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The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.

The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.

In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.

The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.

The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.

The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

The purpose of this paper is to test absorption characteristics of some newly synthesised 4‐hidroxycoumarins, containing phenyl‐prop‐2‐enoyl group at the 3‐position. Change in spectral characteristics in solvents of different polarity (chloroform and acetonitrile) was followed in regard to the influence of the substitution at the phenyl ring and influence of concentration H⁺ ions. Effectiveness of tested substances was compared with well‐known UV absorbers such as benzophenone‐3 and butyl methoxydibenzoylmethane (BMDM).

All the tested substances were dissolved in chloroform and acetonitrile, with 10‐3 mmol concentration range. The pH was adjusted using 0.1 mol/l HCl, glacial acetic acid, 0.1 mol/l NaOH (aqueous solution) and 0.1 mol/l NaOH (methanolic solution). Spectrophotometric measurement was recorded in the range of 200‐800 nm, using 1‐cm quartz cells.

The tested 4‐hydroxycoumarin derivatives showed good UV absorption properties in the range 280‐380 nm. Substitution on the phenyl ring changes the shape of the absorption maxima. The changes depend on the properties of the substituent as well as the acidity of the solution.

Introducing an electron‐donating substituent on the phenyl‐prop‐2‐enoyl group can shift absorption maximums to longer wavelength. In addition, the variation in substituents on the synthesised substances and pH of the solution could also be studied.

The new compounds showed good UV absorption, making them potential candidates for many applications. The practical importance of the tested substances are derived from their stability, relatively easy synthesis and good UV absorption properties.

The paper shows that the tested coumarins derivatives were new compounds with good UV absorption properties, making them good UV absorbers of commercial potential. The tested coumarins showed good UV absorption properties in the range 280‐380 nm, making them potential candidates for many applications.