The paper discusses the effort carried out at VNIIEF to consider the applicability of unstructured Lagrange meshes to multidimensional continuum mechanics problems with high shear strain and vortex flows. Three finite-difference numerical techniques for solving continuum mechanics problems on polyhedral unstructured Lagrange meshes are described. Examples of numerical calculations of benchmark ...

1. Basic Results in Continuum Mechanics 1.1. Kinematics 1.2. Stress Tensors and Balance of Momenta 1.3. Energy Balance Principle and Entropy Inequality 1.4. Fundamental Principles of Constitutive Models 2. Elastic and Hyperelastic Materials 2.1. Isotropic Hyperelastic Materials 2.2. Constitutive Models for Fiber-Reinforced Hyperelastic Materials 2.3. Examples of Numerical Applications 3. Elasto...

Abstract In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between product of area and unit normal vectors relevant corresponding surfaces in two configurations 3D body. A geometric treatment provides equivalent expressions formula by direct elaborations on Euler – Jacobi volume change formula. Meaning limits are underlined. liter...