Numerical Methods for Strong Nonlinearities in Mechanics: Contact and Fracture

This has two direct consequences: on the one hand, the mathematical characteristics of the problem deviate from wellestablished forms, requiring innovative discretization schemes; on the other hand, the low regularity makes it particularly difficult to solve the corresponding large-scale algebraic systems robustly and efficiently. In addition, neither the uniqueness, nor the existence of solutions, remain assured, resulting in bifurcation points, limit loads and structural instabilities, which are always tricky to overcome numerically.