We are going to consider the forces exerted on a material. These can be external or internal. External forces come in two flavors: body forces(given per unit mass or volume) and surface forces(given per unit area). If we cut a body of material in equilibrium under a set of external forces along a plane as shown in fig. 1. and consider one side of it we draw two conclusions: 1 the equilibrium provided by the loads from the side taken out is provided by a set of forces that are distributed among the material particles adjacent to

A Cauchy stress component at a given(fixed) point P of a structure in equilibrium under the action of external loads is defined when 1. the direction of the face on which the stress component acts is specified 2 the direction of the force from which the stress component is derived is specified None of the above statements

The following expression is the right statement of linear momentum balance for a deforming body of an arbitrary material

We seek to characterize the local state of deformation of the material in a neighborhood of a point P. Consider two points P and Q in the undeformed

For the uniform state of plane strain shown in the fig ure,which one(s) of the following statement(s) is(are valid?(Assume Poisson's ratio v+0)

The following stress-strain curves were obtained for dif- ferent materials subjecting the specimen to the loading path(a, b, c, d ). Which one(s) of them correspond to elas- tic material(s)

which generalizes to the statement. This reduces the number of material constants from 81 to 54. In a similar fashion we can make use of the symmetry of the strain tensor This further reduces the number of material constants to 36. To further reduce the number of material constants consider the conclusion from the first law for elastic materials, equation

How can the paradox with the spring be plained? In other words, which of the following statements is true 1. Equilibrium can be derived from the equiv alence of the external and the internal work 2. Equilibrium is an artifact of our imagina- tion

Which of the following expressions most ac curately and simply represents the comple mentary strain energy density Uc of a linear elastic material?

Unit #10- Principle of minimum potential energy and Castigliano's First Theorem Principle of minimum potential energy The principle of virtual displacements applies regardless of the constitutive law. Restrict attention to elastic materials(possibly nonlinear). Start from the Pvd