 Analysis button
Material constitutive law for analysis
CivilFEM has the option of choosing the analysis type in order to define the material behavior that the program will use during the solving process. Available generic types are: Linear, Equivalent plastic strain-stress for Von Mises plasticity and Multilinear elastic analysis diagram.
Linear
The linear elastic model is the most commonly used model to represent typical engineering materials. This model, that showcases a linear relationship between stresses and strains, is represented by Hooke’s Law. The figure below shows that stresses are proportional to strains in a uniaxial tension test. The ratio of stress to strain is the familiar definition of modulus of elasticity (Young’s modulus) of the material.
E (modulus of elasticity) = (axial stress)/(axial strain)
Linear analysis has the characteristic of not limiting the strain while stresses increase.
We could say that a linear diagram does not follow the real material behavior. However, this diagram is very useful if the user wants to perform an analysis in the linear stages of the material and doesn't need a more detailed but slower non-linear calculation.
If the user does not choose a particular analysis type, CivilFEM will apply a linear analysis by default.
Equivalent plastic strain-stress for Von Mises Plasticity
Although many forms of yield conditions are available, the von Mises criterion is the most widely used. The success of the von Mises criterion is due to the continuous nature of the function that defines this criterion and its correlation with observed behavior for the most commonly encountered ductile materials.
The von Mises criterion states that yield occurs when the effective (or equivalent) stress equals the yield stress as measured in a uniaxial test.
Figure below shows the von Mises yield surface in two-dimensional and three-dimensional stress space.
For an isotropic material:
Where  and  are the principal Cauchy stresses.
For isotropic material, the von Mises yield condition is the default condition in CivilFEM.
Multilinear elastic analysis diagram
This option allows the input of simplified nonlinear elastic models that do not have a well defined strain energy function. It allows an easy representation of the behavior that is obtained in real world tests. The theory and algorithms are adequate to accurately define the stress-strain curve for the uniaxial load cases.
This is the graph that represents the material behavior in a multilinear elastic material:
The nonlinear elastic capability satisfy the equivalence of the deformation work per unit volume in the simple tension to the strain energy per unit volume, while the work done for deformation may be defined by a stress-strain curve in simple tension.
The effective strain ε may be defined ahead:
From the total differential of the above equation, the next one is obtained:
Substituting the latter in the first equation above:
The  1 parameter in the graph, correspond to the first slope for which the first elasticity module, in relation with the curve, is required. The E parameter is not a constant thorough the curve.
The  is assumed as a value from which the graph takes a constant value for σ, approaching to 0.1, the maximum value for strain.
A particularity of this analysis in a generic material is that the user must set the strain-stress diagram.
Entering values may be easily done with "Insert row" option.
| 
