This article proposes a linear-by-part approach for elastoplastic 3D multiple-point smooth impacts in multibody systems with perfect constraints. The model is an extension of a previous version, restricted to the perfectly elastic case, able to account for the high sensitivity to initial conditions and for redundancy without assuming any particular collision sequence (Barjau et al., Multibody Syst. Dyn. 31:497–517, 2014). Energy losses associated with compression and expansion in percussive analysis is a matter as complex as the physical phenomena involved, at the nanoscale level, for different materials. Simplified models can be developed for specific purposes, which can retain the most relevant trends of internal damping and at the same time be suitable for a particular analytical approach of impact mechanics. In the context of this article, energy dissipation due to material deformation is introduced through a linear-by-part elastoplastic model consisting on two elementary sets of springs and dry-friction dampers. The first set accounts for inelastic behavior (energy loss without permanent indentation), whereas the second one introduces plasticity (that is, permanent indentation). In inelastic and plastic collisions, instantaneous unilateral constraints may appear, thus reducing the number of degrees of freedom (DOF) of the system. The calculation of the corresponding normal contact force at the constrained points is then necessary in order to detect whether the constraint holds or disappears (either because a new compression or an expansion phase starts, or because contact is lost). Different simulated application examples are presented and thoroughly discussed.
Serrancoli, G.; Font-Llagunes, J.M.; Barjau, A. Proceedings of the Institution of Mechanical Engineers. Part K, journal of multi-body dynamics Vol. 228, num. 3, p. 241-11 DOI: 10.1177/1464419314530110 Date of publication: 2014-09-01 Journal article
The human body is an over-actuated multi-body system, as each joint degree of freedom can be controlled by more than one muscle. Solving the force-sharing problem (i.e. finding out how the resultant joint torque is shared among the muscles actuating that joint) calls for an optimization process where a cost function, representing the strategy followed by the central nervous system to activate muscles, is minimized. The main contribution of the present study has been the particular formulation of that cost function for the case of the pathological gait of a single subject suffering from anterior cruciate ligament rupture. Our hypothesis was that the central nervous system does not weight equally the muscles when trying to compensate for a lower limb injury during gait (in contrast to what is the usual practice for healthy gait where all muscles are weighted equally). This hypothesis is supported by the fact that muscle activity in injured individuals differs from that of healthy subjects. Different functions were tested until we finally came out with a cost function that was consistent with experimental electromyography measurements and inverse dynamics results for a subject suffering this particular pathology.
This article proposes a simple linear-by-part approach for perfectly elastic 3D multiple-point impacts in multibody systems with perfect constraints and no friction, applicable both to nonredundant and redundant cases (where the normal velocities of the contact points are not independent). The approach is based on a vibrational dynamical model, and uses the so called "independent contact space." Two different time and space scales are used. At the macroscale, the impact interval is negligible, and the overall system configuration is assumed to be constant. Consequently, the inertia and Jacobian matrices appearing in the formulation are also constant. The dynamics at the contact points is simulated through stiff springs undergoing very small deformations and generating system vibrations at the microscale. The total impact interval is split into phases, each corresponding to a constant set of compressed springs responsible for an elastic potential energy. For each phase, a reduced inertia matrix associated with a set of contact points, and a reduced stiffness matrix obtained from the potential energy (associated with all contact points undergoing compression) are introduced. From these matrices, a modal analysis is performed yielding an all-analytical solution within each phase. The main difference between the redundant and nonredundant cases concerns the inertia and stiffness matrices for modal analysis. While in the former case, both are related to the total set of contact points (total contact space), in the latter one they are related to two subsets: a subset of independent points for the inertia matrix (independent contact space), and the total set for the stiffness matrix. A second difference concerns the calculation of the normal impulses generated at each contact point. For the nonredundant case, they can be directly obtained from the total incremental normal velocities of the contact points through the inertia and stiffness matrices. For the redundant one, they can be obtained by adding up their incremental values at each impact phase. This requires an updating of a new effective stiffness matrix depending on the contact points undergoing compression at each phase. Four planar application cases are presented involving a single body and a multibody system colliding with a smooth ground.
