USING MATHEMATICA APPLETS MADE FOR THE EDUCATION OF FAILURE CRITERIA FOR METALLIC AND GEOLOGICAL-GEOTECHNICAL MATERIALS

In matters of engineering degrees where the mechanical behaviour of material is studied, the constitutive equations of these materials are analyzed for the elastic range as for situations in which the strains generated by the actions acting begin to be permanent.

To study the combination of stresses that cause the onset of yielding at a particular point of a deformable solid, in recent decades have developed different failure criteria. For metals the main parameter to be defined is the yield strength of it. In this case the mathematical criterion that fits the actual behaviour in the onset of plasticizing a series of surfaces configured to form cylinders and / or hexagonal prisms with a certain orientation in the space defined by the principal stresses.

Likewise for geotechnical materials of geological origin, such as soil, rock or concrete, these criteria are based on the cohesion and the angle of internal friction of the material. In this case the yielding surface that defines the failure criteria in the space of principal stress tends to come represented by a hexagonal pyramid base and / or a cone with a given orientation in the space defined by the principal stresses, so verifying that the behaviour of these materials is much higher compression than in tension.
To bring students to understand graphically the behaviour of the different classical stress levels, such as plane stress and / or plane strain, we have developed a range of applications in Mathematica code. These applications allow the student to see graphically the surface geometry finally generated after the intersection between different boundary conditions of the problem: ellipse, parabola, hexagon, etc.., Once the variables are selected to modify the problem by using a slider to change the Poisson ratio, modulus of elasticity, yield strength, cohesion or internal friction angle in the case.

They also allow an understanding of the evolution of three-dimensional stresses in elastic regime (in the volume enclosed by the surface) or under plastic (on it) in different configurations and problems under static or kinematic conditions that govern this evolution.

Similarly this set of applets to compare the approximation criteria and others to the same family of materials simply by varying the scroll bar the defining characteristics of the student can immediately see graphically how changes each of these surfaces.
These tools developed for the subject of Continuum Mechanics of Engineering degree in Caminos Canales y Puertos (Master or Civil Engineering) at the University of Alicante, have greatly favoured the approach of students to the influence of the parameters that define the failure criteria for the behaviour of materials.