Analysis of crack formation, considered as the creation of new surfaces in a material sample due to its microstructure, leads to nontrivial physical, mathematical and computational difficulties even in the rather simple case of quasistatic cohesive zone modelling inside the linear elastic theory. However, quantitative results from such evaluations are required in practice for the development and design of advanced materials, structures and technologies. Although most available software tools apply ad hoc computational predictions, this paper presents the proper formulation of such model problem, including its verification, and sketches the more-scale construction of finite-dimensional approximation of solutions, utilizing the finite element or similar techniques, together with references to original simulations results from engineering practice.
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