What is meant by stress tensor?
The Stress Tensor Stress is defined as force per unit area. If we take a cube of material and subject it to an arbitrary load we can measure the stress on it in various directions (figure 4). These measurements will form a second rank tensor; the stress tensor.
What are stress invariants?
Stress invariants are the properties of a stress matrix that are unaffected by transformation. Stress state can be represented in terms of a matrix. Hydrostatic stress component of this matrix would be equal to the average of the diagonal terms of the matrix (Principal stresses).
What is 2D stress analysis?
Plane stress analysis is the 2D stress state that is usually covered in undergraduate courses on mechanics of materials. It is based on a thin flat object that is loaded, and supported in a single flat plane. There are two normal stresses and one shear stress component at each point (σx, σy, and τ).
What are strain invariants?
Strain invariants Certain operations on the strain tensor give the same result without regard to which orthonormal coordinate system is used to represent the components of strain. The results of these operations are called strain invariants.
Why stress is second order tensor?
The stress state is a second order tensor since it is a quantity associated with two directions. As a result, stress components have 2 subscripts. A surface traction is a first order tensor (i.e. vector) since it a quantity associated with only one direction.
What are the types of stress tensor?
Stress tensor
- Cauchy stress tensor, in classical physics.
- Stress deviator tensor, in classical physics.
- Piola–Kirchhoff stress tensor, in continuum mechanics.
- Viscous stress tensor, in continuum mechanics.
- Stress–energy tensor, in relativistic theories.
- Maxwell stress tensor, in electromagnetism.
What are stress invariants and why are they called invariants?
Stress values will be different if we change the coordinate system but stress tensor also has so called stress invariants. These are the quantities that are independent on the orientation of the coordinate system.
Do stress invariants have units?
The SI units of both stress tensor and traction vector are N/m2, corresponding to the stress scalar. There are certain invariants associated with the stress tensor, whose values do not depend upon the coordinate system chosen, or the area element upon which the stress tensor operates.
Why do solid elements have 3 DOF?
Solid elements have 3 degrees of freedom per node. Solids only support translational (DOFs) at each node. Therefore, moments cannot be applied to solids directly. A moment acts on the rotational degrees of freedom.
What are 2D elements?
2D elements are three- or four-node elements that must be formulated in the YZ plane. They are used to model and analyze objects such as bearings or seals, or structures such as dams. These elements are formulated in the YZ plane and have only two degrees-of-freedom defined: the Y translation and the Z translation.
What are small strains?
In mechanics of solids: Strain and strain-displacement relations. …to this situation, are called small strain or infinitesimal strain. Expressions for strain will also be given that are valid for rotations and fractional length changes of arbitrary magnitude; such expressions are called finite strain.