Applied & Computational Mathematics seminar: Finite Element Models of Skeletal Muscle: Elastodynamics, Stability, and Beyond

Speaker:  Dr. Javier Almonacid, George Mason University

Title:  Finite Element Models of Skeletal Muscle: Elastodynamics, Stability, and Beyond

Abstract:   Skeletal muscle is a hierarchically structured, actively contracting soft tissue whose function depends as much on its geometry as on its material properties. This talk traces the path from muscle physiology to three-dimensional simulation. We begin with the physiological basis of force generation, namely the sliding filament and cross-bridge theories, and show how these relationships are embedded in continuum, dynamic 3D finite element descriptions of muscle as an anisotropic, nearly incompressible, actively stressed material. We then discuss the stability of muscle deformation from two complementary perspectives: numerical, concerning the performance of different time-stepping schemes under stringent regularity constraints; and dynamical, concerning the seemingly unstable behavior of muscle fibers themselves. Building on this foundation, we introduce Flexodeal, an open-source C++ finite element framework built on deal.II for fully dynamic, 3D musculoskeletal simulation, and show how these theoretical ingredients come together in practice. We close with a discussion of muscle gearing, and how dynamic 3D simulation captures velocity effects that 1D and quasi-static models cannot.

Time:  Friday, September 4, 1:30pm – 2:30pm
Place:  Exploratory Hall, room 4106