Hydrostatic stress
Encyclopedia
In continuum mechanics
, a hydrostatic stress is an isotropic stress that is given by the weight of water above a certain point. It is often used interchangeably with "pressure
" and is also known as confining stress, particularly in the field geomechanics. Its magnitude
can be given by:
where
is an index denoting each distinct layer of material above the point of interest, 
is the density
of each layer,
is the gravitational acceleration
(assumed constant here; this can be substituted with any acceleration
that is important in defining weight
), and
is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would be
where the index
indicates "water".
Because the hydrostatic stress is isotropic, it acts equally in all directions. In tensor
form, the hydrostatic stress is equal to
where
is the 3-by-3 identity matrix
.
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...
, a hydrostatic stress is an isotropic stress that is given by the weight of water above a certain point. It is often used interchangeably with "pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
" and is also known as confining stress, particularly in the field geomechanics. Its magnitude
can be given by:where
is an index denoting each distinct layer of material above the point of interest, is the densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of each layer,
is the gravitational accelerationGravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....
(assumed constant here; this can be substituted with any acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
that is important in defining weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...
), and
is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would bewhere the index
indicates "water".Because the hydrostatic stress is isotropic, it acts equally in all directions. In tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
form, the hydrostatic stress is equal to
where
is the 3-by-3 identity matrixIdentity matrix
In linear algebra, the identity matrix or unit matrix of size n is the n×n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context...
.