material::RnpMaterial Class Reference

A class providing methods to compute energy density and force of peridynamic material. More...

#include <material.h>

Inheritance diagram for material::RnpMaterial:

Collaboration diagram for material::RnpMaterial:

Public Member Functions
	RnpMaterial (inp::MaterialDeck &deck, const size_t &dim, const double &horizon)
	Constructor.
bool	isStateActive () const override
	Returns true if state-based potential is active.
std::pair< double, double >	getBondEF (const double &r, const double &s, bool &fs, const bool &break_bonds) const override
	Returns energy and force between bond due to pairwise interaction.
std::pair< double, double >	getBondEF (const double &r, const double &s, bool &fs, const double &mx, const double &thetax) const override
	Returns energy and force between bond due to state-based model.
util::Point	getBondForceDirection (const util::Point &dx, const util::Point &du) const override
	Returns the unit vector along which bond-force acts.
double	getS (const util::Point &dx, const util::Point &du) const override
	Returns the bond strain.
double	getSc (const double &r) const override
	Returns critical bond strain.
double	getDensity () const override
	Returns the density of the material.
double	getInfFn (const double &r) const override
	Returns the value of influence function.
double	getMoment (const size_t &i) const override
	Returns the moment of influence function.
double	getHorizon () const override
	Returns horizon.
inp::MatData	computeMaterialProperties (const size_t &dim) const override
	Computes elastic and fracture material properties and returns the data.
std::string	printStr (int nt, int lvl) const override
	Returns the string containing printable information about the object.
void	print (int nt, int lvl) const override
	Prints the information about the object.
void	print () const override
	Prints the information about the object.
Public Member Functions inherited from material::Material
	Material (std::string name="")
	Constructor.
virtual	~Material ()
	Destructor.
std::string	name ()
	Returns name of the material.
size_t	getDimension ()
	Returns dimension of the problem.
bool	isPlaneStrain ()
	Returns plane-strain condition.

Private Member Functions
void	computeParameters (inp::MaterialDeck &deck, const size_t &dim)
	Compute material model parameters.

Private Attributes
double	d_horizon
	Horizon.
double	d_density
	Density.
double	d_rbar
	Inflection point of nonlinear function = \( 1/\sqrt{2\beta}\).
double	d_invFactor
	Inverse of factor = \( \epsilon |B_\epsilon(0)|\).
double	d_factorSc
	Factor to multiply to critical strain to check if bond is fractured.
bool	d_irrevBondBreak
	Flag which indicates if the breaking of bond is irreversible.
Material parameters
double	d_C
	Parameter C.
double	d_beta
	Parameter \( \beta \).

Detailed Description

A class providing methods to compute energy density and force of peridynamic material.

Definition at line 251 of file material.h.

Constructor & Destructor Documentation

RnpMaterial()

material::RnpMaterial::RnpMaterial ( inp::MaterialDeck &  deck, const size_t &  dim, const double &  horizon  )

inline

Constructor.

Parameters

deck	Input deck which contains user-specified information
dim	Dimension
horizon	Horizon

Definition at line 260 of file material.h.

      : Material("RNPBond"), d_horizon(horizon), d_density(deck.d_density),
        d_C(0.), d_beta(0.), d_rbar(0.), d_invFactor(0.),
        d_factorSc(deck.d_checkScFactor),
        d_irrevBondBreak(deck.d_irreversibleBondBreak) {
 
    // set global fields
    if (dimension != dim)
      dimension = dim;
 
    if (is_plane_strain != deck.d_isPlaneStrain)
      is_plane_strain = deck.d_isPlaneStrain;
 
    // create influence function
    if (deck.d_influenceFnType == 0) {
      if (influence_fn == nullptr)
        influence_fn = std::make_shared<material::ConstInfluenceFn>(
            deck.d_influenceFnParams, dim);
    }
    else if (deck.d_influenceFnType == 1) {
      if (influence_fn == nullptr)
        influence_fn = std::make_shared<material::LinearInfluenceFn>(
            deck.d_influenceFnParams, dim);
    }
    else if (deck.d_influenceFnType == 2) {
      if (influence_fn == nullptr)
        influence_fn = std::make_shared<material::GaussianInfluenceFn>(
            deck.d_influenceFnParams, dim);
    }
    else {
      std::cerr << "Error: Influence function type = "
                << deck.d_influenceFnType
                << " is invalid.\n";
      exit(1);
    }
 
    if (dim == 1)
      d_invFactor = std::pow(horizon, 2) * 2.;
    else if (dim == 2)
      d_invFactor = std::pow(horizon, 3) * M_PI;
    else if (dim == 3)
      d_invFactor = std::pow(horizon, 4) * 4. * M_PI / 3.;
 
