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all right now that we have done some basic definitions about the portal solid we can go ahead and try to obtain what are the equations of poor elasticity and in order to do that we will start with an analogy and this is going to be based on a non-polar solid to get started what is the internal energy of a non-polar solid if we are specifically talking about mechanics and then the internal energy is going to be the strain energy and this strain energy we can break it in two parts the part which depends on the volumetric strain for example if i had a solid i could apply a stress that makes it smaller and thats going to depend on the level of stress and the change in volumetric strain where here sm means the mean stress for example s11 plus s22 plus s33 divided by 3 and remember that this epsilon is a volumetric strain so if i want to add work to this solid i can add work by straining the solid so this is a differential amount of work okay solids also compare shear strains and shears st