surfaces. The peculiar characteristics of bipolar electrochemistry in these fields are emphasized.

Identification of the parameters of the quadratic model of the elastic anisotropic material

Рассмотрена модель упругости второго порядка для ортотропного материала. Проведенный анализ показывает, что квадратичная часть предложенной модели содержит тринадцать упругих постоянных, из которых девять являются линейно независимыми. Параметры модели определены по данным экспериментов с композитными пластинами. Модель позволяет описывать наблюдаемые в экспериментах нелинейные зависимости между напряжениями и деформациями в процессах растяжения, сжатия и сдвига, а также разносопротивляемость анизотропных материалов. A second-order elasticity model for an orthotropic material is considered. The analysis shows that the quadratic part of the proposed model contains thirteen elastic constants, nine of which are linearly independent. The parameters of the model are determined from the data of experiments with composite plates. The model allows one to describe experimentally observed nonlinear dependences of stresses and strains in the processes of tension, compression, and shear, as well as the difference in resistance of anisotropic materials.

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the $$C^1$$ C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of $$C^1$$ C 1 -continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for $$C^0$$ C 0 -continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these $$C^1$$ C 1 -continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.