In the talk I will give a few examples from our research concerning the
complex dynamical response of soft and biological materials to
perturbations via forces or deformation. The systems we study are, in
general, far from thermal equilibrium. Phenomena will range from the
emergence of flow instabilities (shear-banding, rheo-chaos) in complex
fluids, over the visco-elasto-plastic behavior of biological cells and
their sub-cellular components, to the fluid-to-solid jamming transition
in a-thermal granular particles. The goal is to define suitable model
systems where the relevant physical mechanisms can be identified and
understood. To this end we use different simulation tools going hand in
hand with analytical modeling and, whenever possible, experimental
verification.