Damage Modeling

It is our responsibility as engineers to design structures safely and economically while providing the necessary functionality and serviceability. Be it buildings, airplanes, cars, machines, or even furniture, several external and internal factors shall be taken into account during the design process, in order to ensure a safe and prolonged service life of the structure. External factors are determined by the surrounding, such as the loads a structure is supposed to resist and the maximum deformations it is allowed to undergo for it to retain its functionality. A bridge, for example, shall resist traffic, seismic, wind, and dead loads while not exhibiting excessive vibrations and being able to expand and contract without cracking. On the other hand, internal factors are those that are inherent to the structure such as its geometry, material, and imperfections. These internal inherent factors determine how the structure responds to external loads. For instance, a beam made of steel would behave differently from a geomtrically identical beam made of reinforced concrete.

In order to optimize the design of structures, the material characteristic changes as a function of external ones (cyclic loading, impact, material imperfections...) shall be handled more explicitly. By doing so, we can better understand the structural response of the structure over time. Not only that, but we can also predict and prevent failure. Structural failure is a result of material failure. It generally starts locally, as a crack or cavity, and expands until it causes complete failure.

There exists different techniques to model failure. The major ones are fracture mechanics, eigenerosion, phase-field, and damage mechanics. Each of these approaches has its own advantages and disadvantages. In damage modelling, the underlying system of differential equations becomes ill-posed due to the material softening behaviour introduced. Therefore, a unique solution doesn't exist and remedies are required. The remedy of such ill-posedness problem comes in the form of regularization. Different regularization techniques exist such as viscous regularization, integral formulation and gradient-enhanced. In general, damage modelling is a numerically demanding process.

At the institute of continuum mechanics we seek new approaches for modelling damage in order to reduce the numerical effort, as well as model complicated structural elements such metal billets formed of different types of metals.

The neighbored element method for damage processes at large deformations

The developed damage model was extended for the treatment of hyperelastic material subjected to large deformations. Along with the model derivation, a technique for element erosion in the case of severely damaged materials was also developed. Numerical results showed convergence for different mesh sizes and increasing regularization parameter. Efficiency and robustness of the approach is demonstrated by numerical examples including snapback and springback phenomena.

Led by: P. Junker

Year: 2021
The neighbored element method for damage processes

Damage processes are modeled by a softening behavior in a stress/strain diagram. This reveals that the stiffness loses its ellipticity and the energy is thus not coercive. The underlying partial differental equation wouldn't have a unique solution and the numerical implementation of such an ill-posed problem yields results that are strongly dependent on the chosen spatial discretization. Consequently, regularization strategies have to be employed that render the problem well-posed. A prominent method for regularization is a gradient enhancement of the free energy. This, however, results in field equations that have to be solved in parallel to the Euler-Lagrange equation for the displacement field. Therefore the number of degrees of freedom (unknowns) would increase and the system solution using a finite element approach would be cumbersome and numerically demanding. A gradient-enhanced material model for brittle damage using Hamilton’s principle for nonconservative continua was developed. The model is based on an improved algorithm, combining the finite element with strategies from meshless methods, for a fast update of the damage field function. This numerical treatment is referred to as neighbored element method (NEM). The model proves to be numerically stable and fast, with simulation times close to purely elastic problems. In addition, the model provides mesh-independent results.

Led by: P. Junker, D. R. Jantos

Year: 2018