Now more specifically the Jacobian, which is short for the Jacobian Matrix Determinate, is really the best measure of finite element mesh quality. It is one number which defines how good or bad an element is. The Jacobian is a measure of the normals of the element faces relative to each other. Unfortunately, Hypermesh does not show the element face normals on solid elements, but it is basically an arrow on each face pointing out perpendicular to the face. The range of a Jacobian is from 1, a perfect cube, to something lower, -1 or even lower. The smallest Jacobian I have seen was -1.45. When the element face normals start to cross, that is they are not perpendicular to each other, your element quality gets worse.
For several examples I created the image below. In all of the elements, except for the red one, I simply translated one node (vertex) to a new location and kept the other seven in the original cube positions. You can see that as the node moves farther away from the cube position the element quality gets worse.
How bad is bad? Abaqus will not run a job with a Jacobian below 0, at least not for me. Ansys on the other hand has less strict mesh quality requirements. Often times Abaqus will not run a solid element Jacobian below 0.2 and a shell element Jacobian below 0.3. And yes, I have had one element with a negative Jacobian prevent an Abaqus job with over 100,000 elements from running. If you can get all of the Jacobians in your model above .5 you can typically say you have a good quality mesh.
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