Recent Development and Application of Methods in Computational Mechanics

Dear Colleagues,

Computational mechanics, a discipline of physics, mathematics, and computer science, has had a profound impact on science and technology over the past few decades. It has transformed much of the classical Newtonian theory into practical tools to predict and understand complex systems, particularly when it becomes too difficult to obtain analytical solutions in realistic conditions.

Conventional computational methods, such as the finite element method (FEM) that ensures a wide range of applications and the boundary element method (BEM) that enables a potentially more-accurate analysis when fundamental analytical solutions exist, are still popular in industrial applications. Those methods, however, suffer from some computational issues that limit the efficiency and accuracy. Thus, revision or improvement of the conventional methods is still required for more-efficient, more-accurate, and even more-general applications.

On the other hand, some new methods have been raised and developed to overcome disadvantages of the conventional methods in the recent decades. For example, the phase-field method does not need special criteria to model crack nucleation or propagation, as required by the extended finite element method (XFEM), making itself a satisfactory alternative for simulating complex fracture patterns. In addition, methods based on neural networks have attracted intensive attention in recent years, such as the physical-informed neural networks (PINNs) to solve the Buckley–Leverett problem that is notoriously challenging for conventional methods in fluid mechanics in porous media. In a word, computational methods incorporated with models based on quantum, molecular, and biological mechanics have an enormous potential for future growth and applicability.

As a result, the Special Issue concentrates on the state of the art in computational-mechanics methods, combined with other recent experiments and analytical analyses, offering a more-in-depth insight. Therefore, you are invited to submit original research papers and/or comprehenssive review articles on, but not limited to, the following topics:

1. Modern methods on modeling fracture patterns;
2. Neural-network-based methods for fluid flow in porous media;
3. Computational simulation of magnetohydrodynamics (MHD);
4. Multi-dimensional simulation of (multi-phase) fluid flow;
5. Biomedical applications of computational mechanics;
6. Revision/improvement of conventional numerical methods.

It is worth noting again that computational mechanics covers a tremendously large number of different research areas that can by no means be indicated specifically in a short summary. Authors, whose studies on computational mechanics happen not to fall in the areas mentioned above, are also welcomed to submit their work. 

Dr. Gongbo Long
Prof. Dr. Guanshui Xu
Prof. Dr. Boqi Xiao
Guest Editors

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