Damping Options

NairnMPM has two forms of grid damping. Their most common use to to damp dynamic effects an converge to static solution.

Introduction

Grid damping is damping term applied each node on the grid that alters the grid forces (or accelerations). In brief, the force update on node i is calculated from:

      [math]\displaystyle{ f_{i}(t+\Delta t) = f_{i}(t) - \alpha p_i }[/math]

where f_i is total force on node i from all sources, p_i is nodal momentum, and α is the grid damping constant (in units of 1/sec). The nodal velocity update becomes:

      [math]\displaystyle{ v_{i}(t+\Delta t) = v_{i}(t) +(a_i^* - \alpha v_i^*) \Delta t }[/math]

where a_i^* = f_i/m_i is nodal acceleration without damping, v_i^* = p_i/m_i is nodal velocity, and m_i is nodal mass. The two types of grid damping differ only in entry end evolution of the damping term α.