6 days ago · In continuum mechanics, the Cauchy stress tensor (symbol , named after Augustin-Louis Cauchy), also called true stress tensor [1] or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration.

6 days ago · The fundamental assumptions of linear elasticity are infinitesimal strains — meaning, "small" deformations — and linear relationships between the components of stress and strain — hence the "linear" in its name. Linear elasticity is valid only for stress states that do not produce yielding. Its assumptions are reasonable for many ...

Apr 18, 2025 · For understanding the mechanical behavior of a material, a stress-strain curve provides an invaluable amount of information about its strength, deformation, and rigidity. Thus, in this work we ...

5 days ago · The first part (Chapters 1-5) introduces fundamental and descriptive aspects common to all continuous media (motion, deformation, stress and conservation-balance equations).

3 days ago · 1. INTRODUCTION. Hertz [] formulated several fundamental models and principles for evaluating the force and deformation behavior at the contact point between two bodies under load.These formulas have been employed to calculate the contact response in many engineering applications. For example, Perez et al. [] utilized Hertz theory to examine the stress distribution …

Apr 18, 2025 · We explored the stress-strain behaviour and the evolution of stress and strain increment vectors at the macroscopic level, while at the microscopic level, we analyzed the mechanical coordination number (MCN), sliding contact fractions, and fabric anisotropy. The Matsuoka-Nakai failure criterion was employed to investigate friction dependency on .

4 days ago · Fracture mechanics is a field that explores how materials break under stress.Understanding fracture mechanics is crucial for engineers, scientists, and anyone interested in material science. This discipline helps predict failure in structures, ensuring safety and reliability. Fracture mechanics combines principles from physics, materials science, and …

5 days ago · Mechanical Behavior — Metals For most metallic materials, elastic deformation persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain (Hooke’s law, Equation 7.5, ceases to be valid), and permanent, nonrecoverable, or plastic deformation occurs. • Typical stress – strain behavior for a metal, …

3 days ago · First, we relate the tensor of stress auto-correlation functions to its corresponding tensor of generalized Onsager transport kernels. The relation is valid at finite wavelengths and frequencies, and serves as basis for continuum mechanics approximations, where it leads to the viscosities in a fluid and to the elastic constants in a solid.

2 days ago · Measuring stress fields in fluids and soft materials is crucial in various fields such as mechanical engineering, medicine, and bioengineering. However, conventional methods that calculate stress fields from velocity fields struggle to measure complex fluids where the stress constitutive equation is unknown. To address this, we propose a novel approach that …