User Tianyikillua was very kind to give me some insight into this problem but I am posting it here for further comments. The UFL below is taken from Solid Mechanics chapter of Fenics book. The linear form 'L' in row 22 is weak form of linear elasticity. But what exactly do they mean when they use a = [ C . ε(u) : ε(w) ] dx in row 21. The step is related to linearisation and utilises the linearised elastoplastic tangent with strain but what exactly does it stand for and is it described/derived explicitly in any document? I need to understand this so I can extend this variational form to apply for wave equation.