    // check if we need to compute the material parameters
    if (deck.d_computeParamsFromElastic)
      computeParameters(deck, dim);
    else {
      d_C = deck.d_bondPotentialParams[0];
      d_beta = deck.d_bondPotentialParams[1];
      d_rbar = std::sqrt(0.5 / d_beta);
    }
  };

References computeParameters(), d_beta, inp::MaterialDeck::d_bondPotentialParams, d_C, inp::MaterialDeck::d_computeParamsFromElastic, inp::MaterialDeck::d_influenceFnParams, inp::MaterialDeck::d_influenceFnType, d_invFactor, inp::MaterialDeck::d_isPlaneStrain, and d_rbar.

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Member Function Documentation

computeMaterialProperties()

inp::MatData material::RnpMaterial::computeMaterialProperties ( const size_t &  dim ) const

inlineoverridevirtual

Computes elastic and fracture material properties and returns the data.

Parameters

dim	Dimension of the problem

Returns

Data Material data

Implements material::Material.

Definition at line 461 of file material.h.

                                                                         {
 
    auto data = inp::MatData();
 
    // set Poisson's ratio to 1/4
    data.d_nu = 0.25;
 
    // get moment of influence function
    double M = getMoment(dim);
 
    // compute peridynamic parameters
    if (dim == 2) {
      data.d_Gc = 4. * M * d_C / M_PI;
      data.d_lambda = d_C * M * d_beta / 4.;
    } else if (dim == 3) {
      data.d_Gc = 3. * M * d_C / 2.;
      data.d_lambda = d_C * M * d_beta / 5.;
    }
    data.d_mu = data.d_lambda;
    data.d_G = data.d_lambda;
    data.d_E = data.toELambda(data.d_lambda,
                              data.d_nu);
    data.d_K =
        data.toK(data.d_E, data.d_nu);
    data.d_KIc = data.toKIc(
        data.d_Gc, data.d_nu, data.d_E);
 
    return data;
  };

References d_beta, d_C, and getMoment().

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computeParameters()

void material::RnpMaterial::computeParameters ( inp::MaterialDeck &  deck, const size_t &  dim  )

inlineprivate

Compute material model parameters.

Parameters

deck	MaterialDeck
dim	Dimension of the domain

Definition at line 541 of file material.h.

                                                                   {
    //
    // Need following elastic and fracture properties
    // 1. E or K
    // 2. Gc or KIc
    // For bond-based, Poisson's ratio is fixed to 1/4
    //
    if (util::isLess(deck.d_matData.d_E, 0.) &&
        util::isLess(deck.d_matData.d_K, 0.)) {
      std::cerr << "Error: Require either Young's modulus E or Bulk modulus K"
                   " to compute the RNP bond-based peridynamic parameters.\n";
      exit(1);
    }
    if (util::isGreater(deck.d_matData.d_E, 0.) &&
        util::isGreater(deck.d_matData.d_K, 0.)) {
      std::cout << "Warning: Both Young's modulus E and Bulk modulus K are "
                   "provided.\n";
      std::cout << "Warning: To compute the RNP bond-based peridynamic "
                   "parameters, we only require one of those.\n";
      std::cout
          << "Warning: Selecting Young's modulus to compute parameters.\n";
    }
 
    if (util::isLess(deck.d_matData.d_Gc, 0.) &&
        util::isLess(deck.d_matData.d_KIc, 0.)) {
      std::cerr << "Error: Require either critical energy release rate Gc or "
                   "critical stress intensity factor KIc to compute the RNP "
                   "bond-based peridynamic parameters.\n";
      exit(1);
    } else if (util::isGreater(deck.d_matData.d_Gc, 0.) &&
               util::isGreater(deck.d_matData.d_KIc, 0.)) {
      std::cout << "Warning: Both critical energy release rate Gc and critical "
                   "stress intensity factor KIc are provided.\n";
      std::cout << "Warning: To compute the RNP bond-based peridynamic "
                   "parameters, we only require one of those.\n";
      std::cout << "Warning: Selecting critical energy release rate Gc to "
                   "compute parameters.\n";
    }
 
