Plane stress | EPFL Graph Search

In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 (representable as a 2×2 matrix rather than 3×3). A related notion, plane strain, is often applicable to very thick members. Plane stress typically occurs in thin flat plates that are acted upon only by load forces that are parallel to them. In certain situations, a gently curved thin plate may also be assumed to have plane stress for the purpose of stress analysis. This is the case, for example, of a thin-walled cylinder filled with a fluid under pressure. In such cases, stress components perpendicular to the plate are negligible compared to those parallel to it. In other situations, however, the bending stress of a thin plate cannot be neglected. One can still simplify the analysis by using a two-dimensional domain, but the plane stress tensor at each point must be complemented with bending terms. Mathematically, the stress at some point in the material is a plane stress if one of the three principal stresses (the eigenvalues of the Cauchy stress tensor) is zero. That is, there is Cartesian coordinate system in which the stress tensor has the form For example, consider a rectangular block of material measuring 10, 40 and 5 cm along the , , and , that is being stretched in the direction and compressed in the direction, by pairs of opposite forces with magnitudes 10 N and 20 N, respectively, uniformly distributed over the corresponding faces. The stress tensor inside the block will be More generally, if one chooses the first two coordinate axes arbitrarily but perpendicular to the direction of zero stress, the stress tensor will have the form and can therefore be represented by a 2 × 2 matrix, Hooke's law#Plane stress In certain cases, the plane stress model can be used in the analysis of gently curved surfaces.

Experimental and ab initio derivation of interface stress in nanomultilayered coatings: Application to immiscible Cu/W system with variable in-plane stress

Pandula Manura Liyanage, Claudia Cancellieri, Giacomo Lorenzin

Interface stress is a fundamental descriptor for interphase boundaries and is defined in strict relation to the interface energy. In nanomultilayers with their intrinsically high interface density, the functional properties are dictated by the interface st ...

Elsevier2024

Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution

Tobias Kippenberg, Alberto Beccari, Nils Johan Engelsen

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by f ...

Berlin2024

Shearing and opening of a pre-existing discontinuity in response to fluid injection

Brice Tanguy Alphonse Lecampion, Ankit Gupta, Alexis Alejandro Sáez Uribe

We investigate the fluid-driven growth of a shear crack along a frictional discontinuity and its transition to hydraulic fracturing (sometimes referred to as hydraulic jacking) under plane-strain conditions. We focus on the case of a constant friction coef ...

2023