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To deal with permanent deformations and residual stresses, we consider amorphoelastic model for the scar formation as the result of wound healing aftera skin trauma. Next to the mechanical components such as strain anddisplacements, the model accounts for biological constituents such as theconcentration of signaling molecules, the cellular densities of fibroblasts andmyofibroblasts, and the density of collagen. Here we present stabilityconstraints for the one-dimensional counterpart of this morphoelastic model,for both the continuous and (semi-) discrete problem. We show that thetruncation error between these eigenvalues associated with the continuous andsemi-discrete problem is of order $\mathcal{O}(h^2)$. Next, we performnumerical validation to these constraints and provide a biologicalinterpretation of the (in)stability. For the mechanical part of the model, theresults show the components reach equilibria in a (non) monotonic way,depending on the value of the viscosity. The results show that the parametersof the chemical part of the model need to meet the stability constraint,depending on the decay rate of the signaling molecules, to avoid unrealisticresults.

A one-dimensional morphoelastic model for burn injuries: stability analysis, numerical validation and biological interpretation