The paper presents dynamic and static response of a slightly compressible hyperelastic solid. Material models under consideration are obtained by extending incompressible material models which are consistent second and third order approximation of existing stored energy function in terms of a deformation measure, namely MCMV and MCIZ. The problems of a uniaxial compression of a rod and a twisting column are solved using ABAQUS which is a powerful finite element program designed for general use in nonlinear problems. The models are defined with a help of user subroutine UHYPER. In the case of including dynamic effects, an implicit integration scheme available in the software is used. For the twisting column problem, results are compared against available in the ABAQUS library polynomial model where the volumetric stored energy function does not meet basic growth conditions. Experimental data on synthetic rubber neoprene published in the literature is utilized.

The presented results are for the numerical verification of a method devised to identify an unknown spatio-temporal distribution of heat flux that occurs at the surface of a thin aluminum plate, as a result of pulsed laser beam excitation. The presented identification of boundary heat flux function is a part of the newly proposed laser beam profiling method and utilizes artificial neural networks trained on temperature distributions generated with the ANSYS Fluent solver. The paper focuses on the selection of the most effective neural network hyperparameters and compares the results of neural network identification with the Levenberg-Marquardt method used earlier and discussed in previous articles. For the levels of noise measured in physical experiments (0.25-0.5 K), the accuracy of the current parameter estimation method is between 5 and 10%. Design changes that may increase its accuracy are thoroughly discussed.