In materials science, microstructure evolution plays a central role in understanding and predicting the behavior of materials under different conditions. The development of the microstructure is often subject to certain constraints. A classic example of such a constraint is volume conservation during plastic deformation in the context of elasto-plasticity. Within the talk, two principles are compared for the imposition of constraints in evolution equations: the principle of maximum dissipation with respect to the stresses and the principle of the minimum of the dissipation potential with respect to the rate of thermodynamic state variables, which can be derived from a Hamiltonean principle. These principles serve as a basis for the formulation of material models that describe the internal structure and the reaction of materials to external influences. The principle of maximum dissipation provides the most energetically unfavorable form of stress distribution, while the principle of minimum dissipation seeks the most energetically efficient rate of change of the state variables. In general, a discretization has to be applied for the numerical implementation of material models. Frequently, the discretization does not pay sufficient attention to the exact fulfillment of the constraints, which can severely limit the robustness and accuracy of the resulting model. Discretizations that guarantee compliance with the constraints, such as the exponential map, are often complex and challenging to implement. However, the principle of minimum dissipation illustrates that it is generally possible to fulfill constraints precisely with more simple time derivatives via the method of Lagrange multipliers. Using the example of finite elasto-plasticity, a volume-preserving time integration method based on backward Euler is presented.