To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological parameters such as the concentration of chemokines , the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. We present separate stability constraints for the mechanical part of the one-dimensional morphoelastic model and stability constraints for the chemical part of the one-dimensional morphoelastic model. Stability results are developed for both the continuous and (semi-) discrete problems. For the mechanical part, we distinguish between elasticity and plasticity. We perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical  model, the results show that the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. Furthermore, the results show that the parameters of the chemical  model need to meet the stability constraint  to avoid unrealistic results.
To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules , the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order \mathcal{O perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint , depending on the decay rate of the signaling molecules, to avoid unrealistic results.
R
parameters
constituents
R
chemokines
signaling molecules
R
We present separate
Here we present
D
mechanical part of the
R
morphoelastic model and stability constraints for the chemical part of the one-dimensional morphoelastic model. Stability results are developed
counterpart of this morphoelastic model,
R
problems. For the mechanical part, we distinguish between elasticity and plasticity. We
problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order \mathcal{O
A
part of the
D
that
R
Furthermore, the
The
A
part of the
A
, depending on the decay rate of the signaling molecules,