    // set Poisson's ratio to 1/4
    deck.d_matData.d_nu = 0.25;
 
    // compute E if not provided or K if not provided
    if (deck.d_matData.d_E > 0.)
      deck.d_matData.d_K =
          deck.d_matData.toK(deck.d_matData.d_E, deck.d_matData.d_nu);
 
    if (deck.d_matData.d_K > 0. && deck.d_matData.d_E < 0.)
      deck.d_matData.d_E =
          deck.d_matData.toE(deck.d_matData.d_K, deck.d_matData.d_nu);
 
    if (deck.d_matData.d_Gc > 0.)
      deck.d_matData.d_KIc = deck.d_matData.toKIc(
          deck.d_matData.d_Gc, deck.d_matData.d_nu, deck.d_matData.d_E);
 
    if (deck.d_matData.d_KIc > 0. && deck.d_matData.d_Gc < 0.)
      deck.d_matData.d_Gc = deck.d_matData.toGc(
          deck.d_matData.d_KIc, deck.d_matData.d_nu, deck.d_matData.d_E);
 
    // compute lame parameter
    deck.d_matData.d_lambda =
        deck.d_matData.toLambdaE(deck.d_matData.d_E, deck.d_matData.d_nu);
    deck.d_matData.d_G =
        deck.d_matData.toGE(deck.d_matData.d_E, deck.d_matData.d_nu);
    deck.d_matData.d_mu = deck.d_matData.d_G;
 
    // get moment of influence function
    double M = getMoment(dim);
 
    // compute peridynamic parameters
    if (dim == 2) {
      d_C = M_PI * deck.d_matData.d_Gc / (4. * M);
      d_beta = 4. * deck.d_matData.d_lambda / (d_C * M);
    } else if (dim == 3) {
      d_C = 2. * deck.d_matData.d_Gc / (3. * M);
      d_beta = 5. * deck.d_matData.d_lambda / (d_C * M);
    }
 
    d_rbar = std::sqrt(0.5 / d_beta);
  };

References d_beta, d_C, inp::MatData::d_E, inp::MatData::d_G, inp::MatData::d_Gc, inp::MatData::d_K, inp::MatData::d_KIc, inp::MatData::d_lambda, inp::MaterialDeck::d_matData, inp::MatData::d_mu, inp::MatData::d_nu, d_rbar, getMoment(), util::isGreater(), util::isLess(), inp::MatData::toE(), inp::MatData::toGc(), inp::MatData::toGE(), inp::MatData::toK(), inp::MatData::toKIc(), and inp::MatData::toLambdaE().

Referenced by RnpMaterial().

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getBondEF() [1/2]

std::pair< double, double > material::RnpMaterial::getBondEF ( const double &  r, const double &  s, bool &  fs, const bool &  break_bonds  ) const

inlineoverridevirtual

Returns energy and force between bond due to pairwise interaction.

Peridynamic energy at point \( x \) is

\[ e(x) = \frac{1}{|B_\epsilon(0)|} \int_{B_\epsilon(x)} \frac{J^\epsilon(|y-x|)}{\epsilon} \psi(|y-x|S^2) dy \]

and force at point x is

\[ f(x) = \frac{4}{|B_\epsilon(0)|} \int_{B_\epsilon(x)} \frac{J^\epsilon(|y-x|)}{\epsilon} \psi'(|y-x|S^2) S \frac{y-x}{|y-x|} dy, \]

where \( \psi(r) = C(1-\exp(-\beta r))\).

For given initial bond length \( r \) and bond strain \( s\), this function returns pair of

\[ \hat{e} = \frac{J^\epsilon(r)}{\epsilon |B_\epsilon(0)|} \psi(r s^2) \]

and

\[ \hat{f} = \frac{4 J^\epsilon(r) s}{\epsilon |B_\epsilon(0)|} \psi'(r s^2). \]

Parameters

r	Reference (initial) bond length
s	Bond strain
fs	Bond fracture state
break_bonds	Flag to specify whether bonds are allowed to break or not

Returns

value Pair of energy and force

Implements material::Material.

Definition at line 342 of file material.h.