Serrancoli, G.; Walter, J.P.; Kinney, A.L.; Barjau, A.; Fregly, B.J.; Font-Llagunes, J.M. Reunión del Capítulo Español de la Sociedad Europea de Biomecánica p. 1 Presentation's date: 2013-10-24 Presentation of work at congresses
The human body has more muscles than Degrees of Freedom (DoF), and that leads to indeterminacy in the muscle force calculation. This study proposes the
formulation of an optimization problem to estimate the lower-limb muscle forces during a gait cycle of a patient wearing an instrumented knee prosthesis. The
originality of that formulation consists of simulating muscle excitations in a physiological way while muscle
parameters are calibrated. Two approaches have been considered. In Approach A, measured contact forces are applied to the model and all inverse dynamics loads are matched in order to get a physiological
calibration of muscle parameters. In Approach B, only the inverse dynamics loads not affected by the knee contact loads are matched. With that approach, contact forces can be predicted and validated by comparison with the experimental ones. Approach B is a test of the optimization method and
it can be used for cases where no knee contact forces are available
The dynamics associated with the impact of the crutch with the ground is an important
topic of research, since this is known to be the main cause of mechanical energy
loss during swing-through gait. In this work, a multibody system representing a subject
walking with crutches is used to investigate the behavior of two different contact models,
impulsive and continuous, used for impact analysis. In the impulsive (discrete) approach,
the impact interval is considered to be negligible and, therefore, the system configuration
is constant. The postimpact state is directly obtained from the preimpact one through algebraic
equations. In the continuous approach, the stiffness and dissipation characteristics of
the contact surfaces are modeled through nonlinear springs and dampers. The equations of
motion are integrated during the impact time interval to obtain the postimpact state, which,
in principle, can differ from that obtained by means of the impulsive approach. Although
both approaches have been widely used in the field of biomechanics, we have not found any
comparative study in the existing literature justifying the model chosen for impact analysis.
In this work, we present detailed numerical results and discussions to investigate several
dynamic and energetic features associated with crutch impact. Based on the results, we compare
the implications of using one contact model or the other.
Two main approaches are used when studying impact problems involving rigid bodies: impulsive and compliant. In an impulsive approach, the impact time interval is considered to be negligible, and so the system configuration is assumed
to be constant. The final mechanical state can be obtained directly from the initial
one by means of algebraic equations and energy dissipation assumptions. In a compliant approach, the colliding surfaces are modeled through nonlinear springs and dampers, and the differential equations of motion are integrated to solve the forward dynamics. In this paper, the performance of the two approaches is compared in two
biomechanical application examples.
Two approaches are used when studying impact problems: impulsive ones and compliant ones. In an
impulsive approach, the time interval where the collision takes place is considered to be negligible, and so
the system configuration is assumed to be constant. The final mechanical state of the colliding system is
obtained directly from the initial one through algebraic equations and energy dissipation assumptions. In a
compliant approach, the colliding surfaces are modelled through springs and dampers (usually nonlinear),
and the equations of motion are integrated during the impact time interval to obtain the final state.
Though both approaches have been widely used in the field of biomechanics, no comparative study can
be found in the literature that could justify choosing one or another. In this paper, we present both
approaches and compare them when applied to two examples related to gait problems: a passive walker
and a simple model of crutch locomotion. We will show that the results are really close whenever
nonsliding conditions are assumed at the impact points.
Vincent, G.; Barjau, A.; Kaelig, C.; Etienne, B. Physical review E, statistical physics, plasmas, fluids, and related interdisciplinary topics Vol. 67, p. 006660-9 DOI: 10.1103/PhysRevE.67.066609 Date of publication: 2003-06 Journal article
Barjau, A.; Gibiat, V.; Chareyron, D. FORUM ACUSTICUM Sevilla 2002. 3rd. European Congress on Acoustics XXXIII SPANISH CONGRESS ON ACOUSTICS-Tecniacústica 2002 p. 1-6 Presentation of work at congresses