A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy–momentum consistent schemes

Liu，Ju1,2; Guan，Jiashen1

2023

10.1016/j.cma.2023.116308

Computer Methods in Applied Mechanics and Engineering   Impact Factor & Quartile

0045-7825

We continue our investigation of finite deformation linear viscoelastodynamics by focusing on constructing accurate and reliable numerical schemes. The concrete thermomechanical foundation developed in the previous study paves the way for pursuing discrete formulations with critical physical and mathematical structures preserved. Energy stability, momentum conservation, and temporal accuracy constitute the primary factors in our algorithm design. For inelastic materials, the directionality condition, a property for the stress to be energy consistent, is extended with the dissipation effect taken into account. Moreover, the integration of the constitutive relations calls for an algorithm design of the internal state variables and their conjugate variables. A directionality condition for the conjugate variables is introduced as an indispensable ingredient for ensuring physically correct numerical dissipation. By leveraging the particular structure of the configurational free energy, a set of update formulas for the internal state variables is obtained. Detailed analysis reveals that the overall discrete schemes are energy–momentum consistent and achieve first- and second-order accuracy in time, respectively. Numerical examples are provided to justify the appealing features of the proposed methodology.

Continuum mechanics Energy–momentum method Integration algorithm for constitutive equations Isogeometric analysis Nonlinear stability Viscoelasticity

English

First ; Corresponding

National Natural Science Foundation of China[12172160];Southern University of Science and Technology[Y01326127]];

COMPUTER SCIENCE

2-s2.0-85166986201

Scopus

1.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
2.Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Liu，Ju,Guan，Jiashen. A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy–momentum consistent schemes[J]. Computer Methods in Applied Mechanics and Engineering,2023.

Liu，Ju,&Guan，Jiashen.(2023).A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy–momentum consistent schemes.Computer Methods in Applied Mechanics and Engineering.

Liu，Ju,et al."A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy–momentum consistent schemes".Computer Methods in Applied Mechanics and Engineering (2023).