Constitutive model development
Constitutive equations establish material-specific relations between field quantities, such as stress and strain in a purely mechanical problem. They are essential to solve and simulate mechanical problems in addition to the universal balance laws of physics. However, for the complex types of material behaviors observed in biomechanics and biomedical engineering, new constitutive laws are often needed, or existing ones have to be refined, adapted and parametrized. We develop constitutive equations for biological and engineering materials based on continuum mechanical and thermodynamic principles. Due to the large deformations and complex material behaviors displayed by the materials systems appearing in our research, we focus on non-linear constitutive laws. Our groups' contributions include constitutive equations for hyperelastic [1-3] and viscoelastic/plastic [4-6] materials at large strains, as well as material changes due to e.g. damage processes [7], cross-linking [8] or tissue activation [9].
We address both deformation and fracture behavior with a focus on concepts that allow including multi-scale, multi-phase and multi-physical information when needed. Particular aspects of our work concern the representation of anisotropy [10] and particular kinematics arising from fiber-reinforcement and network structures in soft biological tissues and bioinspired materials [1,4,11,12].
Moreover, recent challenges in biomechanics and mechanobiology raise the necessity to consider the mechanical problem together with other field equations in physics, and the presence of different solid and liquid phases within the tissue. To this end, we have developed chemomechanically coupled models of soft biological tissues to model the flow of tissue fluids and to account for the volumetric behavior of collagenous tissues, which depends on the osmolarity of the external environment [12-14].
[1] Buerzle, W., & Mazza, E. (2013). On the deformation behavior of human amnion. J. Biomech. 46, 1777-1783. DOI: 10.1016/j.jbiomech.2013.05.018
[2] Ehret, A.E., 2015, On a molecular statistical basis for Ogden's model of rubber elasticity, J. Mech. Phys. Solids 78, 249-268. DOI: 10.1016/j.jmps.2015.02.006
[3] Rubin, M.B., Ehret A.E., An invariant-based Ogden-type model for incompressible isotropic hyperelastic materials. J. Elast. 125, 63-71. DOI: 10.1007/s10659-016-9570-9
[4] Mauri A., Ehret A.E. et al., 2015, A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter, Biomech. Model. Mechanobiol., 15, 1005-1017. DOI: 10.1007/s10237-015-0739-0
[5] Bircher K., Ehret A.E., Mazza E. (2016) Mechanical characteristics of bovine Glisson's Capsule as a model tissue for soft collagenous membranes. J. Biomech. Eng. 138, 081005. DOI: 10.1115/1.4033917
[6] Weickenmeier J. Jabareen M., Mazza E. (2015) Suction based mechanical characterization of superficial facial soft tissues. J. Biomech. 48, 4279-4286. DOI: 10.1016/j.jbiomech.2015.10.039
[7] Ehret A.E., Hollenstein M., Mazza E., Itskov M., 2011, Porcine dermis in uniaxial cyclic loading: sample preparation, experimental results and modeling, J. Mech. Mater. Struct. 6, 1125-1136. DOI: 10.2140/jomms.2011.6.1125
[8] Hopf R., Bernardi L., Menze J., Zündel M., Mazza E., Ehret A.E. (2016) Experimental and theoretical analyses of the age-dependent large-strain behavior of Sylgard 184 (10:1) silicone elastomer. J. Mech. Behav. Biomed. Mater. 60, 425-437. DOI: 10.1016/j.jmbbm.2016.02.022
[9] Weickenmeier J., Itskov M., Mazza E., Jabareen M. (2014) A physically motivated constitutive model for 3D numerical simulation of skeletal muscles. Int. J. Num. Meth. Biomed. Eng., 30, 545-562. DOI: 10.1002/cnm.2618
[10] Rubin M.B., Ehret A.E. (2018) Invariants for rari- and multi-constant theories with generalization to anisotropy in biological tissues. J. Elast. 133, 119-127. DOI: 10.1007/s10659-018-9674-
[11] Domaschke S., Morel A., Fortunato G., Ehret A.E. (2019) Random auxetics from buckling fibre networks. Nat. Commun. 10, 4863. DOI: 10.1038/s41467-019-12757-7
[12] Ehret A.E., Bircher K., Stracuzzi A., Marina V., Zundel M., Mazza E. (2017) Inverse poroelasticity as a fundamental mechanism in biomechanics and mechanobiology. Nat. Commun. 8, 1002. DOI: 10.1038/s41467-017-00801-3
[13] Stracuzzi A., Mazza E., Ehret A.E., 2018, Chemomechanical models for soft tissues based on the reconciliation of porous media and swelling polymer theories, Z. Angew. Math. Mech. 98: 2135-2154. DOI: 10.1002/zamm.201700344
[14] Sachs D., Wahlsten, A., Kozerke S., Restivo G., Mazza E. (2021) A biphasic multilayer computational model of human skin. Biomech. Model. Mechanobiol. 20, 969-982. DOI: 10.1007/s10237-021-01424-w