A generalized finite‐strain damage model for quasi‐incompressible hyperelasticity using hybrid formulation

Abstract

SUMMARYA new generalized damage model for quasi-incompressible hyperelasticity in a total Lagrangian finite strain framework is presented. A Kachanov-like reduction factor (1 − D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetricisochoric split of the Helmholtz free energy. However, in the present work it has been implemented in an in-house finite element code for neo-Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three-dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature.

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues

“…Here, e C 0 corresponds to the material elasticity tensor of the undamaged material, e C 0 ¼ The derivative of the mechanical damage variable with respect to t for the linear and exponential softening laws (2.8) considered is [79] The derivative of the healing variable with respect to D eff , taking into account the healing rate defined in (2.9), is given by …”

“…The linear and exponential softening laws used in rsif.royalsocietypublishing.org J. R. Soc. Interface 13: 20151081 the generalized damage model described in Comellas et al [79] are considered for the evolution of the variable D: …”

“…Finally, the structural instability encountered in the low healing rate case of the AAA example is attributable to the numerical limitations of the generalized damage model [79]. From a numerical point of view, in problems with negligible healing effects the HTR model is limited by stress-locking owing to the smeared approach of the damage formulation.…”

Computational predictions of damage propagation preceding dissection of ascending thoracic aortic aneurysms

“…The damage model here is formulated in agreement with the principles of CDM applied in many mechanobiological studies . Therefore, it is assumed that apparent density of damage evolves with mechanical loadings.…”

“…It was basically based on the multiplicative decomposition of the deformation gradient into a isochoric (volume‐preserving) and a volumetric part in which damage only affects the former. Recently, damage models with a volumetric‐deviatoric decoupling have been introduced to model the behavior of fibrous soft biological tissues . The fact that damage is applied only on the deviatoric part of the model means that, for a completely damaged structure, a volumetric quasi‐incompressible undamaged part will always remain.…”