A familiar example of the elastic behavior of solids is the spring. Whether it is a coil, a bending beam or some other configuration, it is designed to move a prescribed amount for a given force and return to their original configuration when the load is removed. Another property that is not as obvious is that most materials expand in size as they are heated. If you bond two materials together that expand at different rates and heat or cool the resulting composite object, it will bend to accomodate the different thermal shape change or strain. Many temperature switches use this bimetallic strip concept. Elasticity and thermal expansion are two of the primary solid mechanics phenomena that are modeled by the Truchas code.

The field of solid mechanics describes the way that solid bodies deform when they are subjected to forces. These forces may result from external loads, gravitational acceleration or changes in volume when a material changes temperature. The equations to describe three dimensional elastic behavior were developed in the first half of the 19th century. Plastic deformation is one type of deformation that does not reverse when the load is removed. For example, if you bend a paper clip or wire coat hanger far enough, it does not return to its original shape. Plasticity theory has been developed continuously since the mid 19th century. In order to solve the equations of elasticity and plasticity for arbitrarily shaped objects modern computer technology is required.

The solid mechanics capability in the TRUCHAS code calculates stresses and distortion in solid parts that result primarily from differences in temperature. Processes such as casting and welding involve high temperatures and large differences in temperature from one point to another. The resulting stresses are large enough to produce elastic and plastic deformation. The stresses and distortions that result from casting or welding are very important because they can lead to manufacturing problems such as material failure or shapes that do not meet tolerances. To model this behavior, TRUCHAS includes small strain elastic and plastic material behavior, volume changes caused by thermal expansion or solid state phase changes and small displacement contact between solid bodies.

The contact algorithm in TRUCHAS allows small sliding displacements and gaps at interfaces between solid bodies. As a casting cools inside the mold, it will generally contract or expand at different rates than the mold. The model must allow relative movement between the parts to accurately model the displacements and stresses. A contact algorithm is a necessary capability for modeling complex assemblies for casting. heat treatment and welding.