Formulation of the model suitable for the description of the full material deformation diagram is considered, with axial compression applied, and a loosening component added to elastic and plastic deformation. The materials involved are initially heterogeneous environments like rocks and artificial construction materials, like concrete. Such materials, being in a stationary state, stable for small disturbances, can be interpreted as dissipative structures after the limit of elasticity is reached. The deformation and destruction processes are analysed as instability hierarchy, resulting from self-organization. Methods of mathematical catastrophe theory are applied for the model construction. The energy state function is presented as the sum of the potential function, responsible for reversible deformations and disturbances. The latter involves an imperfection parameter (a controlling one), connected with damageability and responsible for the structurization process. The state equation is obtained by energy function minimization on the order parameter and is supplemented with the kinetic equation for the imperfection parameter. The synergetic methods are shown to be advantageous for the problems of formulating physically well-grounded nonlinear defining equations.