A physically motivated constitutive model for 3D numerical simulation of skeletal muscles

Abstract

A detailed numerical implementation within the FEM is presented for a physically motivated three-dimensional constitutive model describing the passive and active mechanical behaviors of the skeletal muscle. The derivations for the Cauchy stress tensor and the consistent material tangent are provided. For nearly incompressible skeletal muscle tissue, the strain energy function may be represented either by a coupling or a decoupling of the distortional and volumetric material response. In the present paper, both functionally different formulations are introduced allowing for a direct comparison between the coupled and decoupled isochoric-volumetric approach. The numerical validation of both implementations revealed significant limitations for the decoupled approach. For an extensive characterization of the model response to different muscle contraction modes, a benchmark model is introduced. Finally, the proposed implementation is shown to provide a reliable tool for the analysis of complex and highly nonlinear problems through the example of the human mastication system by studying bite force and three-dimensional muscle shape changes during mastication.

A unified theoretical structure for modeling interstitial growth and muscle activation in soft tissues

“…The use of an exponential function has been motivated by the work of Fung (1993) and the functional form for the dependence on J e has been motivated by the work in (Schroder & Neff, 2003). Also, it was observed in Bodner, 2002, Helfenstein, Jabareen, Mazza, andGovindjee (2010) and Weickenmeier, Itskov, Maza, and Jabareen (2014) that it is desirable to maintain a balance of the effects of the matrix, area stretch and fiber stretch by defining a function Q which appears as the argument of the exponential function. This is in contrast with proposing exponential forms for each of the components.…”

Experimental Characterization and Simulation of Layer Interaction in Facial Soft Tissues

“…In proximity of the temporal fusion line, these two tissue layers are tied together, to accurately represent the dense connectivity between all tissues in the transition zone from medial to temporal forehead as described by [8]. The mechanical behavior of the active muscle and passive soft tissue layers is based on the implementation of constitutive material models as presented in [15,16]. The corresponding material parameters for facial skin were determined from suction-based in-vivo experiments on the same subject.…”

“…In recent papers we have demonstrated the implementation of advanced active and passive constitutive models of face tissue [15,16], as well as the accurate representation of anatomical features, and realistic boundary conditions [3]. Our model allows to simulate facial expressions and wrinkling by incorporating experimentally quantified interaction properties of individual tissue layers.…”

Modeling Bioactive Materials

“…The active contribution was later coupled to include dependence on the electric potential (Böl et al, 2012). Weickenmeier et al (2014) investigated slightly compressible behavior of skeletal muscle modifying an incompressible model proposed by Ehret et al (2011). Sharifimajd and Stålhand (2013) proposed a skeletal muscle model in 1D with the active stretch additively decomposed (Stålhand et al, 2008(Stålhand et al, , 2011.…”

“…Sharifimajd and Stålhand (2013) proposed a skeletal muscle model in 1D with the active stretch additively decomposed (Stålhand et al, 2008(Stålhand et al, , 2011. Numerical simulations using various bioactive models have been conducted to simulate the response of a rat tibialis anterior muscle (Hernández-Gascón et al, 2013), the human biceps and the human masseter muscle (Weickenmeier et al, 2014).…”