ContactForceT_SDSLinear class

Contents

Description

This is a sub-class of the ContactForceT class for the implementation of the Linear Spring-Dashpot-Slider tangent contact force model.

This model assumes that the tangent contact force has an elastic component $F_{t}^{e}$, provided by a linear spring, a viscous component $F_{t}^{v}$, provided by a linear dashpot, and a friction component $F_{t}^{f}$, provided by a slider, which limits the total force according to Coulomb law.

$$\left \{ F_{t} \right \} = min\left ( \left | F_{t}^{e}+F_{t}^{v} \right |,F_{t}^{f} \right ) \{-\hat{t}\}$$

$$F_{t}^{e} = K_{t} \delta_{t}$$

$$F_{t}^{v} = \eta_{t} \dot{\delta_{t}}$$

$$F_{t}^{f} = \mu \left | F_{n} \right |$$

The tangent stiffness coefficient $K_{t}$ can be computed as a function of the normal stiffness coefficient $K_{n}$ and the effective Poisson ratio $\nu_{eff}$:

$$K_{t} = \frac{1-\nu_{eff}}{1-\frac{\nu_{eff}}{2}}K_{n}$$

The tangent damping coefficient $\eta_{t}$ can be computes as:

$$\eta_{t} = 2\sqrt{\frac{2m_{eff}K_{t}}{7}}$$

$$\eta_{t} = -2ln(e)\sqrt{\frac{2m_{eff}K_{t}}{7(ln(e)^{2} + \pi^{2})}}$$

The tangent coefficient of restitution $e$ and the friction coefficient $\mu$ must be provided.

Notation:

$\hat{t}$: Tangent direction between elements

$\delta_{t}$: Tangent overlap

$\dot{\delta_{t}}$: Time rate of change of tangent overlap

$F_{n}$: Normal contact force vector

$m_{eff}$: Effective mass

References:

classdef ContactForceT_SDSLinear < ContactForceT

Public properties

    properties (SetAccess = public, GetAccess = public)
        % Formulation options
        auto_stiff logical = logical.empty;   % flag for computing stiffness coefficient automatically
        auto_damp  logical = logical.empty;   % flag for computing damping coefficient automatically

        % Contact parameters
        stiff double = double.empty;   % stiffness coefficient
        damp  double = double.empty;   % damping coefficient
        fric  double = double.empty;   % friction coefficient
    end

Constructor method

    methods
        function this = ContactForceT_SDSLinear()
            this = this@ContactForceT(ContactForceT.SDS_LINEAR);
            this = this.setDefaultProps();
        end
    end

Public methods: implementation of super-class declarations

    methods
        %------------------------------------------------------------------
        function this = setDefaultProps(this)
            this.auto_stiff = true;
            this.auto_damp  = false;
        end

        %------------------------------------------------------------------
        function this = setCteParams(this,int)
            if (this.auto_stiff)
                if (~isempty(int.cforcen))
                    % Assumption: average poisson ratio
                    this.stiff = (1-int.avg_poisson)/(1-int.avg_poisson/2) * int.cforcen.stiff;
                else
                    this.stiff = 0;
                end
            end
            if (this.auto_damp)
                if (this.restitution == 0)
                    this.damp = 2 * sqrt(2 * int.eff_mass * this.stiff / 7);
                else
                    ln = log(this.restitution);
                    this.damp = -2 * ln * sqrt(2 * int.eff_mass * this.stiff / 7) / sqrt(ln^2 + pi^2);
                end
            end
        end

        %------------------------------------------------------------------
        function this = evalForce(this,int)
            % Force modulus (viscoelastic and friction contributions)
            fe = this.stiff * int.kinemat.ovlp_t;
            fv = this.damp  * int.kinemat.vel_t;
            if (~isempty(int.cforcen))
                ff = this.fric * norm(int.cforcen.total_force);
            else
                ff = 0;
            end

            % Limit viscoelastic force by Coulomb law
            f = min(abs(fe+fv),abs(ff));

            % Total tangential force vector (against deformation and motion)
            this.total_force = -f * int.kinemat.dir_t;
        end
    end

end


Published with MATLAB® R2019b