                                                                              {
 
    if (break_bonds) {
      // check if fracture state of the bond need to be updated
      if (d_irrevBondBreak && !fs &&
          util::isGreater(std::abs(s), d_factorSc * getSc(r)))
        fs = true;
 
      // if bond is not fractured, return energy and force from nonlinear
      // potential otherwise return energy of fractured bond, and zero force
      if (!fs)
        return std::make_pair(
            getInfFn(r) * d_C *
                (1. - std::exp(-d_beta * r * s * s)) / d_invFactor,
            getInfFn(r) * 4. * s * d_C * d_beta *
                std::exp(-d_beta * r * s * s) / d_invFactor);
      else
        return std::make_pair(d_C / d_invFactor, 0.);
    } else {
      return std::make_pair(getInfFn(r) * d_C * d_beta *
                                r * s * s / d_invFactor,
                            getInfFn(r) * 4. * s * d_C *
                                d_beta / d_invFactor);
    }
  };

References d_beta, d_C, d_factorSc, d_invFactor, d_irrevBondBreak, getInfFn(), getSc(), and util::isGreater().

Referenced by getBondEF().

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getBondEF() [2/2]

std::pair< double, double > material::RnpMaterial::getBondEF ( const double &  r, const double &  s, bool &  fs, const double &  mx, const double &  thetax  ) const

inlineoverridevirtual

Returns energy and force between bond due to state-based model.

Parameters

r	Reference (initial) bond length
s	Bond strain
fs	Bond fracture state
mx	Weighted volume at node
thetax	Dilation

Returns

value Pair of energy and force

Implements material::Material.

Definition at line 381 of file material.h.

                                            {
 
    return this->getBondEF(r, s, fs, true);
  };

References getBondEF().

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getBondForceDirection()

util::Point material::RnpMaterial::getBondForceDirection ( const util::Point &  dx, const util::Point &  du  ) const

inlineoverridevirtual

Returns the unit vector along which bond-force acts.

Parameters

dx	Reference bond vector
du	Difference of displacement

Returns

vector Unit vector

Implements material::Material.

Definition at line 394 of file material.h.

                                                                         {
    return dx / dx.length();
  };

References util::Point::length().

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getDensity()

double material::RnpMaterial::getDensity ( ) const

inlineoverridevirtual

Returns the density of the material.

Returns

density Density of the material

Implements material::Material.

Definition at line 423 of file material.h.

{ return d_density; };

References d_density.

getHorizon()

double material::RnpMaterial::getHorizon ( ) const

inlineoverridevirtual

Returns horizon.

Returns

horizon Horizon

Implements material::Material.

Definition at line 452 of file material.h.

{ return d_horizon; };

References d_horizon.

getInfFn()

double material::RnpMaterial::getInfFn ( const double &  r ) const

inlineoverridevirtual

Returns the value of influence function.

Parameters

r	Reference (initial) bond length

Returns

value Influence function at r

Implements material::Material.

Definition at line 431 of file material.h.

                                                  {
    return getGlobalInfFn(r / d_horizon);
  };

References d_horizon.

Referenced by getBondEF().

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getMoment()

double material::RnpMaterial::getMoment ( const size_t &  i ) const

inlineoverridevirtual

Returns the moment of influence function.

If \( J(r) \) is the influence function for \( r\in [0,1)\) then \( i^{th}\) moment is given by

\[ M_i = \int_0^1 J(r) r^i dr. \]

Parameters

i	ith moment

Returns

value Moment

Implements material::Material.

Definition at line 444 of file material.h.

                                                   {
    return getGlobalMoment(i);
  };

Referenced by computeMaterialProperties(), and computeParameters().

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getS()

double material::RnpMaterial::getS ( const util::Point &  dx, const util::Point &  du  ) const

inlineoverridevirtual

Returns the bond strain.

Parameters

dx	Reference bond vector
du	Difference of displacement

Returns

strain Bond strain \( S = \frac{du \cdot dx}{|dx|^2} \)

Implements material::Material.

Definition at line 405 of file material.h.

                                                                       {
    return dx.dot(du) / dx.dot(dx);
  };

References util::Point::dot().

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getSc()

double material::RnpMaterial::getSc ( const double &  r ) const

inlineoverridevirtual

Returns critical bond strain.

Parameters

r	Reference length of bond

Returns

strain Critical strain

Implements material::Material.

Definition at line 415 of file material.h.

                                               {
    return d_rbar / std::sqrt(r);
  };

References d_rbar.

