Novel hyperelastic models for large volumetric deformations

Abstract

Materials such as elastomeric foams, lattices, and cellular solids are capable of undergoing large elastic volume changes. Although many hyperelastic constitutive formulations have been proposed for deviatoric (shape changing) behaviour, few variations exist for large deformation volumetric behaviour. The first section of this paper presents a critical analysis of current volumetric hyperelastic models and highlights their limitations for large volumetric strains. In the second section of the paper we propose three novel volumetric strain energy density functions, which: 1) are valid for large volumetric deformations, 2) offer separate control of the volumetric strain stiffening behaviour during shrinkage (volume reduction) and expansion (volume increase), and 3) provide precise control of non-monotonic volumetric strain stiffening. To illustrate the ability of the novel formulations to capture complex volumetric material behaviour they are fitted and compared to a range of published experimental data.

Blood clot fracture properties are dependent on red blood cell and fibrin content

“…in which 1 and 2 are the initial small-strain and large-strain bulk modulus, respectively, the parameters 1 and 2 control the transition volumetric strains, and , , and are obtained in a similar manner as equation ( 2) by using the corresponding volumetric parameters. For further discussion on the volumetric strain energy density function the reader is referred to the recent paper by Moerman et al [50].…”

The Lu-Pister Multiplicative Decomposition Applied to Thermoelastic Geometrically-Exact Rods

“…We also refer to Kaliske et al [24] for a discussion of various forms of the isochoric part W iso . For further discussions and extended formulations concerning the additive splitting of the isothermal strain energy into volumetric and isochoric parts, the reader is referred, e.g., to Hartmann et al [25], Pence et al [26] and Moerman et al [27]. It is to be noted that the various isothermal forms of the strain energy discussed in the above papers [23][24][25][26][27] may be utilized in context with the Lu-Pister decomposition [2] for isotropic thermoelastic deformations in a quite straight-forward manner.…”

“…For further discussions and extended formulations concerning the additive splitting of the isothermal strain energy into volumetric and isochoric parts, the reader is referred, e.g., to Hartmann et al [25], Pence et al [26] and Moerman et al [27]. It is to be noted that the various isothermal forms of the strain energy discussed in the above papers [23][24][25][26][27] may be utilized in context with the Lu-Pister decomposition [2] for isotropic thermoelastic deformations in a quite straight-forward manner. Exemplary, we mention the paper by Yosibash et al [28], where the volumetric part of the strain energy has been formulated according to a suggestion presented by Hartmann et al [25], which we treat as case '2' now…”