Modelling the passive and active response of skeletal muscles within the adapted Voigt representation framework

TL;DR

This paper introduces a novel constitutive model for skeletal muscles using adapted Voigt representations, enabling clearer interpretation of passive and active responses and distinguishing roles of fibers and extracellular matrix.

Contribution

It develops a new nonlinear elasticity framework that directly links experimental data to stress-strain relations, improving understanding of muscle mechanics.

Findings

The passive model accurately predicts nonlinear stress responses at various orientations.

The active model captures isometric stress behavior effectively.

The extracellular matrix plays a dominant role in passive response.

Abstract

We present a constitutive model for the passive and active response of skeletal muscles. At variance with more classical approaches, the model is developed exploiting adapted Voigt representations of strain and stress tensors within the context of nonlinear Cauchy elasticity. This framework allows us to identify non-trivial stress-strain relations in a rather direct way from experimental data, enhancing the mechanical interpretability of the material functions that describe the tissue response and obtaining additional insight on the distinct role of the contractile fibres and of the surrounding extracellular matrix. We propose a two-material model, with an additive splitting of the stress contributions, in which only one component depends on an activation parameter. The constitutive model for the passive behaviour satisfactorily predicts the nonlinear stress response to elongation at different relative orientations with respect to the fibre direction and highlights the dominant role of the extracellular matrix. The activation model, essentially determined by the mechanics of the contractile fibres, captures well the isometric stress response through the prescription of an elasto-plastic evolution of the along-fibre active strain.