Referenced by getBondEF().

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isStateActive()

bool material::RnpMaterial::isStateActive ( ) const

inlineoverridevirtual

Returns true if state-based potential is active.

Returns

bool True/false

Implements material::Material.

Definition at line 314 of file material.h.

{ return false; };

print() [1/2]

void material::RnpMaterial::print ( ) const

inlineoverridevirtual

Prints the information about the object.

Reimplemented from material::Material.

Definition at line 532 of file material.h.

{ print(0, 0); }

References print().

Referenced by print().

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print() [2/2]

void material::RnpMaterial::print ( int  nt, int  lvl  ) const

inlineoverridevirtual

Prints the information about the object.

Parameters

nt	Number of tabs to append before printing
lvl	Information level (higher means more information)

Reimplemented from material::Material.

Definition at line 527 of file material.h.

                                             {
    std::cout << printStr(nt, lvl);
  }

References printStr().

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printStr()

std::string material::RnpMaterial::printStr ( int  nt, int  lvl  ) const

inlineoverridevirtual

Returns the string containing printable information about the object.

Parameters

nt	Number of tabs to append before printing
lvl	Information level (higher means more information)

Returns

string String containing printable information about the object

Reimplemented from material::Material.

Definition at line 498 of file material.h.

                                                     {
 
    auto tabS = util::io::getTabS(nt);
    std::ostringstream oss;
    oss << tabS << "------- particle::RnpMaterial --------" << std::endl
        << std::endl;
    oss << tabS << "State active = " << 0 << std::endl;
    oss << tabS << "Horizon = " << d_horizon << std::endl;
    oss << tabS << "Influence fn address = " << influence_fn.get() << std::endl;
    oss << tabS << "Influence fn info: " << std::endl;
    oss << influence_fn->printStr(nt + 1, lvl);
    oss << tabS << "Peridynamic parameters: " << std::endl;
    oss << tabS << "  C = " << d_C << std::endl;
    oss << tabS << "  beta = " << d_beta << std::endl;
    oss << tabS << "  r_bar = " << d_rbar << std::endl;
    oss << tabS << "  inv_factor = " << d_invFactor << std::endl;
    oss << tabS << "  factor_Sc = " << d_factorSc << std::endl;
    oss << tabS << "  irrev_bond_breaking = " << d_irrevBondBreak << std::endl;
    oss << tabS << std::endl;
 
    return oss.str();
  }

References d_beta, d_C, d_factorSc, d_horizon, d_invFactor, d_irrevBondBreak, d_rbar, and util::io::getTabS().

Referenced by print().

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Field Documentation

d_beta

double material::RnpMaterial::d_beta

private

Parameter \( \beta \).

Definition at line 639 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getBondEF(), printStr(), and RnpMaterial().

d_C

double material::RnpMaterial::d_C

private

Parameter C.

Definition at line 636 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getBondEF(), printStr(), and RnpMaterial().

d_density

double material::RnpMaterial::d_density

private

Density.

Definition at line 628 of file material.h.

Referenced by getDensity().

d_factorSc

double material::RnpMaterial::d_factorSc

private

Factor to multiply to critical strain to check if bond is fractured.

For nonlinear model, we consider bond is broken when it exceeds 10 times of critical strain. Typical value of factor is 10.

Definition at line 655 of file material.h.

Referenced by getBondEF(), and printStr().

d_horizon

double material::RnpMaterial::d_horizon

private

Horizon.

Definition at line 625 of file material.h.

Referenced by getHorizon(), getInfFn(), and printStr().

d_invFactor

double material::RnpMaterial::d_invFactor

private

Inverse of factor = \( \epsilon |B_\epsilon(0)|\).

Definition at line 647 of file material.h.

Referenced by getBondEF(), printStr(), and RnpMaterial().

d_irrevBondBreak

bool material::RnpMaterial::d_irrevBondBreak

private

Flag which indicates if the breaking of bond is irreversible.

Definition at line 658 of file material.h.

Referenced by getBondEF(), and printStr().

d_rbar

double material::RnpMaterial::d_rbar

private

Inflection point of nonlinear function = \( 1/\sqrt{2\beta}\).

Definition at line 644 of file material.h.

Referenced by computeParameters(), getSc(), printStr(), and RnpMaterial().

---

The documentation for this class was generated from the following file:

• /home/user/project/src/material/mparticle/material.h