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<p>A general user material subroutine (UMAT) has been developed, which allows to implement a certain class of visco-hyperelastic models into a non-commercial FE program CalculiX. Any volumetric and first-invariant based isochoric stored-energy functions can be easily defined using the developed UMAT code. Numerous numerical simulations have been conducted to validate the performance of the UMAT procedure. Selected results are reported in this work. The UMAT subroutine is attached as a supplementary material. Moreover, a material parameter identification algorithm, suitable for the considered constitutive theory of finite viscoelasticity, is presented. Instead of assuming the relaxation time values “a&#xa0;priori”, they are evaluated using optimization methods along with other material parameters. This approach allows to reduce the number of Maxwell elements necessary to capture the time-dependent material response, which significantly simplifies the constitutive model, and reduces the computational cost of numerical simulations. Furthermore, several formulations of visco-hyperelastic model have been applied to capture the mechanical behavior of polyurethane. Excellent agreement has been obtained between the experimental measurements and model predictions. The models analyzed in this study utilize some new or less popular first-invariant based stored elastic energy functions.</p>

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First invariant-based visco-hyperelasticity: Formulation, determination of material parameters and finite element implementation

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Cyprian Suchocki

摘要

A general user material subroutine (UMAT) has been developed, which allows to implement a certain class of visco-hyperelastic models into a non-commercial FE program CalculiX. Any volumetric and first-invariant based isochoric stored-energy functions can be easily defined using the developed UMAT code. Numerous numerical simulations have been conducted to validate the performance of the UMAT procedure. Selected results are reported in this work. The UMAT subroutine is attached as a supplementary material. Moreover, a material parameter identification algorithm, suitable for the considered constitutive theory of finite viscoelasticity, is presented. Instead of assuming the relaxation time values “a priori”, they are evaluated using optimization methods along with other material parameters. This approach allows to reduce the number of Maxwell elements necessary to capture the time-dependent material response, which significantly simplifies the constitutive model, and reduces the computational cost of numerical simulations. Furthermore, several formulations of visco-hyperelastic model have been applied to capture the mechanical behavior of polyurethane. Excellent agreement has been obtained between the experimental measurements and model predictions. The models analyzed in this study utilize some new or less popular first-invariant based stored elastic energy functions.