Adaptive damping for dynamic relaxation problems with non-monotonic spectral response

Non-inertial transients may be e ectively solved using explicit time integration with arbitrary inertial and damping properties. The usual approach relies on a diagonal lumped mass on which strictly mass proportional damping is based. While the damping coe cient can be adaptively determined on the basis of the estimated frequency of the predominant response, local changes in sti ness, often associated with changing contact conditions, can cause abrupt changes in the damping coe cient. This can substantially impede the progress of the solution, particularly when deformations involve large translations or rotations of parts of the system. A modi cation to the mass proportional damping is developed and implemented to avoid the deleterious e ects of sudden changes in the damping coe cient. A new procedure is thus implemented so that the usual dynamic relaxation method will automatically adapt to changing conditions of response in such a way as to avoid overdamping low modes due to subsequent higher frequency events