According to the Statistical Office of the Republic of Serbia , the total value of the civil engineering construction works in Serbia in 2021 was nearly 5 billion EUR. Most civil engineering structures are made of concrete and steel, whereas metals dominate mechanical engineering structures. New materials are conquering the market, such as polymers, alloys, and composites, but the total share is still significantly smaller than concrete and steel. However, these materials are evolving, with innovative reinforcements (fiber reinforcement, fiber-reinforced polymer bars, textiles) used in concrete. As a result, concrete is the second most consumed material after water, with more than 14 billion m3 of concrete manufactured globally in 2020 and the global cement and concrete products market value of $440 billion (according to the Global Cement and Concrete Association ). Also, world crude steel production was near 1.95 billion tons in 2021 and increasing (according to The World Steel Association ).
Engineering structures are increasingly complex, so the design process needs more sophisticated tools to satisfy the demands of structural safety. During their use, structures are designed to be exposed to predicted loading conditions depending on their purpose. However, in some cases, due to unpredicted loading conditions (static, dynamic, or cyclic loading in case of accidental loading, seismic loading, tsunami blast), environments (corrosive or high temperature), or deviations in the design process, a non-permissible deformation and strain in the structure can be noticed. Such behavior can lead to the initiation and evolution of damage which often terminates in the failure of the structure. A failure is catastrophic, and an accident is a lesser catastrophic type of incident. The accidents can progressively lead to a catastrophic failure (e.g. through so-called progressive collapse), so it is crucial to monitor and predict accidents to prevent failures.
The prevention of damage-induced failure is crucial in structural design. There is a pressing need to understand the causes of failure to help minimize such occurrences in the future. European ICOLD Working Group “Management of Dam Incidents” was established to collect experiences and the best practices and improve the practices in handling dam incidents. American Society of Civil Engineers (ASCE) concluded in 2017 that in order to improve public safety and resilience, the risk and consequences of dam failure must be lowered. One of the suggested measures was the development of tools, training, and technology. That is also in scope with the Smart Specialization Strategy Serbia 2020-2027 (4S), which recognizes the field of Information-Communication Technologies, and Software Development as a priority, and the document “Industrial Policy Strategy 2021-2030”, where the second specific objective is “Development of industry based on innovation” and the suggested Measure 2.1 is “Incentives for industrial economic entities for the development of innovative solutions through cooperation projects with the scientific and research community”.
Therefore, there is a strong demand to provide procedures and tools for efficient monitoring of damage initiation, evolution and prevention of failure. The experimental techniques for investigating of the state of the structures’ material are one direction of possible solutions. However, in many cases, the experiments are too expensive or impracticable (concrete in fire, punching of concrete slabs, large-scale steel structures). Various scientific concepts exist (molecular dynamics, discrete element methods, lattice models, multiscale fracture analysis) for fracture simulation. However, Continuum Damage Mechanics (CDM) is selected as a widely accepted and the most scientifically based theory in the engineering community. CDM approach has been utilized to investigate the possibility of predicting crack initiation, material degradation, and structure failure. CDM focuses on the effect of cracks evolution phenomenologically by introducing damage variables. Some recent cutting-edge research results proposed in top international journals have been implemented in commercial Finite Element Method (FEM) software. CDM is a method for modeling the damage process at the macroscopic continuum level without modeling micromechanics around defects. CDM can be employed to simulate damage evolution as the material degradation via strength and stiffness reduction and to follow the state of the material. Phase-field theory for modeling damage is related to CDM. Separately, the displacement field and the set of cracks can be determined (Griffith’s theory) by minimizing the total potential energy. Numerical implementation was given in Bourdin et al. where the sharp crack topology is regularized by the introduction of a scalar phase-field variable. A length scale parameter l0 related to the width of the crack is introduced, and when l0 → 0, the solution converges to the original solution. Phase-Field damage Modeling (PFM) is the theory for modeling damage based on a variational approach which provides the displacement field and damage in the form of phase-field that determines the intact and damaged material. The field variable can take a value between 0 and 1 to describe the state of the material as undamaged or damaged. In this case, the Fracture Mechanics problem is solved by a set of partial differential equations for the displacement field and the scalar phase-field. Using the PFM, the brittle, quasi-brittle, ductile, and cohesive fractures in quasi-static and dynamic regimes can be modeled by implementation into the FEM. The advantages of the PFM are recognized by the computational mechanics community as essential for damage evaluation in structures such as no assumption of pre-defined cracks is needed such that crack nucleation, growth, and coalescence can be automatically determined; the model can deal with merging and branching of multiple cracks; the model allows incorporating the multi-field physics owing to its variational structure; the model can be generalized to three dimensions (3D), and its computational implementation is straightforward in any dimension.
