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Abstract Soft biological tissues like cartilage exhibit swelling and shrink ing behaviour due to mechanical and chemical loadings A mixture theory is used to simulate this behaviour First the biphasic mixture theory is investigated In this theory the mechanical behaviour is described by mass and momentum balances and constitutive equations As a result a system of coupled timedependent nonlinear equations is obtained These equations are discretised in space by a mixedhybrid nite element method and in time by a suitable implicit time integrator Unlike the up formulation the mixedhybrid nite element method yields a conservative velocityeld of the uid which is a sound basis for accurate computations of for example diusion of particles inside the uid Then the biphasic mixture theory is extended to a four components mixture theory in order to model chemical and electrical phenomena inside the materia