Differential equation of equilibrium:
In Moldex3D Stress analysis, the following assumptions are made:
(1) The materials of parts are linearly elastic
(2) The strains and displacement are small
(3) The behavior of structure is static and linear
The behavior of a material is said to be linearly elastic when the strain is linearly proportional to the stress, and the geometry would return to its undeformed state when the loads are removed.
Under the above conditions, the following governing equilibrium equations are used:
σij, j + fi = 0
where σij denotes the stress components and fi is the body force.
Material constitutive models:
For linearly elastic materials, stress is proportional to the strain which is indicated below,
σij = cijklεkl
where cijkl denotes the elastic constants and εij is the strain components.
The above equation is an approximation of stress that is valid as the strain quantity is located within the elastic range. The above relation is known as the constitutive equation. Different types of materials will have different forms of constitutive equations as explained in the following.