Advancements in Computational Mechanics of Solids

The field of computational mechanics of solids is witnessing significant advancements, driven by the development of innovative numerical methods and techniques. A key direction of research is the improvement of finite element methods for analyzing complex phenomena, such as crack-tip fields and damage initiation in composite materials. Notably, researchers are exploring the use of nonlinear constitutive relationships and modified boundary conditions to enhance the accuracy and robustness of simulations. Another area of focus is the development of adaptive finite element methods, which can efficiently refine meshes to capture localized features and improve the overall accuracy of solutions. The integration of computational methods with computer-aided design (CAD) tools is also gaining traction, enabling the creation of more realistic and efficient models for complex systems. Noteworthy papers in this area include: The paper on computational investigation of crack-tip fields in a compressed nonlinear strain-limiting material, which presents a significant advancement in the formulation of boundary value problems for complex scenarios. The paper on the Hu-Zhang element for linear elasticity on curved domains, which extends the Hu-Zhang element to curved domains while preserving strong symmetry and H(div)-conformity.

Sources

Computational investigation of crack-tip fields in a compressed nonlinear strain-limiting material

Representative Volume Element: Existence and Extent in Cracked Heterogeneous Medium

Optimality of adaptive $H(\operatorname{div}\operatorname{div})$ mixed finite element methods for the Kirchhoff-Love plate bending problem

Isogeometric multi-patch shell analysis using the Geometry + Simulation Modules

The Hu-Zhang element for linear elasticity on curved domains

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