Speaker
Description
We present an open-source computational framework for the numerical solution of mechanochemical continuum models based on viscoelastic mechanics, with optional coupling to reaction-diffusion-advection dynamics of biochemical species. The framework is implemented in Python and adopts a method-of-lines formulation: spatial derivatives are discretised using finite-difference schemes, transforming the governing partial differential equations into a large system of ordinary differential equations with a structured, possibly state-dependent mass matrix. The resulting semi-discrete system is advanced in time using modern implicit solvers suitable for stiff systems, avoiding bespoke time-stepping or operator splitting whilst preserving full mechanical time dependence. The framework supports heterogeneous material parameters and general boundary conditions in one or more spatial dimensions, and is designed to be modular and reproducible. Core functionality is illustrated through a minimal, runnable implementation of deformation in Kelvin-Voigt, Maxwell, and Standard Linear Solid materials, with mechanical properties coupled to material biochemistry. This is followed by application to a detailed model of cell-substrate interaction. These examples demonstrate that existing open-source solver infrastructure provides a robust and extensible route for studying a broad class of biologically driven viscoelastic systems.
